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 UNITS(1)                                                           UNITS(1)
                              12 November 2020



 NAME
      units - unit conversion and calculation program

 SYNOPSIS
      [options] [from-unit [to-unit]]

 DESCRIPTION
      The units program converts quantities expressed in various systems of
      measurement to their equivalents in other systems of measurement.
      Like many similar programs, it can handle multiplicative scale
      changes. It can also handle nonlinear conversions such as Fahrenheit
      to Celsius; see Temperature Conversions.  The program can also perform
      conversions from and to sums of units, such as converting between
      meters and feet plus inches.

      Basic operation is simple: you enter the units that you want to
      convert from and the units that you want to convert to.  You can use
      the program interactively with prompts, or you can use it from the
      command line.

      Beyond simple unit conversions, units can be used as a general-purpose
      scientific calculator that keeps track of units in its calculations.
      You can form arbitrary complex mathematical expressions of dimensions
      including sums, products, quotients, powers, and even roots of
      dimensions.  Thus you can ensure accuracy and dimensional consistency
      when working with long expressions that involve many different units
      that may combine in complex ways; for an illustration, see Complicated
      Unit Expressions.

      The units are defined in an external data file.  You can use the
      extensive data file that comes with this program, or you can provide
      your own data file to suit your needs.  You can also use your own data
      file to supplement the standard data file.

      You can change the default behavior of units with various options
      given on the command line. See Invoking Units for a description of the
      available options.

 INTERACTING WITH UNITS
      To invoke units for interactive use, type units at your shell prompt.
      The program will print something like this:

      Currency exchange rates from www.timegenie.com on 2014-03-05 2860
      units, 109 prefixes, 85 nonlinear units

      You have:

      At the You have: prompt, type the quantity and units that you are
      converting from.  For example, if you want to convert ten meters to
      feet, type 10 meters.  Next, units will print You want:.  You should
      type the units you want to convert to.  To convert to feet, you would



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 UNITS(1)                                                           UNITS(1)
                              12 November 2020



      type feet.  If the readline library was compiled in, then tab will
      complete unit names. See Readline Support for more information about
      readline.  To quit the program type quit or exit at either prompt.

      The result will be displayed in two ways.  The first line of output,
      which is marked with a * to indicate multiplication, gives the result
      of the conversion you have asked for.  The second line of output,
      which is marked with a / to indicate division, gives the inverse of
      the conversion factor.  If you convert 10 meters to feet, units will
      print

          * 32.808399
          / 0.03048

      which tells you that 10 meters equals about 32.8 feet.  The second
      number gives the conversion in the opposite direction.  In this case,
      it tells you that 1 foot is equal to about 0.03 dekameters since the
      dekameter is 10 meters.  It also tells you that 1/32.8 is about 0.03.

      The units program prints the inverse because sometimes it is a more
      convenient number.  In the example above, for example, the inverse
      value is an exact conversion: a foot is exactly 0.03048 dekameters.
      But the number given the other direction is inexact.

      If you convert grains to pounds, you will see the following:

      You have: grains You want: pounds
              * 0.00014285714
              / 7000

         From the second line of the output you can immediately see that a
      grain is equal to a seven thousandth of a pound.  This is not so
      obvious from the first line of the output.  If you find  the output
      format  confusing, try using the --verbose option:

      You have: grain You want: aeginamina
              grain = 0.00010416667 aeginamina
              grain = (1 / 9600) aeginamina

      If you request a conversion between units that measure reciprocal
      dimensions, then units will display the conversion results with an
      extra note indicating that reciprocal conversion has been done:

      You have: 6 ohms You want: siemens
              reciprocal conversion
              * 0.16666667
              / 6

      Reciprocal conversion can be suppressed by using the --strict option.
      As usual, use the --verbose option to get more comprehensible output:




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 UNITS(1)                                                           UNITS(1)
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      You have: tex You want: typp
              reciprocal conversion
              1 / tex = 496.05465 typp
              1 / tex = (1 / 0.0020159069) typp

      You have: 20 mph You want: sec/mile
              reciprocal conversion
              1 / 20 mph = 180 sec/mile
              1 / 20 mph = (1 / 0.0055555556) sec/mile

      If you enter incompatible unit types, the units program will print a
      message indicating that the units are not conformable and it will
      display the reduced form for each unit:

      You have: ergs/hour You want: fathoms kg 2 / day conformability error
              2.7777778e-11 kg m 2 / sec 3
              2.1166667e-05 kg 2 m / sec

      If you only want to find the reduced form or definition of a unit,
      simply press Enter at the You want: prompt.  Here is an example:

      You have: jansky You want:
              Definition: fluxunit = 1e-26 W/m 2 Hz = 1e-26 kg / s 2

      The output from units indicates that the jansky is defined to be equal
      to a fluxunit which in turn is defined to be a certain combination of
      watts, meters, and hertz.  The fully reduced (and in this case
      somewhat more cryptic) form appears on the far right.

      Some named units are treated as dimensionless in some situations.
      These units include the radian and steradian.  These units will be
      treated as equal to 1 in units conversions.  Power is equal to torque
      times angular velocity.  This conversion can only be performed if the
      radian is dimensionless.

      You have: (14 ft lbf) (12 radians/sec) You want: watts
              * 227.77742
              / 0.0043902509

      It is also possible to compute roots and other non-integer powers of
      dimensionless units; this allows computations such as the altitude of
      geosynchronous orbit:

      You have: cuberoot(G earthmass / (circle/siderealday) 2) - earthradius
      You want: miles
              * 22243.267
              / 4.4957425e-05

      Named dimensionless units are not treated as dimensionless in other
      contexts.  They cannot be used as exponents so for example,
      meter radian is forbidden.



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 UNITS(1)                                                           UNITS(1)
                              12 November 2020



      If you want a list of options you can type ? at the You want: prompt.
      The program will display a list of named units that are conformable
      with the unit that you entered at the You have: prompt above.
      Conformable unit combinations will not appear on this list.

      Typing help at either prompt displays a short help message.  You can
      also type help followed by a unit name.  This will invoke a pager on
      the units data base at the point where that unit is defined.  You can
      read the definition and comments that may give more details or
      historical information about the unit.  (You can generally quit out of
      the page by pressing q.)

      Typing search text will display a list of all of the units whose names
      contain text as a substring along with their definitions.  This may
      help in the case where you aren't sure of the right unit name.

 USING UNITS NON-INTERACTIVELY
      The units program can perform units conversions non-interactively from
      the command line.  To do this, type the command, type the original
      unit expression, and type the new units you want.  If a units
      expression contains non-alphanumeric characters, you may need to
      protect it from interpretation by the shell using single or double
      quote characters.

      If you type

      units "2 liters" quarts

      then units will print

          * 2.1133764
          / 0.47317647

      and then exit.  The output tells you that 2 liters is about 2.1
      quarts, or alternatively that a quart is about 0.47 times 2 liters.

      units does not require a space between a numerical value and the unit,
      so the previous example can be given as

      units 2liters quarts

      to avoid having to quote the first argument.

      If the conversion is successful, units will return success (zero) to
      the calling environment.  If you enter  non-conformable units, then
      units will print a message giving the reduced form of each unit and it
      will return failure (nonzero) to the calling environment.

      If the --conformable option is given, only one unit expression is
      allowed, and units will print all units conformable with that
      expression; it is equivalent to giving ? at the You want: prompt.  For



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 UNITS(1)                                                           UNITS(1)
                              12 November 2020



      example,

      units --conformable gauss B_FIELD   tesla Gs        gauss T
      tesla gauss     abvolt sec / cm 2 stT       stattesla statT
      stattesla stattesla statWb/cm 2 tesla     Wb/m 2

      If you give more than one unit expression with the --conformable
      option, the program will exit with an error message and return
      failure.  This option has no effect in interactive mode.

      If the --terse (-t) option is given with the --conformable option,
      conformable units are shown without definitions; with the previous
      example, this would give

      units --terse --conformable gauss B_FIELD Gs T gauss stT statT
      stattesla tesla

      When the --conformable option is not given and you invoke units with
      only one argument, units will print the definition of the specified
      unit.  It will return failure if the unit is not defined and success
      if the unit is defined.

 UNIT DEFINITIONS
      The conversion information is read from a units data file that is
      called definitions.units and is usually located in the
      /usr/share/units directory.  If you invoke units with the -V option,
      it will print the location of this file.  The default file includes
      definitions for all familiar units, abbreviations and metric prefixes.
      It also includes many obscure or archaic units.  Many common spelled-
      out numbers (e.g., seventeen) are recognized.

      Many constants of nature are defined, including these:

      pi          ratio of circumference to diameter c           speed of
      light e           charge on an electron force       acceleration of
      gravity mole        Avogadro's number water       pressure per unit
      height of water Hg          pressure per unit height of mercury au
      astronomical unit k           Boltzman's constant mu0
      permeability of vacuum epsilon0    permittivity of vacuum G
      Gravitational constant mach        speed of sound

      The standard data file includes atomic masses for all of the elements
      and numerous other constants.  Also included are the densities of
      various ingredients used in baking so that 2 cups flour_sifted can be
      converted to grams.  This is not an exhaustive list.  Consult the
      units data file to see the complete list, or to see the definitions
      that are used.

      The pound is a unit of mass.  To get force, multiply by the force
      conversion unit force or use the shorthand lbf.  (Note that g is
      already taken as the standard abbreviation for the gram.)  The unit



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 UNITS(1)                                                           UNITS(1)
                              12 November 2020



      ounce is also a unit of mass.  The fluid ounce is fluidounce or floz.
      When British capacity units differ from their US counterparts, such as
      the British Imperial gallon, the unit is defined both ways with br and
      us prefixes.  Your locale settings will determine the value of the
      unprefixed unit.  Currency is prefixed with its country name:
      belgiumfranc, britainpound.

      When searching for a unit, if the specified string does not appear
      exactly as a unit name, then the units program will try to remove a
      trailing s, es.  Next units will replace a trailing ies with y.  If
      that fails, units will check for a prefix.  The database includes all
      of the standard metric prefixes.  Only one prefix is permitted per
      unit, so micromicrofarad will fail.  However, prefixes can appear
      alone with no unit following them, so micro*microfarad will work, as
      will micro microfarad.

      To find out which units and prefixes are available, read the standard
      units data file, which is extensively annotated.

    English Customary Units
      English customary units differ in various ways in different regions.
      In Britain a complex system of volume measurements featured different
      gallons for different materials such as a wine gallon and ale gallon
      that different by twenty percent.  This complexity was swept away in
      1824 by a reform that created an entirely new gallon, the British
      Imperial gallon defined as the volume occupied by ten pounds of water.
      Meanwhile in the USA the gallon is derived from the 1707 Winchester
      wine gallon, which is 231 cubic inches.  These gallons differ by about
      twenty percent.  By default if units runs in the en_GB locale you will
      get the British volume measures.  If it runs in the en_US locale you
      will get the US volume measures.  In other locales the default values
      are the US definitions.  If you wish to force different definitions,
      then set the environment variable UNITS_ENGLISH to either US or GB to
      set the desired definitions independent of the locale.

      Before 1959, the value of a yard (and other units of measure defined
      in terms of it) differed slightly among English-speaking countries.
      In 1959, Australia, Canada, New Zealand, the United Kingdom, the
      United States, and South Africa adopted the Canadian value of 1 yard =
      0.9144 m (exactly), which was approximately halfway between the values
      used by the UK and the US; it had the additional advantage of making
      1 inch = 2.54 cm (exactly).  This new standard was termed the
      International Yard.  Australia, Canada, and the UK then defined all
      customary lengths in terms of the International Yard (Australia did
      not define the furlong or rod); because many US land surveys were in
      terms of the pre-1959 units, the US continued to define customary
      surveyors' units (furlong, chain, rod, and link) in terms of the
      previous value for the foot, which was termed the US survey foot.  The
      US defined a US survey mile as 5280 US survey feet, and defined a
      statute mile as a US survey mile.  The US values for these units
      differ from the international values by about 2 ppm.



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 UNITS(1)                                                           UNITS(1)
                              12 November 2020



      The units program uses the international values for these units; the
      US values can be obtained by using either the US or the survey prefix.
      In either case, the simple familiar relationships among the units are
      maintained, e.g., 1 furlong = 660 ft, and 1 USfurlong = 660 USft,
      though the metric equivalents differ slightly between the two cases.
      The US prefix or the survey prefix can also be used to obtain the US
      survey mile and the value of the US yard prior to 1959, e.g., USmile
      or surveymile (but not USsurveymile).  To get the US value of the
      statute mile, use either USstatutemile or USmile.

      Except for distances that extend over hundreds of miles (such as in
      the US State Plane Coordinate System), the differences in the miles
      are usually insignificant:

      You have: 100 surveymile - 100 mile You want: inch
              * 12.672025
              / 0.078913984

      The pre-1959 UK values for these units can be obtained with the prefix
      UK.

      In the US, the acre is officially defined in terms of the US survey
      foot, but units uses a definition based on the international foot.  If
      you want the official US acre use USacre and similarly use USacrefoot
      for the official US version of that unit.  The difference between
      these units is about 4 parts per million.

 UNIT EXPRESSIONS
    Operators
      You can enter more complicated units by combining units with
      operations such as multiplication, division, powers, addition,
      subtraction, and parentheses for grouping.  You can use the customary
      symbols for these operators when units is invoked with its default
      options.  Additionally, units supports some extensions, including high
      priority multiplication using a space, and a high priority numerical
      division operator (|) that can simplify some expressions.

