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 UNITS(1)                                                           UNITS(1)
                                19 March 2019

      units - unit conversion and calculation program

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

      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 con-
      vert 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

      Beyond simple unit conversions, 'units' can be used as a general-
      purpose scientific calculator that keeps track of units in its calcu-
      lations.  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 con-
      sistency when working with long expressions that involve many dif-
      ferent 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.

      To invoke 'units' for interactive use, type

      'units' at your shell prompt.  The program will print something like

         Currency exchange rates from 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

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 UNITS(1)                                                           UNITS(1)
                                19 March 2019

      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 type

      'feet'.  If the 'readline' library was compiled in, then tab will com-
      plete 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 out-
      put, 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 obvi-
      ous 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

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 UNITS(1)                                                           UNITS(1)
                                19 March 2019

      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 comprehensi-
      ble output:

         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 combina-
      tion 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

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 UNITS(1)                                                           UNITS(1)
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      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.

      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.


      'help' at either prompt displays a short help message.  You can also

      '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'.)


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

      The 'units' program can perform units conversions non-interactively
      from the command line.  To do this, type the command, type the origi-
      nal unit expression, and type the new units you want.  If a units
      expression contains non-alphanumeric characters, you may need to pro-
      tect it from interpretation by the shell using single or double quote

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 UNITS(1)                                                           UNITS(1)
                                19 March 2019


      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, then '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 environ-

      When you invoke 'units' with only one argument, it 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.

      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 com-
      mon 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

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 UNITS(1)                                                           UNITS(1)
                                19 March 2019

         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
      'ounce' is also a unit of mass.  The fluid ounce is 'fluidounce