      You multiply units using a space or an asterisk (*).  The next example
      shows both forms:

      You have: arabicfoot * arabictradepound * force You want: ft lbf
              * 0.7296
              / 1.370614

      You can divide units using the slash (/) or with per:

      You have: furlongs per fortnight You want: m/s
              * 0.00016630986
              / 6012.8727





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 UNITS(1)                                                           UNITS(1)
                              12 November 2020



      You can use parentheses for grouping:

      You have: (1/2) kg / (kg/meter) You want: league
              * 0.00010356166
              / 9656.0833

      White space surrounding operators is optional, so the previous example
      could have used (1/2)kg/(kg/meter).  As a consequence, however,
      hyphenated spelled-out numbers (e.g., forty-two) cannot be used;
      forty-two is interpreted as 40 - 2.

      Multiplication using a space has a higher precedence than division
      using a slash and is evaluated left to right; in effect, the first /
      character marks the beginning of the denominator of a unit expression.
      This makes it simple to enter a quotient with several terms in the
      denominator: J / mol K.  The * and / operators have the same
      precedence, and are evaluated left to right; if you multiply with *,
      you must group the terms in the denominator with parentheses:
      J / (mol * K).

      The higher precedence of the space operator may not always be
      advantageous.  For example, m/s s/day is equivalent to m / s s day and
      has dimensions of length per time cubed.  Similarly, 1/2 meter refers
      to a unit of reciprocal length equivalent to 0.5/meter, perhaps not
      what you would intend if you entered that expression.  The get a half
      meter you would need to use parentheses: (1/2) meter.  The * operator
      is convenient for multiplying a sequence of quotients.  For example,
      m/s * s/day is equivalent to m/day.  Similarly, you could write
      1/2 * meter to get half a meter.

      The units program supports another option for numerical fractions: you
      can indicate division of numbers with the vertical bar (|), so if you
      wanted half a meter you could write 1|2 meter.  You cannot use the
      vertical bar to indicate division of non-numerical units (e.g., m|s
      results in an error message).

      Powers of units can be specified using the   character, as shown in
      the following example, or by simple concatenation of a unit and its
      exponent: cm3 is equivalent to cm 3; if the exponent is more than one
      digit, the   is required.  You can also use ** as an exponent
      operator.

      You have: cm 3 You want: gallons
              * 0.00026417205
              / 3785.4118

      Concatenation only works with a single unit name: if you write (m/s)2,
      units will treat it as multiplication by 2.  When a unit includes a
      prefix, exponent operators apply to the combination, so centimeter3
      gives cubic centimeters.  If you separate the prefix from the unit
      with any multiplication operator (e.g., centi meter 3), the prefix is



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 UNITS(1)                                                           UNITS(1)
                              12 November 2020



      treated as a separate unit, so the exponent applies only to the unit
      without the prefix.  The second example is equivalent to centi *
      (meter 3), and gives a hundredth of a cubic meter, not a cubic
      centimeter.  The units program is limited internally to products of 99
      units; accordingly, expressions like meter 100 or joule 34
      (represented internally as kg 34 m 68 / s 68) will fail.

      The | operator has the highest precedence, so you can write the square
      root of two thirds as 2|3 1|2.  The   operator has the second highest
      precedence, and is evaluated right to left, as usual:

      You have: 5 * 2 3 2 You want:
              Definition: 2560

      With a dimensionless base unit, any dimensionless exponent is
      meaningful (e.g., pi exp(2.371)).  Even though angle is sometimes
      treated as dimensionless, exponents cannot have dimensions of angle:

      You have: 2 radian
                         Exponent not dimensionless

      If the base unit is not dimensionless, the exponent must be a rational
      number p/q, and the dimension of the unit must be a power of q, so
      gallon 2|3 works but acre 2|3 fails.  An exponent using the slash (/)
      operator (e.g., gallon (2/3)) is also acceptable; the parentheses are
      needed because the precedence of   is higher than that of /.  Since
      units cannot represent dimensions with exponents greater than 99, a
      fully reduced exponent must have q < 100.  When raising a non-
      dimensionless unit to a power, units attempts to convert a decimal
      exponent to a rational number with q < 100.  If this is not possible
      units displays an error message:

      You have: ft 1.234 Base unit not dimensionless; rational exponent
      required

      A decimal exponent must match its rational representation to machine
      precision, so acre 1.5 works but gallon 0.666 does not.

    Sums and Differences of Units
      You may sometimes want to add values of different units that are
      outside the SI.  You may also wish to use units as a calculator that
      keeps track of units.  Sums of conformable units are written with the
      + character, and differences with the - character.

      You have: 2 hours + 23 minutes + 32 seconds You want: seconds
              * 8612
              / 0.00011611705

      You have: 12 ft + 3 in You want: cm
              * 373.38
              / 0.0026782366



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 UNITS(1)                                                           UNITS(1)
                              12 November 2020



      You have: 2 btu + 450 ft lbf You want: btu
              * 2.5782804
              / 0.38785542

      The expressions that are added or subtracted must reduce to identical
      expressions in primitive units, or an error message will be displayed:

      You have: 12 printerspoint - 4 heredium
                                              Illegal sum of non-conformable
      units

      If you add two values of vastly different scale you may exceed the
      available precision of floating point (about 15 digits). The effect is
      that the addition of the smaller value makes no change to the larger
      value; in other words, the smaller value is treated as if it were
      zero.

      You have: lightyear + cm

      No warning is given, however.  As usual, the precedence for + and - is
      lower than that of the other operators.  A fractional quantity such as
      2 1/2 cups can be given as (2+1|2) cups; the parentheses are necessary
      because multiplication has higher precedence than addition.  If you
      omit the parentheses, units attempts to add 2 and 1|2 cups, and you
      get an error message:

      You have: 2+1|2 cups
                           Illegal sum or difference of non-conformable
      units

      The expression could also be correctly written as (2+1/2) cups.  If
      you write 2 1|2 cups the space is interpreted as multiplication so the
      result is the same as 1 cup.

      The + and - characters sometimes appears in exponents like 3.43e+8.
      This leads to an ambiguity in an expression like 3e+2 yC.  The unit e
      is a small unit of charge, so this can be regarded as equivalent to
      (3e+2) yC or (3 e)+(2 yC).  This ambiguity is resolved by always
      interpreting + and - as part of an exponent if possible.

    Numbers as Units
      For units, numbers are just another kind of unit.  They can appear as
      many times as you like and in any order in a unit expression.  For
      example, to find the volume of a box that is 2 ft by 3 ft by 12 ft in
      steres, you could do the following:

      You have: 2 ft 3 ft 12 ft You want: stere
              * 2.038813
              / 0.49048148

      You have: $ 5 / yard You want: cents / inch



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 UNITS(1)                                                           UNITS(1)
                              12 November 2020



              * 13.888889
              / 0.072

      And the second example shows how the dollar sign in the units
      conversion can precede the five.  Be careful:  units will interpret $5
      with no space as equivalent to dollar 5.

    Built-in Functions
      Several built-in functions are provided: sin, cos, tan, asin, acos,
      atan, sinh, cosh, tanh, asinh, acosh, atanh, exp, ln, log, abs, round,
      floor, ceil, factorial, Gamma, lnGamma, erf, and erfc; the function
      lnGamma is the natural logarithm of the Gamma function.

      The sin, cos, and tan functions require either a dimensionless
      argument or an argument with dimensions of angle.

      You have: sin(30 degrees) You want:
              Definition: 0.5

      You have: sin(pi/2) You want:
              Definition: 1

      You have: sin(3 kg)
                          Unit not dimensionless

      The other functions on the list require dimensionless arguments.  The
      inverse trigonometric functions return arguments with dimensions of
      angle.

      The ln and log functions give natural log and log base 10
      respectively.  To obtain logs for any integer base, enter the desired
      base immediately after log.  For example, to get log base 2 you would
      write log2 and to get log base 47 you could write log47.

      You have: log2(32) You want:
              Definition: 5 You have: log3(32) You want:
              Definition: 3.1546488 You have: log4(32) You want:
              Definition: 2.5 You have: log32(32) You want:
              Definition: 1 You have: log(32) You want:
              Definition: 1.50515 You have: log10(32) You want:
              Definition: 1.50515

      If you wish to take roots of units, you may use the sqrt or cuberoot
      functions.  These functions require that the argument have the
      appropriate root.  You can obtain higher roots by using fractional
      exponents:

      You have: sqrt(acre) You want: feet
              * 208.71074
              / 0.0047913202




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 UNITS(1)                                                           UNITS(1)
                              12 November 2020



      You have: (400 W/m 2 / stefanboltzmann) (1/4) You have:
              Definition: 289.80882 K

      You have: cuberoot(hectare)
                                  Unit not a root

    Previous Result
      You can insert the result of the previous conversion using the
      underscore (_).  It is useful when you want to convert the same input
      to several different units, for example

      You have: 2.3 tonrefrigeration You want: btu/hr
              * 27600
              / 3.6231884e-005 You have: _ You want: kW
              * 8.0887615
              / 0.12362832

      Suppose you want to do some deep frying that requires an oil depth of
      2 inches.  You have 1/2 gallon of oil, and want to know the largest-
      diameter pan that will maintain the required depth.  The nonlinear
      unit circlearea gives the radius of the circle (see Other Nonlinear
      Units, for a more detailed description) in SI units; you want the
      diameter in inches:

      You have: 1|2 gallon / 2 in You want: circlearea
              0.10890173 m You have: 2 _ You want: in
              * 8.5749393
              / 0.1166189

      In most cases, surrounding white space is optional, so the previous
      example could have used 2_.  If _ follows a non-numerical unit symbol,
      however, the space is required:

      You have: m_
                   Parse error

      When _ is followed by a digit, the operation is multiplication rather
      than exponentiation, so that _2, is equivalent to _ * 2 rather than
      _ 2.

      You can use the _ symbol any number of times; for example,

      You have: m You want:
              Definition: 1 m You have: _ _ You want:
              Definition: 1 m 2

      Using _ before a conversion has been performed (e.g., immediately
      after invocation) generates an error:

      You have: _
                  No previous result;  _  not set



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 UNITS(1)                                                           UNITS(1)
                              12 November 2020



      Accordingly, _ serves no purpose when units is invoked non-
      interactively.

      If units is invoked with the --verbose option (see Invoking Units),
      the value of _ is not expanded:

      You have: mile You want: ft
              mile = 5280 ft
              mile = (1 / 0.00018939394) ft You have: _ You want: m
              _ = 1609.344 m
              _ = (1 / 0.00062137119) m

      You can give _ at the You want: prompt, but it usually is not very
      useful.

    Complicated Unit Expressions
      The units program is especially helpful in ensuring accuracy and
      dimensional consistency when converting lengthy unit expressions.  For
      example, one form of the Darcy-Weisbach fluid-flow equation is

           Delta P = (8 / pi) 2 (rho fLQ 2) / d 5,

      where Delta P is the pressure drop, rho is the mass density, f is the
      (dimensionless) friction factor, L is the length of the pipe, Q is the
      volumetric flow rate, and d is the pipe diameter.  It might be desired
      to have the equation in the form

           Delta P = A1 rho fLQ 2 / d 5

      that accepted the user s normal units; for typical units used in the
      US, the required conversion could be something like

      You have: (8/pi 2)(lbm/ft 3)ft(ft 3/s) 2(1/in 5) You want: psi
              * 43.533969
              / 0.022970568

      The parentheses allow individual terms in the expression to be entered
      naturally, as they might be read from the formula.  Alternatively, the
      multiplication could be done with the * rather than a space; then
      parentheses are needed only around ft 3/s because of its exponent:

      You have: 8/pi 2 * lbm/ft 3 * ft * (ft 3/s) 2 /in 5 You want: psi
              * 43.533969
              / 0.022970568

      Without parentheses, and using spaces for multiplication, the previous
      conversion would need to be entered as

      You have: 8 lb ft ft 3 ft 3 / pi 2 ft 3 s 2 in 5 You want: psi
              * 43.533969
              / 0.022970568



                                   - 13 -      Formatted:  November 26, 2020






 UNITS(1)                                                           UNITS(1)
                              12 November 2020



    Backwards Compatibility: * and -
      The original units assigned multiplication a higher precedence than
      division using the slash.  This differs from the usual precedence
      rules, which give multiplication and division equal precedence, and
      can be confusing for people who think of units as a calculator.

      The star operator (*) included in this units program has, by default,
      the same precedence as division, and hence follows the usual
      precedence rules.  For backwards compatibility you can invoke units
      with the --oldstar option.  Then * has a higher precedence than
      division, and the same precedence as multiplication using the space.

      Historically, the hyphen (-) has been used in technical publications
      to indicate products of units, and the original units program treated
      it as a multiplication operator.  Because units provides several other
      ways to obtain unit products, and because - is a subtraction operator
      in general algebraic expressions, units treats the binary - as a
      subtraction operator by default.  For backwards compatibility use the
      --product option, which causes units to treat the binary - operator as
      a product operator.  When - is a multiplication operator it has the
      same precedence as multiplication with a space, giving it a higher
      precedence than division.

      When - is used as a unary operator it negates its operand.  Regardless
      of the units options, if - appears after ( or after +, then it will
      act as a negation operator.  So you can always compute 20 degrees
      minus 12 minutes by entering 20 degrees + -12 arcmin.  You must use
      this construction when you define new units because you cannot know
      what options will be in force when your definition is processed.

 NONLINEAR UNIT CONVERSIONS
      Nonlinear units are represented using functional notation.  They make
      possible nonlinear unit conversions such as temperature.

    Temperature Conversions
      Conversions between temperatures are different from linear conversions
      between temperature increments-see the example below.  The absolute
      temperature conversions are handled by units starting with temp, and
      you must use functional notation.  The temperature-increment
      conversions are done using units starting with deg and they do not
      require functional notation.

      You have: tempF(45) You want: tempC
              7.2222222

      You have: 45 degF You want: degC
              * 25
              / 0.04

      Think of tempF(x) not as a function but as a notation that indicates
      that x should have units of tempF attached to it.  See Defining



                                   - 14 -      Formatted:  November 26, 2020






 UNITS(1)                                                           UNITS(1)
                              12 November 2020



      Nonlinear Units.  The first conversion shows that if it s 45 degrees
      Fahrenheit outside, it s 7.2 degrees Celsius.  The second conversion
      indicates that a change of 45 degrees Fahrenheit corresponds to a
      change of 25 degrees Celsius.  The conversion from tempF(x) is to
      absolute temperature, so that

      You have: tempF(45) You want: degR
              * 504.67
              / 0.0019814929

      gives the same result as

      You have: tempF(45) You want: tempR
              * 504.67
              / 0.0019814929

      But if you convert tempF(x) to degC, the output is probably not what
      you expect:

      You have: tempF(45) You want: degC
              * 280.37222
              / 0.0035666871

      The result is the temperature in K, because degC is defined as K, the
      Kelvin. For consistent results, use the tempX units when converting to
      a temperature rather than converting a temperature increment.

      The tempC() and tempF() definitions are limited to positive absolute
      temperatures, and giving a value that would result in a negative
      absolute temperature generates an error message:

      You have: tempC(-275)
                            Argument of function outside domain

    Other Nonlinear Units
      Some other examples of nonlinear units are numerous different ring
      sizes and wire gauges, the grit sizes used for abrasives, the decibel
      scale, shoe size, scales for the density of sugar (e.g., baume).  The
      standard data file also supplies units for computing the area of a
      circle and the volume of a sphere.  See the standard units data file
      for more details.  Wire gauges with multiple zeroes are signified
      using negative numbers where two zeroes is -1.  Alternatively, you can
      use the synonyms g00, g000, and so on that are defined in the standard
      units data file.

      You have: wiregauge(11) You want: inches
              * 0.090742002
              / 11.020255

      You have: brwiregauge(g00) You want: inches
              * 0.348



                                   - 15 -      Formatted:  November 26, 2020






 UNITS(1)                                                           UNITS(1)
                              12 November 2020



              / 2.8735632

      You have: 1 mm You want: wiregauge
              18.201919

      You have: grit_P(600) You want: grit_ansicoated
              342.76923

      The last example shows the conversion from P graded sand paper, which
      is the European standard and may be marked P600 on the back, to the
      USA standard.

      You can compute the area of a circle using the nonlinear unit,
      circlearea.  You can also do this using the circularinch or
      circleinch.  The next example shows two ways to compute the area of a
      circle with a five inch radius and one way to compute the volume of a
      sphere with a radius of one meter.

      You have: circlearea(5 in) You want: in2
              * 78.539816
              / 0.012732395

      You have: 10 2 circleinch You want: in2
              * 78.539816
              / 0.012732395

      You have: spherevol(meter) You want: ft3
              * 147.92573
              / 0.0067601492

      The inverse of a nonlinear conversion is indicated by prefixing a
      tilde ( ) to the nonlinear unit name:

      You have:  wiregauge(0.090742002 inches) You want:
              Definition: 11

      You can give a nonlinear unit definition without an argument or
      parentheses, and press Enter at the You want: prompt to get the
      definition of a nonlinear unit; if the definition is not valid for all
      real numbers, the range of validity is also given.  If the definition
      requires specific units this information is also displayed:

      You have: tempC
              Definition: tempC(x) = x K + stdtemp
                          defined for x >= -273.15 You have:  tempC
              Definition:  tempC(tempC) = (tempC +(-stdtemp))/K
                          defined for tempC >= 0 K You have: circlearea
              Definition: circlearea(r) = pi r 2
                          r has units m





                                   - 16 -      Formatted:  November 26, 2020






 UNITS(1)                                                           UNITS(1)
                              12 November 2020



      To see the definition of the inverse use the   notation.  In this case
      the parameter in the functional definition will usually be the name of
      the unit.  Note that the inverse for tempC shows that it requires
      units of K in the specification of the allowed range of values.
      Nonlinear unit conversions are described in more detail in Defining
      Nonlinear Units.

 UNIT LISTS: CONVERSION TO SUMS OF
      Outside of the SI, it is sometimes desirable to convert a single unit
      to a sum of units-for example, feet to feet plus inches.  The
      conversion from sums of units was described in Sums and Differences of
      Units, and is a simple matter of adding the units with the + sign:

      You have: 12 ft + 3 in + 3|8 in You want: ft
              * 12.28125
              / 0.081424936

      Although you can similarly write a sum of units to convert to, the
      result will not be the conversion to the units in the sum, but rather
      the conversion to the particular sum that you have entered:

      You have: 12.28125 ft You want: ft + in + 1|8 in
              * 11.228571
              / 0.089058524

      The unit expression given at the You want: prompt is equivalent to
      asking for conversion to multiples of 1 ft + 1 in + 1|8 in, which is
      1.09375 ft, so the conversion in the previous example is equivalent to

      You have: 12.28125 ft You want: 1.09375 ft
              * 11.228571
              / 0.089058524

      In converting to a sum of units like miles, feet and inches, you
      typically want the largest integral value for the first unit, followed
      by the largest integral value for the next, and the remainder
      converted to the last unit.  You can do this conversion easily with
      units using a special syntax for lists of units.  You must list the
      desired units in order from largest to smallest, separated by the
      semicolon (;) character:

      You have: 12.28125 ft You want: ft;in;1|8 in
              12 ft + 3 in + 3|8 in

      The conversion always gives integer coefficients on the units in the
      list, except possibly the last unit when the conversion is not exact:

      You have: 12.28126 ft You want: ft;in;1|8 in
              12 ft + 3 in + 3.00096 * 1|8 in





                                   - 17 -      Formatted:  November 26, 2020






 UNITS(1)                                                           UNITS(1)
                              12 November 2020



      The order in which you list the units is important:

      You have: 3 kg You want: oz;lb
              105 oz + 0.051367866 lb

      You have: 3 kg You want: lb;oz
              6 lb + 9.8218858 oz

      Listing ounces before pounds produces a technically correct result,
      but not a very useful one.  You must list the units in descending
      order of size in order to get the most useful result.

      Ending a unit list with the separator ; has the same effect as
      repeating the last unit on the list, so ft;in;1|8 in; is equivalent to
      ft;in;1|8 in;1|8 in.  With the example above, this gives

      You have: 12.28126 ft You want: ft;in;1|8 in;
              12 ft + 3 in + 3|8 in + 0.00096 * 1|8 in

      in effect separating the integer and fractional parts of the
      coefficient for the last unit.  If you instead prefer to round the
      last coefficient to an integer you can do this with the --round (-r)
      option.  With the previous example, the result is

      You have: 12.28126 ft You want: ft;in;1|8 in
              12 ft + 3 in + 3|8 in (rounded down to nearest 1|8 in)

      When you use the -r option, repeating the last unit on the list has no
      effect (e.g., ft;in;1|8 in;1|8 in is equivalent to ft;in;1|8 in), and
      hence neither does ending a list with a ;.  With a single unit and the
      -r option, a terminal ; does have an effect: it causes units to treat
      the single unit as a list and produce a rounded value for the single
      unit.  Without the extra ;, the -r option has no effect on single unit
      conversions.  This example shows the output using the -r option:

      You have: 12.28126 ft You want: in
              * 147.37512
              / 0.0067854058

      You have: 12.28126 ft You want: in;
              147 in (rounded down to nearest in)

      Each unit that appears in the list must be conformable with the first
      unit on the list, and of course the listed units must also be
      conformable with the unit that you enter at the You have: prompt.

      You have: meter You want: ft;kg
                     conformability error
              ft = 0.3048 m
              kg = 1 kg




                                   - 18 -      Formatted:  November 26, 2020






 UNITS(1)                                                           UNITS(1)
                              12 November 2020



      You have: meter You want: lb;oz conformability error
              1 m
              0.45359237 kg

      In the first case, units reports the disagreement between units
      appearing on the list.  In the second case, units reports disagreement
      between the unit you entered and the desired conversion.  This
      conformability error is based on the first unit on the unit list.

      Other common candidates for conversion to sums of units are angles and
      time:

      You have: 23.437754 deg You want; deg;arcmin;arcsec
          23 deg + 26 arcmin + 15.9144 arcsec

      You have: 7.2319 hr You want: hr;min;sec
          7 hr + 13 min + 54.84 sec

      Some applications for unit lists may be less obvious.  Suppose that
      you have a postal scale and wish to ensure that it s accurate at 1 oz,
      but have only metric calibration weights.  You might try

      You have: 1 oz You want: 100 g;50 g; 20 g;10 g;5 g;2 g;1 g;
              20 g + 5 g + 2 g + 1 g + 0.34952312 * 1 g

      You might then place one each of the 20 g, 5 g, 2 g, and 1 g weights
      on the scale and hope that it indicates close to

      You have: 20 g + 5 g + 2 g + 1 g You want: oz;
              0.98767093 oz

      Appending ; to oz forces a one-line display that includes the unit;
      here the integer part of the result is zero, so it is not displayed.

      If a non-empty list item differs vastly in scale from the quantity
      from which the list is to be converted, you may exceed the available
      precision of floating point (about 15 digits), in which case you will
      get a warning, e.g.,

      You have: lightyear You want: mile;100 inch;10 inch;mm;micron
              5.8786254e+12 mile + 390 * 100 inch (at 15-digit precision
      limit)

    Cooking Measure
      In North America, recipes for cooking typically measure ingredients by
      volume, and use units that are not always convenient multiples of each
      other.  Suppose that you have a recipe for 6 and you wish to make a
      portion for 1.  If the recipe calls for 2 1/2 cups of an ingredient,
      you might wish to know the measurements in terms of measuring devices
      you have available, you could use units and enter




                                   - 19 -      Formatted:  November 26, 2020






 UNITS(1)                                                           UNITS(1)
                              12 November 2020



      You have: (2+1|2) cup / 6 You want: cup;1|2 cup;1|3 cup;1|4
      cup;tbsp;tsp;1|2 tsp;1|4 tsp
              1|3 cup + 1 tbsp + 1 tsp

      By default, if a unit in a list begins with fraction of the form 1|x
      and its multiplier is an integer, the fraction is given as the product
      of the multiplier and the numerator; for example,

      You have: 12.28125 ft You want: ft;in;1|8 in;
              12 ft + 3 in + 3|8 in

      In many cases, such as the example above, this is what is wanted, but
      sometimes it is not.  For example, a cooking recipe for 6 might call
      for 5 1/4 cup of an ingredient, but you want a portion for 2, and your
      1-cup measure is not available; you might try

      You have: (5+1|4) cup / 3 You want: 1|2 cup;1|3 cup;1|4 cup
              3|2 cup + 1|4 cup

      This result might be fine for a baker who has a 1 1/2-cup measure (and
      recognizes the equivalence), but it may not be as useful to someone
      with more limited set of measures, who does want to do additional
      calculations, and only wants to know How many 1/2-cup measures to I
      need to add?  After all, that s what was actually asked.  With the
      --show-factor option, the factor will not be combined with a unity
      numerator, so that you get

      You have: (5+1|4) cup / 3 You want: 1|2 cup;1|3 cup;1|4 cup
              3 * 1|2 cup + 1|4 cup

      A user-specified fractional unit with a numerator other than 1 is
      never overridden, however-if a unit list specifies 3|4 cup;1|2 cup, a
      result equivalent to 1 1/2 cups will always be shown as 2 * 3|4 cup
      whether or not the --show-factor option is given.

    Unit List Aliases
      A unit list such as

      cup;1|2 cup;1|3 cup;1|4 cup;tbsp;tsp;1|2 tsp;1|4 tsp

      can be tedious to enter.  The units program provides shorthand names
      for some common combinations:

      hms         hours, minutes, seconds dms         angle: degrees,
      minutes, seconds time        years, days, hours, minutes and seconds
      usvol       US cooking volume: cups and smaller ftin        feet,
      inches and 1/8 inches inchfine    inches subdivided to 1/64 inch

      Using these shorthands, or unit list aliases, you can do the following
      conversions:




                                   - 20 -      Formatted:  November 26, 2020






 UNITS(1)                                                           UNITS(1)
                              12 November 2020



      You have: anomalisticyear You want: time
              1 year + 25 min + 3.4653216 sec You have: 1|6 cup You want:
      usvol
              2 tbsp + 2 tsp

      You can define your own unit list aliases; see Defining Unit List
      Aliases.

      You cannot combine a unit list alias with other units: it must appear
      alone at the You want: prompt.

      You can display the definition of a unit list alias by entering it at
      the You have: prompt:

      You have: dms
              Definition: unit list, deg;arcmin;arcsec

      When you specify compact output with --compact, --terse or -t and
      perform conversion to a unit list, units lists the conversion factors
      for each unit in the list, separated by semicolons.

      You have: year You want: day;min;sec 365;348;45.974678

      Unlike the case of regular output, zeros are included in this output
      list:

      You have: liter You want: cup;1|2 cup;1|4 cup;tbsp 4;0;0;3.6280454

 ALTERNATIVE UNIT SYSTEMS
    CGS Units
      The SI-an extension of the MKS (meterkilogramsecond) system-has
      largely supplanted the older CGS (centimetergramsecond) system, but
      CGS units are still used in a few specialized fields, especially in
      physics where they lead to a more elegant formulation of Maxwell s
      equations.  Conversions between SI and CGS involving mechanical units
      are straightforward, involving powers of 10 (e.g., 1 m = 100 cm).
      Conversions involving electromagnetic units are more complicated, and
      units supports four different systems of CGS units: electrostatic
      units (ESU), electromagnetic units (EMU), the Gaussian system and the
      HeavisideLorentz system. The differences between these systems arise
      from different choices made for proportionality constants in
      electromagnetic equations.  Coulomb s law gives electrostatic force
      between two charges separated by a distance delim $$ r:

           F = k_C q_1 q_2 / r 2.

      Ampere s law gives the electromagnetic force per unit length between
      two current-carrying conductors separated by a distance r:

           F/l = 2 k_A I_1 I_2 / r.




                                   - 21 -      Formatted:  November 26, 2020






 UNITS(1)                                                           UNITS(1)
                              12 November 2020



      The two constants, k_C and k_A, are related by the square of the speed
      of light: k_A = k_C / c 2.

      In the SI, the constants have dimensions, and an additional base unit,
      the ampere, measures electric current.  The CGS systems do not define
      new base units, but express charge and current as derived units in
      terms of mass, length, and time.  In the ESU system, the constant for
      Coulomb s law is chosen to be unity and dimensionless, which defines
      the unit of charge.  In the EMU system, the constant for Ampere s law
      is chosen to be unity and dimensionless, which defines a unit of
      current.  The Gaussian system usually uses the ESU units for charge
      and current; it chooses another constant so that the units for the
      electric and magnetic fields are the same.  The HeavisideLorentz
      system is rationalized so that factors of 4{pi} do not appear in
      Maxwell s equations.  The SI system is similarly rationalized, but the
      other CGS systems are not.  In the HeavisideLorentz (HLU) system the
      factor of 4{pi} appears in Coulomb s law instead; this system differs
      from the Gaussian system by factors of the square root of 4{pi}

      The dimensions of electrical quantities in the various CGS systems are
      different from the SI dimensions for the same units; strictly,
      conversions between these systems and SI are not possible.  But units
      in different systems relate to the same physical quantities, so there
      is a correspondence between these units.  The units program defines
      the units so that you can convert between corresponding units in the
      various systems.

      The CGS definitions involve cm (1/2) and g (1/2), which is problematic
      because units does not normally support fractional roots of base
      units.  The --units (-u) option allows selection of a CGS unit system
      and works around this restriction by introducing base units for the
      square roots of length and mass: sqrt_cm and sqrt_g.  The centimeter
      then becomes sqrt_cm 2 and the gram, sqrt_g 2.  This allows working
      from equations using the units in the CGS system, and enforcing
      dimensional conformity within that system.  Recognized CGS arguments
      to the --units option are gauss[ian], esu, emu, lhu; the argument is
      case insensitive.  You can also give si which just enforces the
      default SI mode and displays (SI) at the You have: prompt to emphasize
      the units mode.  Some other types of units are also supported as
      described below.  Giving an unrecognized system generates a warning,
      and units uses SI units.

      The changes resulting from the --units option are actually controlled
      by the UNITS_SYSTEM environment variable.  If you frequently work with
      one of the supported CGS units systems, you may set this environment
      variable rather than giving the --units option at each invocation.  As
      usual, an option given on the command line overrides the setting of
      the environment variable. For example, if you would normally work with
      Gaussian units but might occasionally work with SI, you could set
      UNITS_SYSTEM to gaussian and specify SI with the --units option.
      Unlike the argument to the --units option, the value of UNITS_SYSTEM



                                   - 22 -      Formatted:  November 26, 2020






 UNITS(1)                                                           UNITS(1)
                              12 November 2020



      is case sensitive, so setting a value of EMU will have no effect other
      than to give an error message and set SI units.

      The CGS definitions appear as conditional settings in the standard
      units data file, which you can consult for more information on how
      these units are defined, or on how to define an alternate units
      system.

      The ESU system derives the electromagnetic units from its unit of
      charge, the statcoulomb, which is defined from Coulomb s law.  The
      statcoulomb equals dyne (1/2) cm, or cm (3/2) g (1/2) s (-1).  The
      unit of current, the statampere, is statcoulomb sec, analogous to the
      relationship in SI.  Other electrical units are then derived in a
      manner similar to that for SI units; the units use the SI names
      prefixed by stat-, e.g., statvolt or statV.  The prefix st- is also
      recognized (e.g., stV).

      The EMU system derives the electromagnetic units from its unit of
      current, the abampere, which is defined in terms of Ampere s law.  The
      abampere is equal to dyne (1/2), or cm (1/2) g (1/2) s (-1).  delim
      off The unit of charge, the abcoulomb, is abampere sec, again
      analogous to the SI relationship.  Other electrical units are then
      derived in a manner similar to that for SI units; the units use the SI
      names prefixed by ab-, e.g., abvolt or abV.  The magnetic field units
      include the gauss, the oersted and the maxwell.

      The Gaussian units system, which was also known as the Symmetric
      System, uses the same charge and current units as the ESU system
      (e.g., statC, statA); it differs by defining the magnetic field so
      that it has the same units as the electric field.  The resulting
      magnetic field units are the same ones used in the EMU system: the
      gauss, the oersted and the maxwell.

      The HeavisideLorentz system appears to lack named units.  We define
      five basic units, hlu_charge, hlu_current, hlu_volt, hlu_efield and
      hlu_bfield for conversions with this system.  It is important to
      remember that with all of the CGS systems, the units may look the same
      but mean something different.  The HLU system and Gaussian systems
      both measure magnetic field using the same CGS dimensions, but the
      amount of magnetic field with the same units is different in the two
      systems.

      The CGS systems define units that measure the same thing but may have
      conflicting dimensions.  Furthermore, the dimensions of the
      electromagnetic CGS units are never compatible with SI.  But if you
      measure charge in two different systems you have measured the same
      physical thing, so there is a correspondence between the units in the
      different systems, and units supports conversions between
      corresponding units.  When running with SI, units defines all of the
      CGS units in terms of SI.  When you select a CGS system, units defines
      the SI units and the other CGS system units in terms of the system you



                                   - 23 -      Formatted:  November 26, 2020






 UNITS(1)                                                           UNITS(1)
                              12 November 2020



      have selected.

      (Gaussian) You have: statA
                 You want: abA
              * 3.335641e-11
              / 2.9979246e+10 (Gaussian) You have: abA
                 You want: sqrt(dyne) conformability error
              2.9979246e+10 sqrt_cm 3 sqrt_g / s 2
              1 sqrt_cm sqrt_g / s

      In the above example, units converts between the current units statA
      and abA even though the abA, from the EMU system, has incompatible
      dimensions.  This works because in Gaussian mode, the abA is defined
      in terms of the statA, so it does not have the correct definition for
      EMU; consequently, you cannot convert the abA to its EMU definition.

      One challenge of conversion is that because the CGS system has fewer
      base units, quantities that have different dimensions in SI may have
      the same dimension in a CGS system.  And yet, they may not have the
      same conversion factor.  For example, the unit for the E field and B
      fields are the same in the Gaussian system, but the conversion factors
      to SI are quite different.  This means that correct conversion is only
      possible if you keep track of what quantity is being measured.  You
      cannot convert statV/cm to SI without indicating which type of field
      the unit measures.  To aid in dimensional analysis, units defines
      various dimension units such as LENGTH, TIME, and CHARGE to be the
      appropriate dimension in SI.  The electromagnetic dimensions such as
      B_FIELD or E_FIELD may be useful aids both for conversion and
      dimensional analysis in CGS.  You can convert them to or from CGS in
      order to perform SI conversions that in some cases will not work
      directly due to dimensional incompatibilities.  This example shows how
      the Gaussian system uses the same units for all of the fields, but
      they all have different conversion factors with SI.

      (Gaussian) You have: statV/cm
                 You want: E_FIELD
              * 29979.246
              / 3.335641e-05 (Gaussian) You have: statV/cm
                 You want: B_FIELD
              * 0.0001
              / 10000 (Gaussian) You have: statV/cm
                 You want: H_FIELD
              * 79.577472
              / 0.012566371 (Gaussian) You have: statV/cm
                 You want: D_FIELD
              * 2.6544187e-07
              / 3767303.1

      The next example shows that the oersted cannot be converted directly
      to the SI unit of magnetic field, A/m, because the dimensions
      conflict.  We cannot redefine the ampere to make this work because



                                   - 24 -      Formatted:  November 26, 2020






 UNITS(1)                                                           UNITS(1)
                              12 November 2020



      then it would not convert with the statampere.  But you can still do
      this conversion as shown below.

      (Gaussian) You have: oersted
                 You want: A/m conformability error
              1 sqrt_g / s sqrt_cm
              29979246 sqrt_cm sqrt_g / s 2 (Gaussian) You have: oersted
                 You want: H_FIELD
              * 79.577472
              / 0.012566371

    Natural Units
      Like the CGS units, natural units are an alternative to the SI system
      used primarily physicists in different fields, with different systems
      tailored to different fields of study.  These systems are natural
      because the base measurements are defined using physical constants
      instead of arbitrary values such as the meter or second.  In different
      branches of physics, different physical constants are more
      fundamental, which has given rise to a variety of incompatible natural
      unit systems.

      The supported systems are the natural units (which seem to have no
      better name) used in high energy physics and cosmology, the Planck
      units, often used my scientists working with gravity, and the Hartree
      atomic units are favored by those working in physical chemistry and
      condensed matter physics.

      You can select the various natural units using the --units option in
      the same way that you select the CGS units.  The natural units come in
      two types, a rationalized system derived from the HeavisideLorentz
      units and an unrationalized system derived from the Gaussian system.
      You can select these using natural and natural-gauss respectively.
      For conversions in SI mode, several unit names starting with natural
      are available.  This natural system is defined by setting {hbar}, c
      and the Boltzman constant to 1.  Only a single base unit remains: the
      electron volt.

      The Planck units exist in a variety of forms, and units supports two.
      Both supported forms are rationalized, in that factors of 4{pi} do not
      appear in Maxwell s equations.  However, Planck units can also differ
      based on how the gravitational constant is treated.  This system is
      similar to the natural units in that c, {hbar}, and Boltzman s
      constant are set to 1, but in this system, Newton s gravitational
      constant, G is also fixed.  In the reduced Planck system, delim $$
      8{pi}G = 1 whereas in the unreduced system G = 1.  The reduced system
      eliminates factors of 8{pi} delim off from the Einstein field
      equations for gravitation, so this is similar to the process of
      forming rationalized units to simplify Maxwell s equations.  To obtain
      the unreduced system use the name planck and for the reduced Planck
      units, planck-red.  Units such as planckenergy and planckenergy_red
      enable you to convert the unreduced and reduced Planck energy unit in



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 UNITS(1)                                                           UNITS(1)
                              12 November 2020



      SI mode between the various systems.  In Planck units, all
      measurements are dimensionless.

      The final natural unit system is the Hartree atomic units.  Like the
      Planck units, all measurements in the Hartree units are dimensionless,
      but this system is defined by defined from completely different
      physical constants: the electron mass, Planck s constant, the electron
      charge, and the Coulomb constant are the defining physical quantities,
      which are all set to unity.  To invoke this system with the --units
      option use the name hartree.

    Prompt Prefix
      If a unit system is specified with the --units option, the selected
      system s name is prepended to the You have: prompt as a reminder,
      e.g.,

      (Gaussian) You have: stC
                 You want:
              Definition: statcoulomb = sqrt(dyne) cm = 1 sqrt_cm 3 sqrt_g /
      s

      You can suppressed the prefix by including a line

      !prompt

      with no argument in a site or personal units data file.  The prompt
      can be conditionally suppressed by including such a line within !var
      ... !endvar constructs, e.g.,

      !var UNITS_SYSTEM gaussian gauss !prompt !endvar

      This might be appropriate if you normally use Gaussian units and find
      the prefix distracting but want to be reminded when you have selected
      a different CGS system.

 LOGGING CALCULATIONS
      The --log option allows you to save the results of calculations in a
      file; this can be useful if you need a permanent record of your work.
      For example, the fluid-flow conversion in Complicated Unit
      Expressions, is lengthy, and if you were to use it in designing a
      piping system, you might want a record of it for the project file.  If
      the interactive session

      # Conversion factor A1 for pressure drop # dP = A1 rho f L Q 2/d 5 You
      have: (8/pi 2) (lbm/ft 3)ft(ft 3/s) 2(1/in 5) # Input units You want:
      psi
              * 43.533969
              / 0.022970568

      were logged, the log file would contain




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 UNITS(1)                                                           UNITS(1)
                              12 November 2020



      ### Log started Fri Oct 02 15:55:35 2015

      # Conversion factor A1 for pressure drop # dP = A1 rho f L Q 2/d 5
      From: (8/pi 2) (lbm/ft 3)ft(ft 3/s) 2(1/in 5)   # Input units To:
      psi
              * 43.533969
              / 0.022970568

      The time is written to the log file when the file is opened.

      The use of comments can help clarify the meaning of calculations for
      the log. The log includes conformability errors between the units at
      the You have: and You want: prompts, but not other errors, including
      lack of conformability of items in sums or differences or among items
      in a unit list.  For example, a conversion between zenith angle and
      elevation angle could involve

      You have: 90 deg - (5 deg + 22 min + 9 sec)
                                           Illegal sum or difference of
      non-conformable units You have: 90 deg - (5 deg + 22 arcmin + 9
      arcsec) You want: dms
              84 deg + 37 arcmin + 51 arcsec You have: _ You want: deg
              * 84.630833
              / 0.011816024 You have:

      The log file would contain

      From: 90 deg - (5 deg + 22 arcmin + 9 arcsec) To:   deg;arcmin;arcsec
              84 deg + 37 arcmin + 51 arcsec From: _ To:   deg
              * 84.630833
              / 0.011816024

      The initial entry error (forgetting that minutes have dimension of
      time, and that arcminutes must be used for dimensions of angle) does
      not appear in the output.  When converting to a unit list alias, units
      expands the alias in the log file.

      The From: and To: tags are written to the log file even if the --quiet
      option is given.  If the log file exists when units is invoked, the
      new results are appended to the log file.  The time is written to the
      log file each time the file is opened.  The --log option is ignored
      when units is used non-interactively.

 INVOKING UNITS
      You invoke units like this:

      units [options] [from-unit [to-unit]]

      If the from-unit and to-unit are omitted, the program will use
      interactive prompts to determine which conversions to perform.  See
      Interactive Use.  If both from-unit and to-unit are given, units will



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                              12 November 2020



      print the result of that single conversion and then exit.  If only
      from-unit appears on the command line, units will display the
      definition of that unit and exit.  Units specified on the command line
      may need to be quoted to protect them from shell interpretation and to
      group them into two arguments.  Note also that the --quiet option is
      enabled by default if you specify from-unit on the command line. See
      Command Line Use.

      The default behavior of units can be changed by various options given
      on the command line.  In most cases, the options may be given in
      either short form (a single - followed by a single character) or long
      form (-- followed by a word or hyphen-separated words).  Short-form
      options are cryptic but require less typing; long-form options require
      more typing but are more explanatory and may be more mnemonic.  With
      long-form options you need only enter sufficient characters to
      uniquely identify the option to the program.  For example, --out %f
      works, but --o %f fails because units has other long options beginning
      with o.  However, --q works because --quiet is the only long option
      beginning with q.

      Some options require arguments to specify a value (e.g., -d 12 or
      --digits 12).  Short-form options that do not take arguments may be
      concatenated (e.g., -erS is equivalent to -e -r -S); the last option
      in such a list may be one that takes an argument (e.g., -ed 12).  With
      short-form options, the space between an option and its argument is
      optional (e.g., -d12 is equivalent to -d 12).  Long-form options may
      not be concatenated, and the space between a long-form option and its
      argument is required.  Short-form and long-form options may be
      intermixed on the command line.  Options may be given in any order,
      but when incompatible options (e.g., --output-format and
      --exponential) are given in combination, behavior is controlled by the
      last option given.  For example, -o%.12f -e gives exponential format
      with the default eight significant digits).

      The following options are available:

      -c, --check
           Check that all units and prefixes defined in the units data file
           reduce to primitive units.  Print a list of all units that cannot
           be reduced.  Also display some other diagnostics about suspicious
           definitions in the units data file.  Only definitions active in
           the current locale are checked.  You should always run units with
           this option after modifying a units data file.

      --check-verbose, --verbose-check
           Like the --check option, this option prints a list of units that
           cannot be reduced.  But to help find unit  definitions that cause
           endless loops, it lists the units as they are checked.  If units
           hangs, then the last unit to be printed has a bad definition.
           Only definitions active in the current locale are checked.




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 UNITS(1)                                                           UNITS(1)
                              12 November 2020



      -d ndigits, --digits ndigits
           Set the number of significant digits in the output to the value
           specified (which must be greater than zero).  For example, -d 12
           sets the number of significant digits to 12.  With exponential
           output units displays one digit to the left of the decimal point
           and eleven digits to the right of the decimal point.  On most
           systems, the maximum number of internally meaningful digits is
           15; if you specify a greater number than your system s maximum,
           units will print a warning and set the number to the largest
           meaningful value.  To directly set the maximum value, give an
           argument of max (e.g., -d max).  Be aware, of course, that
           significant here refers only to the display of numbers; if
           results depend on physical constants not known to this precision,
           the physically meaningful precision may be less than that shown.
           The --digits option conflicts with the --output-format option.

      -e, --exponential
           Set the numeric output format to exponential (i.e., scientific
           notation), like that used in the Unix units program.  The default
           precision is eight significant digits (seven digits to the right
           of the decimal point); this can be changed with the --digits
           option.  The --exponential option conflicts with the
           --output-format option.

      -o format, --output-format format
           This option affords complete control over the numeric output
           format using the specified format. The format is a single
           floating point numeric format for the printf() function in the C
           programming language.  All compilers support the format types g
           and G to specify significant digits, e and E for scientific
           notation, and f for fixed-point decimal.  The ISO C99 standard
           introduced the F type for fixed-point decimal and the a and A
           types for hexadecimal floating point; these types are allowed
           with compilers that support them.  The default format is %.8g;
           for greater precision, you could specify -o %.15g. See Numeric
           Output Format and the documentation for printf() for more
           detailed descriptions of the format specification.  The
           --output-format option affords the greatest control of the output
           appearance, but requires at least rudimentary knowledge of the
           printf() format syntax.  If you don t want to bother with the
           printf() syntax, you can specify greater precision more simply
           with the --digits option or select exponential format with
           --exponential.  The --output-format option is incompatible with
           the --exponential and --digits options.

      -f filename, --file filename
           Instruct units to load the units file filename.  You can specify
           up to 25 units files on the command line.  When you use this
           option, units will load only the files you list on the command
           line; it will not load the standard file or your personal units
           file unless you explicitly list them.  If filename is the empty



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 UNITS(1)                                                           UNITS(1)
                              12 November 2020



           string (-f ""), the default units file (or that specified by
           UNITSFILE) will be loaded in addition to any others specified
           with -f.

      -L logfile, --log logfile
           Save the results of calculations in the file logfile; this can be
           useful if it is important to have a record of unit conversions or
           other calculations that are to be used extensively or in a
           critical activity such as a program or design project.  If
           logfile exits, the new results are appended to the file.  This
           option is ignored when units is used non-interactively.  See
           Logging Calculations for a more detailed description and some
           examples.

      -H filename, --history filename
           Instruct units to save history to filename, so that a record of
           your commands is available for retrieval across different units
           invocations.  To prevent the history from being saved set
           filename to the empty string (-H "").  This option has no effect
           if readline is not available.

      -h, --help
           Print out a summary of the options for units.

      -m, --minus
           Causes - to be interpreted as a subtraction operator.  This is
           the default behavior.

      -p, --product
           Causes - to be interpreted as a multiplication operator when it
           has two operands.  It will act as a negation operator when it has
           only one operand: (-3).  By default - is treated as a subtraction
           operator.

      --oldstar
           Causes * to have the old-style precedence, higher than the
           precedence of division so that 1/2*3 will equal 1/6.

      --newstar
           Forces * to have the new (default) precedence that follows the
           usual rules of algebra: the precedence of * is the same as the
           precedence of /, so that 1/2*3 will equal 3/2.

      -r, --round
           When converting to a combination of units given by a unit list,
           round the value of the last unit in the list to the nearest
           integer.

      -S, --show-factor
           When converting to a combination of units specified in a list,
           always show a non-unity factor before a unit that begins with a



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 UNITS(1)                                                           UNITS(1)
                              12 November 2020



           fraction with a unity denominator.  By default, if the unit in a
           list begins with fraction of the form 1|x and its multiplier is
           an integer other than 1, the fraction is given as the product of
           the multiplier and the numerator (e.g., 3|8 in rather than 3 *
           1|8 in).  In some cases, this is not what is wanted; for example,
           the results for a cooking recipe might show 3 * 1|2 cup as
           3|2 cup.  With the --show-factor option, a result equivalent to
           1.5 cups will display as 3 * 1|2 cup rather than 3|2 cup.  A
           user-specified fractional unit with a numerator other than 1 is
           never overridden, however-if a unit list specifies 3|4 cup;1|2
           cup, a result equivalent to 1 1/2 cups will always be shown as 2
           * 3|4 cup whether or not the --show-factor option is given.

      --conformable
           In non-interactive mode, show all units conformable with the
           original unit expression.  Only one unit expression is allowed;
           if you give more than one, units will exit with an error message
           and return failure.

      -v, --verbose
           Give slightly more verbose output when converting units.  When
           combined with the -c option this gives the same effect as
           --check-verbose.  When combined with --version produces a more
           detailed output, equivalent to the --info option.

      -V, --version
           Print the program version number, tell whether the readline
           library has been included, tell whether UTF-8 support has been
           included; give the locale, the location of the default units data
           file, and the location of the personal units data file; indicate
           if the personal units data file does not exist.

           When given in combination with the --terse option, the program
           prints only the version number and exits.

           When given in combination with the --verbose option, the program,
           the --version option has the same effect as the --info option
           below.

      -I, --info
           Print the information given with the --version option, show the
           pathname of the units program, show the status of the UNITSFILE
           and MYUNITSFILE environment variables, and additional information
           about how units locates the related files.  On systems running
           Microsoft Windows, the status of the UNITSLOCALE environment
           variable and information about the related locale map are also
           given.  This option is usually of interest only to developers and
           administrators, but it can sometimes be useful for
           troubleshooting.





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                              12 November 2020



           Combining the --version and --verbose options has the same effect
           as giving --info.

      -U, --unitsfile
           Print the location of the default units data file and exit; if
           the file cannot be found, print Units data file not found.

      -u (gauss[ian]|esu|emu), --units (gauss[ian]|esu|emu)
           Specify a CGS units system: Gaussian, ESU, or EMU.

      -l locale, --locale locale
           Force a specified locale such as en_GB to get British definitions
           by default.  This overrides the locale determined from system
           settings or environment variables.  See Locale for a description
           of locale format.

      -n, --nolists
           Disable conversion to unit lists.

      -s, --strict
           Suppress conversion of units to their reciprocal units.  For
           example, units will normally convert hertz to seconds because
           these units are reciprocals of each other.  The strict option
           requires that units be strictly conformable to perform a
           conversion, and will give an error if you attempt to convert
           hertz to seconds.

      -1, --one-line
           Give only one line of output (the forward conversion); do not
           print the reverse conversion.  If a reciprocal conversion is
           performed, then units will still print the reciprocal conversion
           line.

      -t, --terse
           Print only a single conversion factor.  This option can be used
           when calling units from another program so that the output is
           easy to parse.  This option has the combined effect of these
           options:  --strict --quiet --one-line --compact.  When combined
           with --version it produces a display showing only the program
           name and version number.

      --compact
           Give compact output featuring only the conversion factor; the
           multiplication and division signs are not shown, and there is no
           leading whitespace.  If you convert to a unit list, then the
           output is a semicolon separated list of factors. This turns off
           the --verbose option.

      -q, --quiet, --silent
           Suppress the display of statistics about the number of units
           loaded, any messages printed by the units database, and the



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                              12 November 2020



           prompting of the user for units.  This option does not affect how
           units displays the results.  This option is turned on by default
           if you invoke units with a unit expression on the command line.



 SCRIPTING WITH UNITS
      Despite its numerous options, units cannot cover every conceivable
      unit-conversion task.  For example, suppose we have found some
      mysterious scale, but cannot figure out the units in which it is
      reporting.  We reach into our pocket, place a 3.75-gram coin on the
      scale, and observe the scale reading 0.120.  How do we quickly
      determine the units?  Or we might wonder if a unit has any synonyms,
      i.e., other units with the same value.

      The capabilities of units are easily extended with simple scripting.
      Both questions above involve conformable units; on a system with
      Unix-like utilities, conversions to conformable units could be shown
      accomplished with the following script:

      #!/bin/sh

      progname=`basename $0 .sh` umsg="Usage: $progname [<number>] unit"

      if [ $# -lt 1 ] then
          echo "$progname: missing quantity to convert"
          echo "$umsg"
          exit 1 fi

      for unit in `units --conformable "$*" | cut -f 1 -d    ` do
          echo "$*"   # have -- quantity to convert
          echo $unit  # want -- conformable unit done | units --terse --
      verbose

      When units is invoked with no non-option arguments, it reads have/want
      pairs, on alternating lines, from its standard input, so the task can
      be accomplished with only two invocations of units.  This avoids the
      computational overhead of needlessly reprocessing the units database
      for each conformable unit, as well as the inherent system overhead of
      process invocation.

      By itself, the script is not very useful.  But it could be used in
      combination with other commands to address specific tasks.  For
      example, running the script through a simple output filter could help
      solve the scale problem above.  If the script is named conformable,
      running

      $ conformable 3.75g | grep 0.120

      gives
              3.75g = 0.1205653 apounce



                                   - 33 -      Formatted:  November 26, 2020






 UNITS(1)                                                           UNITS(1)
                              12 November 2020



              3.75g = 0.1205653 fineounce
              3.75g = 0.1205653 ozt
              3.75g = 0.1205653 tradewukiyeh
              3.75g = 0.1205653 troyounce

      So we might conclude that the scale is calibrated in troy ounces.

      We might run $ units --verbose are
              Definition: 100 m 2 = 100 m 2

      and wonder if are has any synonyms, value.  To find out, we could run

      $ conformable are | grep "= 1 "
              are = 1 a
              are = 1 are

 OUTPUT STYLES
      The output can be tweaked in various ways using command line options.
      With no options, the output looks like this

      $ units Currency exchange rates from FloatRates (USD base) on 2019-
      02-20 3070 units, 109 prefixes, 109 nonlinear units

      You have: 23ft You want: m
              * 7.0104
              / 0.14264521 You have: m You want: ft;in
              3 ft + 3.3700787 in

      This is arguably a bit cryptic; the --verbose option makes clear what
      the output means:

      $ units --verbose Currency exchange rates from FloatRates (USD base)
      on 2019-02-20 3070 units, 109 prefixes, 109 nonlinear units

      You have: 23 ft You want: m
              23 ft = 7.0104 m
              23 ft = (1 / 0.14264521) m You have: meter You want: ft;in
              meter = 3 ft + 3.3700787 in

      The --quiet option suppresses the clutter displayed when units starts,
      as well as the prompts to the user.  This option is enabled by default
      when you give units on the command line.

      $ units --quiet 23 ft m
              * 7.0104
              / 0.14264521

      $ units 23ft m
              * 7.0104
              / 0.14264521




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 UNITS(1)                                                           UNITS(1)
                              12 November 2020



      The remaining style options allow you to display only numerical values
      without the tab or the multiplication and division signs, or to
      display just a single line showing the forward conversion:

      $ units --compact 23ft m 7.0104 0.14264521

      $ units --compact m  ft;in  3;3.3700787

      $ units --one-line 23ft m
              * 7.0104

      $ units --one-line 23ft 1/m
              reciprocal conversion
              * 0.14264521

      $ units --one-line 23ft kg conformability error
              7.0104 m
              1 kg

      Note that when converting to a unit list, the --compact option
      displays a semicolon separated list of results.  Also be aware that
      the one-line option doesn t live up to its name if you execute a
      reciprocal conversion or if you get a conformability error.  The
      former case can be prevented using the --strict option, which
      suppresses reciprocal conversions. Similarly you can suppress unit
      list conversion using --nolists.  It is impossible to prevent the
      three line error output.

      $ units --compact --nolists m  ft;in  Error in  ft;in : Parse error

      $ units --one-line --strict 23ft 1/m

      The various style options can be combined appropriately.  The ultimate
      combination is the --terse option, which combines --strict, --quiet,
      --one-line, and --compact to produce the minimal output, just a single
      number for regular conversions and a semicolon separated list for
      conversion to unit lists.  This will likely be the best choice for
      programs that want to call units and then process its result.

      $ units --terse 23ft m 7.0104

      $ units --terse m  ft;in  3;3.3700787

      $ units --terse 23ft 1/m conformability error 7.0104 m 1 / m

 ADDING YOUR OWN DEFINITIONS
    Units Data Files
      The units and prefixes that units can convert are defined in the units
      data file, typically /usr/share/units/definitions.units.  If you can t
      find this file, run units --version to get information on the file
      locations for your installation.  Although you can extend or modify



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                              12 November 2020



      this data file if you have appropriate user privileges, it s usually
      better to put extensions in separate files so that the definitions
      will be preserved if you update units.

      You can include additional data files in the units database using the
      !include command in the standard units data file. For example

      !include    /usr/local/share/units/local.units

      might be appropriate for a site-wide supplemental data file.  The
      location of the !include statement in the standard units data file is
      important; later definitions replace earlier ones, so any definitions
      in an included file will override definitions before the !include
      statement in the standard units data file.  With normal invocation, no
      warning is given about redefinitions; to ensure that you don t have an
      unintended redefinition, run units -c after making changes to any
      units data file.

      If you want to add your own units in addition to or in place of
      standard or site-wide supplemental units data files, you can include
      them in the .units file in your home directory.  If this file exists
      it is read after the standard units data file, so that any definitions
      in this file will replace definitions of the same units in the
      standard data file or in files included from the standard data file.
      This file will not be read if any units files are specified on the
      command line.  (Under Windows the personal units file is named
      unitdef.units.)  Running units -V will display the location and name
      of your personal units file.

      The units program first tries to determine your home directory from
      the HOME environment variable.  On systems running Microsoft Windows,
      if HOME does not exist, units attempts to find your home directory
      from HOMEDRIVE, HOMEPATH and USERPROFILE.  You can specify an
      arbitrary file as your personal units data file with the MYUNITSFILE
      environment variable; if this variable exists, its value is used
      without searching your home directory.  The default units data files
      are described in more detail in Data Files.

    Defining New Units and Prefixes
      A unit is specified on a single line by giving its name and an
      equivalence.  Comments start with a # character, which can appear
      anywhere in a line.  The backslash character (\) acts as a
      continuation character if it appears as the last character on a line,
      making it possible to spread definitions out over several lines if
      desired.  A file can be included by giving the command !include
      followed by the file s name.  The ! must be the first character on the
      line.  The file will be sought in the same directory as the parent
      file unless you give a full path.  The name of the file to be included
      cannot contain spaces or the comment character #.





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                              12 November 2020



      Unit names must not contain any of the operator characters +, -, *, /,
      |,  , ;,  , the comment character #, or parentheses.  They cannot
      begin or end with an underscore (_), a comma (,) or a decimal point (-
      .).  The figure dash (U+2012), typographical minus ('- ; U+2212), and
      en dash ('-- ; U+2013) are converted to the operator -, so none of
      these characters can appear in unit names.  Names cannot begin with a
      digit, and if a name ends in a digit other than zero or one, the digit
      must be preceded by a string beginning with an underscore, and
      afterwards consisting only of digits, decimal points, or commas.  For
      example, foo_2, foo_2,1, or foo_3.14 are valid names but foo2 or
      foo_a2 are invalid.  The underscore is necessary because without it,
      units cannot determine whether foo2 is a unit name or represents
      foo 2.  Zero and one are exceptions because units never interprets
      them as exponents.

      You could define nitrous oxide as

      N2O     nitrogen 2  + oxygen

      but would need to define nitrogen dioxide as

      NO_2    nitrogen + oxygen 2

      Be careful to define new units in terms of old ones so that a
      reduction leads to the primitive units, which are marked with !
      characters.  Dimensionless units are indicated by using the string
      !dimensionless for the unit definition.

      When adding new units, be sure to use the -c option to check that the
      new units reduce properly.  If you create a loop in the units
      definitions, then units will hang when invoked with the -c option.
      You will need to use the --check-verbose option, which prints out each
      unit as it is checked.  The program will still hang, but the last unit
      printed will be the unit that caused the infinite loop.

      If you define any units that contain + characters in their
      definitions, carefully check them because the -c option will not catch
      non-conformable sums.  Be careful with the - operator as well.  When
      used as a binary operator, the - character can perform addition or
      multiplication depending on the options used to invoke units.  To
      ensure consistent behavior use - only as a unary negation operator
      when writing units definitions.  To multiply two units leave a space
      or use the * operator with care, recalling that it has two possible
      precedence values and may require parentheses to ensure consistent
      behavior.  To compute the difference of foo and bar write foo+(-bar)
      or even foo+-bar.

      You may wish to intentionally redefine a unit.  When you do this, and
      use the -c option, units displays a warning message about the
      redefinition.  You can suppress these warnings by redefining a unit
      using a + at the beginning of the unit name.  Do not include any white



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      space between the + and the redefined unit name.

      Here is an example of a short data file that defines some basic units:

      m       !               # The meter is a primitive unit sec     !
      # The second is a primitive unit rad     !dimensionless  # A
      dimensionless primitive unit micro-  1e-6            # Define a prefix
      minute  60 sec          # A minute is 60 seconds hour    60 min
      # An hour is 60 minutes inch    72 m            # Inch defined
      incorrectly terms of meters ft      12 inches       # The foot defined
      in terms of inches mile    5280 ft         # And the mile +inch
      0.0254 m        # Correct redefinition, warning suppressed

      A unit that ends with a - character is a prefix.  If a prefix
      definition contains any / characters, be sure they are protected by
      parentheses.  If you define half- 1/2, then halfmeter would be
      equivalent to 1 / (2 meter).

    Defining Nonlinear Units
      Some unit conversions of interest are nonlinear; for example,
      temperature conversions between the Fahrenheit and Celsius scales
      cannot be done by simply multiplying by conversion factors.

      When you give a linear unit definition such as inch 2.54 cm you are
      providing information that units uses to convert values in inches into
      primitive units of meters.  For nonlinear units, you give a functional
      definition that provides the same information.

      Nonlinear units are represented using a functional notation.  It is
      best to regard this notation not as a function call but as a way of
      adding units to a number, much the same way that writing a linear unit
      name after a number adds units to that number.  Internally, nonlinear
      units are defined by a pair of functions that convert to and from
      linear units in the database, so that an eventual conversion to
      primitive units is possible.

      Here is an example nonlinear unit definition:

      tempF(x) units=[1;K] domain=[-459.67,) range=[0,) \
                  (x+(-32)) degF + stdtemp ; (tempF+(-stdtemp))/degF + 32

      A nonlinear unit definition comprises a unit name, a formal parameter
      name, two functions, and optional specifications for units, the
      domain, and the range (the domain of the inverse function).  The
      functions tell units how to convert to and from the new unit.  To
      produce valid results, the arguments of these functions need to have
      the correct dimensions and be within the domains for which the
      functions are defined.

      The definition begins with the unit name followed immediately (with no
      spaces) by a ( character.  In the parentheses is the name of the



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                              12 November 2020



      formal parameter.  Next is an optional specification of the units
      required by the functions in the definition.  In the example above,
      the units=[1;K] specification indicates that the tempF function
      requires an input argument conformable with 1 (i.e., the argument is
      dimensionless), and that the inverse function requires an input
      argument conformable with K.  For normal nonlinear units definition,
      the forward function will always take a dimensionless argument; in
      general, the inverse function will need units that match the quantity
      measured by your nonlinear unit.  Specifying the units enables units
      to perform error checking on function arguments, and also to assign
      units to domain and range specifications, which are described later.

      Next the function definitions appear.  In the example above, the tempF
      function is defined by

      tempF(x) = (x+(-32)) degF + stdtemp

      This gives a rule for converting x in the units tempF to linear units
      of absolute temperature, which makes it possible to convert from tempF
      to other units.

      To enable conversions to Fahrenheit, you must give a rule for the
      inverse conversions.  The inverse will be x(tempF) and its definition
      appears after a ; character.  In our example, the inverse is

      x(tempF) = (tempF+(-stdtemp))/degF + 32

      This inverse definition takes an absolute temperature as its argument
      and converts it to the Fahrenheit temperature.  The inverse can be
      omitted by leaving out the ; character and the inverse definition, but
      then conversions to the unit will not be possible.  If the inverse
      definition is omitted, the --check option will display a warning.  It
      is up to you to calculate and enter the correct inverse function to
      obtain proper conversions; the --check option tests the inverse at one
      point and prints an error if it is not valid there, but this is not a
      guarantee that your inverse is correct.

      With some definitions, the units may vary.  For example, the
      definition

      square(x)       x 2

      can have any arbitrary units, and can also take dimensionless
      arguments.  In such a case, you should not specify units.  If a
      definition takes a root of its arguments, the definition is valid only
      for units that yield such a root.  For example,

      squirt(x)       sqrt(x)

      is valid for a dimensionless argument, and for arguments with even
      powers of units.



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      Some definitions may not be valid for all real numbers.  In such
      cases, units can handle errors better if you specify an appropriate
      domain and range.  You specify the domain and range as shown below:

      baume(d) units=[1;g/cm 3] domain=[0,130.5] range=[1,10] \
               (145/(145-d)) g/cm 3 ; (baume+-g/cm 3) 145 / baume

      In this example the domain is specified after domain= with the
      endpoints given in brackets.  In accord with mathematical convention,
      square brackets indicate a closed interval (one that includes its
      endpoints), and parentheses indicate an open interval (one that does
      not include its endpoints).  An interval can be open or closed on one
      or both ends; an interval that is unbounded on either end is indicated
      by omitting the limit on that end.  For example, a quantity to which
      decibel (dB) is applied may have any value greater than zero, so the
      range is indicated by (0,):

      decibel(x) units=[1;1] range=(0,) 10 (x/10); 10 log(decibel)

      If the domain or range is given, the second endpoint must be greater
      than the first.

      The domain and range specifications can appear independently and in
      any order along with the units specification.  The values for the
      domain and range endpoints are attached to the units given in the
      units specification, and if necessary, the parameter value is adjusted
      for comparison with the endpoints.  For example, if a definition
      includes units=[1;ft] and range=[3,), the range will be taken as 3 ft
      to infinity.  If the function is passed a parameter of 900 mm, that
      value will be adjusted to 2.9527559 ft, which is outside the specified
      range.  If you omit the units specification from the previous example,
      units can not tell whether you intend the lower endpoint to be 3 ft or
      3 microfurlongs, and can not adjust the parameter value of 900 mm for
      comparison.  Without units, numerical values other than zero or plus
      or minus infinity for domain or range endpoints are meaningless, and
      accordingly they are not allowed.  If you give other values without
      units, then the definition will be ignored and you will get an error
      message.

      Although the units, domain, and range specifications are optional,
      it s best to give them when they are applicable; doing so allows units
      to perform better error checking and give more helpful error messages.
      Giving the domain and range also enables the --check option to find a
      point in the domain to use for its point check of your inverse
      definition.

      You can make synonyms for nonlinear units by providing both the
      forward and inverse functions; inverse functions can be obtained using
      the   operator.  So to create a synonym for tempF you could write





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                              12 November 2020



      fahrenheit(x) units=[1;K] tempF(x);  tempF(fahrenheit)

      This is useful for creating a nonlinear unit definition that differs
      slightly from an existing definition without having to repeat the
      original functions.  For example,

      dBW(x)     units=[1;W] range=[0,) dB(x) W ;   dB(dBW/W)

      If you wish a synonym to refer to an existing nonlinear unit without
      modification, you can do so more simply by adding the synonym with
      appended parentheses as a new unit, with the existing nonlinear
      unit-without parentheses-as the definition.  So to create a synonym
      for tempF you could write

      fahrenheit()  tempF

      The definition must be a nonlinear unit; for example, the synonym

      fahrenheit()  meter

      will result in an error message when units starts.

      You may occasionally wish to define a function that operates on units.
      This can be done using a nonlinear unit definition.  For example, the
      definition below provides conversion between radius and the area of a
      circle.  This definition requires a length as input and produces an
      area as output, as indicated by the units= specification.  Specifying
      the range as the nonnegative numbers can prevent cryptic error
      messages.

      circlearea(r) units=[m;m 2] range=[0,)   pi r 2 ; sqrt(circlearea/pi)

    Defining Piecewise Linear Units
      Sometimes you may be interested in a piecewise linear unit such as
      many wire gauges.  Piecewise linear units can be defined by specifying
      conversions to linear units on a list of points.  Conversion at other
      points will be done by linear interpolation.  A partial definition of
      zinc gauge is

      zincgauge[in] 1 0.002, 10 0.02, 15 0.04, 19 0.06, 23 0.1

      In this example, zincgauge is the name of the piecewise linear unit.
      The definition of such a unit is indicated by the embedded [
      character.  After the bracket, you should indicate the units to be
      attached to the numbers in the table.  No spaces can appear before the
      ] character, so a definition like foo[kg meters] is invalid; instead
      write foo[kg*meters].  The definition of the unit consists of a list
      of pairs optionally separated by commas.  This list defines a function
      for converting from the piecewise linear unit to linear units.  The
      first item in each pair is the function argument; the second item is
      the value of the function at that argument (in the units specified in



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                              12 November 2020



      brackets).  In this example, we define zincgauge at five points.  For
      example, we set zincgauge(1) equal to 0.002 in.  Definitions like this
      may be  more readable  if written using  continuation characters as

      zincgauge[in] \
           1 0.002  \
          10 0.02   \
          15 0.04   \
          19 0.06   \
          23 0.1

      With the preceding definition, the following conversion can be
      performed:

      You have: zincgauge(10) You want: in
          * 0.02
          / 50 You have: .01 inch You want: zincgauge
          5

      If you define a piecewise linear unit that is not strictly monotonic,
      then the inverse will not be well defined.  If the inverse is
      requested for such a unit, units will return the smallest inverse.

      After adding nonlinear units definitions, you should normally run
      units --check to check for errors.  If the units keyword is not given,
      the --check option checks a nonlinear unit definition using a
      dimensionless argument, and then checks using an arbitrary combination
      of units, as well as the square and cube of that combination; a
      warning is given if any of these tests fail.  For example,

      Warning: function  squirt(x)  defined as  sqrt(x)
               failed for some test inputs:
               squirt(7(kg K) 1): Unit not a root
               squirt(7(kg K) 3): Unit not a root

      Running units --check will print a warning if a non-monotonic
      piecewise linear unit is encountered.  For example, the relationship
      between ANSI coated abrasive designation and mean particle size is
      non-monotonic in the vicinity of 800 grit:

      ansicoated[micron] \
           . . .
          600 10.55 \
          800 11.5 \
          1000 9.5 \

      Running units --check would give the error message

      Table  ansicoated  lacks unique inverse around entry 800





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                              12 November 2020



      Although the inverse is not well defined in this region, it s not
      really an error.  Viewing such error messages can be tedious, and if
      there are enough of them, they can distract from true errors.  Error
      checking for nonlinear unit definitions can be suppressed by giving
      the noerror keyword; for the examples above, this could be done as

      squirt(x) noerror domain=[0,) range=[0,) sqrt(x); squirt 2
      ansicoated[micron] noerror \
           . . .

      Use the noerror keyword with caution.  The safest approach after
      adding a nonlinear unit definition is to run units --check and confirm
      that there are no actual errors before adding the noerror keyword.

    Defining Unit List Aliases
      Unit list aliases are treated differently from unit definitions,
      because they are a data entry shorthand rather than a true definition
      for a new unit.  A unit list alias definition begins with !unitlist
      and includes the alias and the definition;  for example, the aliases
      included in the standard units data file are

      !unitlist   hms     hr;min;sec !unitlist   time    year;day;hr;min;sec
      !unitlist   dms     deg;arcmin;arcsec !unitlist   ftin    ft;in;1|8 in
      !unitlist   usvol   cup;3|4 cup;2|3 cup;1|2 cup;1|3 cup;1|4 cup;\
                          tbsp;tsp;1|2 tsp;1|4 tsp;1|8 tsp

      Unit list aliases are only for unit lists, so the definition must
      include a ;.  Unit list aliases can never be combined with units or
      other unit list aliases, so the definition of time shown above could
      not have been shortened to year;day;hms.

      As usual, be sure to run units --check to ensure that the units listed
      in unit list aliases are conformable.

 NUMERIC OUTPUT FORMAT
      By default, units shows results to eight significant digits. You can
      change this with the --exponential, --digits, and --output-format
      options.  The first sets an exponential format (i.e., scientific
      notation) like that used in the original Unix units program, the
      second allows you to specify a different number of significant digits,
      and the last allows you to control the output appearance using the
      format for the printf() function in the C programming language.  If
      you only want to change the number of significant digits or specify
      exponential format type, use the --digits and --exponential options.
      The --output-format option affords the greatest control of the output
      appearance, but requires at least rudimentary knowledge of the
      printf() format syntax. See Invoking Units for descriptions of these
      options.

    Format Specification
      The format specification recognized with the --output-format option is



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                              12 November 2020



      a subset of that for printf().  The format specification has the form
      %[flags][width][.precision]type; it must begin with %, and must end
      with a floating-point type specifier: g or G to specify the number of
      significant digits, e or E for scientific notation, and f for fixed-
      point decimal.  The ISO C99 standard added the F type for fixed-point
      decimal and the a and A types for hexadecimal floating point; these
      types are allowed with compilers that support them.  Type length
      modifiers (e.g., L to indicate a long double) are inapplicable and are
      not allowed.

      The default format for units is %.8g; for greater precision, you could
      specify -o %.15g.  The g and G format types use exponential format
      whenever the exponent would be less than -4, so the value 0.000013
      displays as 1.3e-005.  These types also use exponential notation when
      the exponent is greater than or equal to the precision, so with the
      default format, the value 5e7 displays as 50000000 and the value 5e8
      displays as 5e+008.  If you prefer fixed-point display, you might
      specify -o %.8f; however, small numbers will display very few
      significant digits, and values less than 0.5e-8 will show nothing but
      zeros.

      The format specification may include one or more optional flags: +,
      (space), #, -, or 0 (the digit zero).  The digit-grouping flag   is
      allowed with compilers that support it.  Flags are followed by an
      optional value for the minimum field width, and an optional precision
      specification that begins with a period (e.g., .6).  The field width
      includes the digits, decimal point, the exponent, thousands separators
      (with the digit-grouping flag), and the sign if any of these are
      shown.

    Flags
      The + flag causes the output to have a sign (+ or -).  The space flag
        is similar to the + flag, except that when the value is positive, it
      is prefixed with a space rather than a plus sign; this flag is ignored
      if the + flag is also given.  The + or   flag could be useful if
      conversions might include positive and negative results, and you
      wanted to align the decimal points in exponential notation.  The #
      flag causes the output value to contain a decimal point in all cases;
      by default, the output contains a decimal point only if there are
      digits (which can be trailing zeros) to the right of the point.  With
      the g or G types, the # flag also prevents the suppression of trailing
      zeros.  The digit-grouping flag '   shows a thousands separator in
      digits to the left of the decimal point.  This can be useful when
      displaying large numbers in fixed-point decimal; for example, with the
      format %f,

      You have: mile You want: microfurlong
              * 8000000.000000
              / 0.000000





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                              12 November 2020



      the magnitude of the first result may not be immediately obvious
      without counting the digits to the left of the decimal point.  If the
      thousands separator is the comma (,), the output with the format '% f
      might be

      You have: mile You want: microfurlong
              * 8,000,000.000000
              / 0.000000

      making the magnitude readily apparent.  Unfortunately, few compilers
      support the digit-grouping flag.

      With the - flag, the output value is left aligned within the specified
      field width.  If a field width greater than needed to show the output
      value is specified, the 0 (zero) flag causes the output value to be
      left padded with zeros until the specified field width is reached; for
      example, with the format %011.6f,

      You have: troypound You want: grain
              * 5760.000000
              / 0000.000174

      The 0 flag has no effect if the - (left align) flag is given.

    Field Width
      By default, the output value is left aligned and shown with the
      minimum width necessary for the specified (or default) precision.  If
      a field width greater than this is specified, the value shown is right
      aligned, and padded on the left with enough spaces to provide the
      specified field width.  A width specification is typically used with
      fixed-point decimal to have columns of numbers align at the decimal
      point; this arguably is less useful with units than with long columnar
      output, but it may nonetheless assist in quickly assessing the
      relative magnitudes of results.  For example, with the format %12.6f,

      You have: km You want: in
              * 39370.078740
              /     0.000025 You have: km You want: rod
              *   198.838782
              /     0.005029 You have: km You want: furlong
              *     4.970970
              /     0.201168

    Precision
      The meaning of precision depends on the format type.  With g or G, it
      specifies the number of significant digits (like the --digits option);
      with e, E, f, or F, it specifies the maximum number of digits to be
      shown after the decimal point.

      With the g and G format types, trailing zeros are suppressed, so the
      results may sometimes have fewer digits than the specified precision



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                              12 November 2020



      (as indicated above, the # flag causes trailing zeros to be
      displayed).

      The default precision is 6, so %g is equivalent to %.6g, and would
      show the output to six significant digits.  Similarly, %e or %f would
      show the output with six digits after the decimal point.

      The C printf() function allows a precision of arbitrary size, whether
      or not all of the digits are meaningful.  With most compilers, the
      maximum internal precision with units is 15 decimal digits (or 13
      hexadecimal digits).  With the --digits option, you are limited to the
      maximum internal precision; with the --output-format option, you may
      specify a precision greater than this, but it may not be meaningful.
      In some cases, specifying excess precision can result in rounding
      artifacts.  For example, a pound is exactly 7000 grains, but with the
      format %.18g, the output might be

      You have: pound You want: grain
              * 6999.9999999999991
              / 0.00014285714285714287

      With the format %.25g you might get the following:

      You have: 1/3 You want:
              Definition: 0.333333333333333314829616256247

      In this case the displayed value includes a series of digits that
      represent the underlying binary floating-point approximation to 1/3
      but are not meaningful for the desired computation.  In general, the
      result with excess precision is system dependent.  The precision
      affects only the display of numbers; if a result relies on physical
      constants that are not known to the specified precision, the number of
      physically meaningful digits may be less than the number of digits
      shown.

      See the documentation for printf() for more detailed descriptions of
      the format specification.

      The --output-format option is incompatible with the --exponential or
      --digits options; if the former is given in combination with either of
      the latter, the format is controlled by the last option given.

 LOCALIZATION
      Some units have different values in different locations.  The
      localization feature accommodates this by allowing a units data file
      to specify definitions that depend on the user s locale.

    Locale
      A locale is a subset of a user s environment that indicates the user s
      language and country, and some attendant preferences, such as the
      formatting of dates.  The units program attempts to determine the



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                              12 November 2020



      locale from the POSIX setlocale function; if this cannot be done,
      units examines the environment variables LC_CTYPE and LANG.  On POSIX
      systems, a locale is of the form language_country, where language is
      the two-character code from ISO 639-1 and country is the two-character
      code from ISO 3166-1; language is lower case and country is upper
      case. For example, the POSIX locale for the United Kingdom is en_GB.

      On systems running Microsoft Windows, the value returned by
      setlocale() is different from that on POSIX systems; units attempts to
      map the Windows value to a POSIX value by means of a table in the file
      locale_map.txt in the same directory as the other data files.  The
      file includes entries for many combinations of language and country,
      and can be extended to include other combinations.  The locale_map.txt
      file comprises two tab-separated columns; each entry is of the form

           Windows-locale   POSIX-locale

      where POSIX-locale is as described above, and Windows-locale typically
      spells out both the language and country.  For example, the entry for
      the United States is

      English_United States   en_US

      You can force units to run in a desired locale by using the -l option.

      In order to create unit definitions for a particular locale you begin
      a block of definitions in a unit datafile with !locale followed by a
      locale name.  The ! must be the first character on the line.  The
      units program reads the following definitions only if the current
      locale matches.  You end the block of localized units with !endlocale.
      Here is an example, which defines the British gallon.

      !locale en_GB gallon       4.54609 liter !endlocale

    Additional Localization
      Sometimes the locale isn t sufficient to determine unit preferences.
      There could be regional preferences, or a company could have specific
      preferences.  Though probably uncommon, such differences could arise
      with the choice of English customary units outside of English-speaking
      countries.  To address this, units allows specifying definitions that
      depend on environment variable settings.  The environment variables
      can be controled based on the current locale, or the user can set them
      to force a particular group of definitions.

      A conditional block of definitions in a units data file begins with
      either !var or !varnot following by an environment variable name and
      then a space separated list of values.  The leading ! must appear in
      the first column of a units data file, and the conditional block is
      terminated by !endvar.  Definitions in blocks beginning with !var are
      executed only if the environment variable is exactly equal to one of
      the listed values.  Definitions in blocks beginning with !varnot are



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                              12 November 2020



      executed only if the environment variable does not equal any of the
      list values.

      The inch has long been a customary measure of length in many places.
      The word comes from the Latin uncia meaning one twelfth, referring to
      its relationship with the foot.  By the 20th century, the inch was
      officially defined in English-speaking countries relative to the yard,
      but until 1959, the yard differed slightly among those countries.  In
      France the customary inch, which was displaced in 1799 by the meter,
      had a different length based on a french foot.  These customary
      definitions could be accommodated as follows:

      !var INCH_UNIT usa yard          3600|3937 m !endvar !var INCH_UNIT
      canada yard          0.9144 meter !endvar !var INCH_UNIT uk yard
      0.91439841 meter !endvar !var INCH_UNIT canada uk usa foot
      1|3 yard inch          1|12 foot !endvar !var INCH_UNIT france foot
      144|443.296 m inch          1|12 foot line          1|12 inch !endvar
      !varnot INCH_UNIT usa uk france canada !message Unknown value for
      INCH_UNIT !endvar

      When units reads the above definitions it will check the environment
      variable INCH_UNIT and load only the definitions for the appropriate
      section.  If INCH_UNIT is unset or is not set to one of the four
      values listed, then units will run the last block.  In this case that
      block uses the !message command to display a warning message.
      Alternatively that block could set default values.

      In order to create default values that are overridden by user settings
      the data file can use the !set command, which sets an environment
      variable only if it is not already set;  these settings are only for
      the current units invocation and do not persist.  So if the example
      above were preceded by !set INCH_UNIT france, then this would make
      france the default value for INCH_UNIT.  If the user had set the
      variable in the environment before invoking units, then units would
      use the user s value.

      To link these settings to the user s locale you combine the !set
      command with the !locale command.  If you wanted to combine the above
      example with suitable locales you could do by preceding the above
      definition with the following:

      !locale en_US !set INCH_UNIT usa !endlocale !locale en_GB !set
      INCH_UNIT uk !endlocale !locale en_CA !set INCH_UNIT canada !endlocale
      !locale fr_FR !set INCH_UNIT france !endlocale !set INCH_UNIT france

      These definitions set the overall default for INCH_UNIT to france and
      set default values for four locales appropriately.  The overall
      default setting comes last so that it only applies when INCH_UNIT was
      not set by one of the other commands or by the user.





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                              12 November 2020



      If the variable given after !var or !varnot is undefined, then units
      prints an error message and ignores the definitions that follow.  Use
      !set to create defaults to prevent this situation from arising.  The
      -c option only checks the definitions that are active for the current
      environment and locale, so when adding new definitions take care to
      check that all cases give rise to a well defined set of definitions.

 ENVIRONMENT VARIABLES
      The units program uses the following environment variables:

      HOME Specifies the location of your home directory; it is used by
           units to find a personal units data file .units.  On systems
           running Microsoft Windows, the file is unitdef.units, and if HOME
           does not exist, units tries to determine your home directory from
           the HOMEDRIVE and HOMEPATH environment variables; if these
           variables do not exist, units finally tries USERPROFILE-typically
           C:\Users\username (Windows Vista and Windows 7) or
           C:\Documents and Settings\username (Windows XP).

      LC_CTYPE, LANG
           Checked to determine the locale if units cannot obtain it from
           the operating system.  Sections of the standard units data file
           are specific to certain locales.

      MYUNITSFILE
           Specifies your personal units data file.  If this variable
           exists, units uses its value rather than searching your home
           directory for .units.  The personal units file will not be loaded
           if any data files are given using the -f option.

      PAGER
           Specifies the pager to use for help and for displaying the
           conformable units.  The help function browses the units database
           and calls the pager using the +nn syntax for specifying a line
           number.  The default pager is more; PAGER can be used to specify
           alternatives such as less, pg, emacs, or vi.

      UNITS_ENGLISH
           Set to either US or GB to choose United States or British volume
           definitions, overriding the default from your locale.

      UNITSFILE
           Specifies the units data file to use (instead of the default).
           You can only specify a single units data file using this
           environment variable.  If units data files are given using the -f
           option, the file specified by UNITSFILE will be not be loaded
           unless the -f option is given with the empty string (units -
           f "").

      UNITSLOCALEMAP
           Windows only; this variable has no effect on Unix-like systems.



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                              12 November 2020



           Specifies the units locale map file to use (instead of the
           default).  This variable seldom needs to be set, but you can use
           it to ensure that the locale map file will be found if you
           specify a location for the units data file using either the -f
           option or the UNITSFILE environment variable, and that location
           does not also contain the locale map file.

      UNITS_SYSTEM
           This environment variable is used in the standard data file to
           select CGS measurement systems.  Currently supported systems are
           esu, emu, gauss[ian], and si.  The default is si.



 DATA FILES
      The units program uses two default data files: definitions.units and
      currency.units.  The program can also use an optional personal units
      data file .units (unitdef.units under Windows) located in the user s
      home directory.  The personal units data file is described in more
      detail in Units Data Files.

      On Unix-like systems, the data files are typically located in
      /usr/share/units if units is provided with the operating system, or in
      /usr/local/share/units if units is compiled from the source
      distribution.  Note that the currency file currency.units is a
      symbolic link to another location.

      On systems running Microsoft Windows, the files may be in the same
      locations if Unix-like commands are available, a Unix-like file
      structure is present (e.g., C:/usr/local), and units is compiled from
      the source distribution.  If Unix-like commands are not available, a
      more common location is C:\Program Files (x86)\GNU\units (for 64-bit
      Windows installations) or C:\Program Files\GNU\units (for 32-bit
      installations).

      If units is obtained from the GNU Win32 Project
      (http://gnuwin32.sourceforge.net/), the files are commonly in
      C:\Program Files\GnuWin32\share\units.

      If the default units data file is not an absolute pathname, units will
      look for the file in the directory that contains the units program; if
      the file is not found there, units will look in a directory
      ../share/units relative to the directory with the units program.

      You can determine the location of the files by running
      units --version.  Running units --info will give you additional
      information about the files, how units will attempt to find them, and
      the status of the related environment variables.

 UNICODE SUPPORT
      The standard units data file is in Unicode, using UTF-8 encoding.



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      Most definitions use only ASCII characters (i.e., code points U+0000
      through U+007F); definitions using non-ASCII characters appear in
      blocks beginning with !utf8 and ending with !endutf8.

      The non-ASCII definitions are loaded only if the platform and the
      locale support UTF-8.  Platform support is determined when units is
      compiled; the locale is checked at every invocation of units.  To see
      if your version of units includes Unicode support, invoke the program
      with the --version option.

      When Unicode support is available, units checks every line within
      UTF-8 blocks in all of the units data files for invalid or non-
      printing UTF-8 sequences; if such sequences occur, units ignores the
      entire line.  In addition to checking validity, units determines the
      display width of non-ASCII characters to ensure proper positioning of
      the pointer in some error messages and to align columns for the search
      and ? commands.

      As of early 2019, Microsoft Windows provides limited support for UTF-8
      in console applications, and accordingly, units does not support
      Unicode on Windows.  The UTF-16 and UTF-32 encodings are not supported
      on any platforms.

      If Unicode support is available and definitions that contain non-ASCII
      UTF-8 characters are added to a units data file, those definitions
      should be enclosed within !utf8 ... !endutf8 to ensure that they are
      only loaded when Unicode support is available.  As usual, the ! must
      appear as the first character on the line.  As discussed in Units Data
      Files, it s usually best to put such definitions in supplemental data
      files linked by an !include command or in a personal units data file.

      When Unicode support is not available, units makes no assumptions
      about character encoding, except that characters in the range 007F
      hexadecimal correspond to ASCII encoding.  Non-ASCII characters are
      simply sequences of bytes, and have no special meanings; for
      definitions in supplementary units data files, you can use any
      encoding consistent with this assumption.  For example, if you wish to
      use non-ASCII characters in definitions when running units under
      Windows, you can use a character set such as Windows ANSI (code page
      1252 in the US and Western Europe); if this is done, the console code
      page must be set to the same encoding for the characters to display
      properly.  You can even use UTF-8, though some messages may be
      improperly aligned, and units will not detect invalid UTF-8 sequences.
      If you use UTF-8 encoding when Unicode support is not available, you
      should place any definitions with non-ASCII characters outside !utf8

      Typeset material other than code examples usually uses the Unicode
      minus (U+2212) rather than the ASCII hyphen-minus operator (U+002D)
      used in units; the figure dash (U+2012) and en dash (U+2013) are also
      occasionally used.  To allow such material to be copied and pasted for
      interactive use or in units data files, units converts these



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                              12 November 2020



      characters to U+002D before further processing.  Because of this, none
      of these characters can appear in unit names.

 READLINE SUPPORT
      If the readline package has been compiled in, then when units is used
      interactively, numerous command line editing features are available.
      To check if your version of units includes readline, invoke the
      program with the --version option.

      For complete information about readline, consult the documentation for
      the readline package.  Without any configuration, units will allow
      editing in the style of emacs.  Of particular use with units are the
      completion commands.

      If you type a few characters and then hit ESC followed by ?, then
      units will display a list of all the units that start with the
      characters typed.  For example, if you type metr and then request
      completion, you will see something like this:

      You have: metr metre             metriccup         metrichorsepower
      metrictenth metretes          metricfifth       metricounce
      metricton metriccarat       metricgrain       metricquart
      metricyarncount You have: metr

      If there is a unique way to complete a unit name, you can hit the TAB
      key and units will provide the rest of the unit name.  If units beeps,
      it means that there is no unique completion.  Pressing the TAB key a
      second time will print the list of all completions.

      The readline library also keeps a history of the values you enter.
      You can move through this history using the up and down arrows.  The
      history is saved to the file .units_history in your home directory so
      that it will persist across multiple units invocations.  If you wish
      to keep work for a certain project separate you can change the history
      filename using the --history option.  You could, for example, make an
      alias for units to units --history .units_history so that units would
      save separate history in the current directory. The length of each
      history file is limited to 5000 lines.  Note also that if you run
      several concurrent copies of units each one will save its new history
      to the history file upon exit.

 UPDATING CURRENCY EXCHANGE RATES
      The units program databacurrency.unitsronnayUnix-like systemaor prices
      C:ProgrampFilesu(x86)\:GNU\:units\:definitions.unitshonga Windowsme,
      system.es verycom/idly, and units cannot provide real-ticurrency.units
      ord/usr/local/hange rates, run units_cur, which reunits/ the file
      containing the currency rates, typically /var/lib/


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 UNITS(1)                                                           UNITS(1)
                              12 November 2020



      This program requires Python (https://www.python.org); either  version
      2  or  3 will work.  The program must be run with suitable permissions
      to write the file.  To keep the rates updated  automatically,  run  it
      using  a  cron  job  on  a  Unix-like  system, or a similar scheduling
      program on a different system.

      Reliable free sources of currency exchange rates have been  annoyingly
      ephemeral.  The program currently supports several sources:

       *  FloatRates (https://www/floatrates.com).  The US dollar  (USD)  is
          the  default base currency.  You can change the base currency with
          the -b option described  below.   Allowable  base  currencies  are
          listed on the FloatRates website.  Exchange rates update daily.

       *  The European Central Bank (https://www.ecb.europa.eu).   The  base
          currency  is  always the euro (EUR).  Exchange rates update daily.
          This source offers a more limited  list  of  currencies  than  the
          others.

       *  Fixer (https://fixer.io).  Registration for  a  free  API  key  is
          required.   With  a  free  API  key,  base  currency  is the euro;
          exchange rates are updated hourly, the  service  has  a  limit  of
          1,000  API calls per month, and SSL encryption (https protocol) is
          not available.  Most  of  these  restrictions  are  eliminated  or
          reduced with paid plans.

       *  open exchange rates (https://openexchangerates.org).  Registration
          for  a  free  API  key is required.  With a free API key, the base
          currency is the US dollar; exchange rates are updated hourly,  and
          there  is  a  limit  of  1,000 API calls per month.  Most of these
          restrictions are eliminated or reduced with paid plans.

      The default source is FloatRates; you can select a different one using
      -s option described below.

      Precious    metals    pricing    is    obtained    from     Packetizer
      (www.packetizer.com).  This site updates once per day.

      You invoke units_cur like this:

      units_cur [options] [outfile]

      By default, the  output  is  written  to  the  default  currency  file
      described  above; this is usually what you want, because this is where
      units looks for the file.  If you wish, you can  specify  a  different
      filename on the command line and units_cur will write the data to that
      file.  If you give - for the file it will write to standard output.

      The following options are available:





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                              12 November 2020



      -h, --help
           Print a summary of the options for units_cur.

      -V, --version
           Print the units_cur version number.

      -v, --verbose
           Give slightly more  verbose  output  when  attempting  to  update
           currency exchange rates.

      -s source, --source source
           Specify  the  source  for  currency  exchange  rates;   currently
           supported values are floatrates (for FloatRates), eubank (for the
           European Central Bank), fixer (for Fixer), and  openexchangerates
           (for  open exchange rates); the last two require an API key to be
           given with the -k option.

      -b base, --base base
           Set the base currency (when allowed by  the  site  providing  the
           data).   base  should be a 3-letter ISO currency code, e.g., USD.
           The specified currency will be the primitive currency  unit  used
           by  units.   You  may  find  it  convenient to specify your local
           currency.  Conversions may be more accurate and you will be  able
           to  convert  to  your  currency  by  simply  hitting Enter at the
           You want: prompt.  This option is ignored if the source does  not
           allow  specifying  the base currency.  (Currently only floatrates
           supports this option.)

      -k key, --key key
           Set the API key to key for sources that require it.



 DATABASE COMMAND SYNTAX
      unit definition
           Define a regular unit.

      prefix- definition
           Define a prefix.

 range=[y1,y2] definition(var) ; inverse(funcname)
      funcname(var)     noerror     units=[in-units,out-
           units]     domain=[x1,x2]
           Define a nonlinear unit or  unit  function.   The  four  optional
           keywords  noerror,  units=,  range= and domain= can appear in any
           order.  The definition of the inverse is optional.

      tabname[out-units] noerror pair-list
           Define a piecewise linear unit.  The pair list gives  the  points
           on  the  table listed in ascending order.  The noerror keyword is
           optional.



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 UNITS(1)                                                           UNITS(1)
                              12 November 2020



      !endlocale
           End a block of definitions beginning with !locale

      !endutf8
           End a block of definitions begun with !utf8

      !endvar
           End a block of definitions begun with !var or !varnot

      !include file
           Include the specified file.

      !locale value
           Load the following definitions only  of  the  locale  is  set  to
           value.

      !message text
           Display text when the database is read unless the quiet option (-
           -q)  is  enabled.   If  you  omit text, then units will display a
           blank line.  Messages will also appear in the log file.

      !prompt text
           Prefix the You have: prompt with the specified text.  If you omit
           text, then any existing prefix is canceled.

      !set variable value
           Sets the environment variable, variable, to the  specified  value
           only if it is not already set.

      !unitlist alias definition
           Define a unit list alias.

      !utf8
           Load the following definitions only  if  units  is  running  with
           UTF-8 enabled.

      !var envar value-list
           Load  the  block  of  definitions  that  follows  only   if   the
           environment  variable envar is set to one of the values listed in
           the space-separated value list.   If  envar  is  not  set,  units
           prints an error message and ignores the block of definitions.

      !varnot envar value-list
           Load  the  block  of  definitions  that  follows  only   if   the
           environment  variable envar is set to value that is not listed in
           the space-separated value list.   If  envar  is  not  set,  units
           prints an error message and ignores the block of definitions.







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 UNITS(1)                                                           UNITS(1)
                              12 November 2020



 FILES
      @DATAFILE@ - the standard units data file

 AUTHOR
      units was written by Adrian Mariano

















































                                   - 56 -      Formatted:  November 26, 2020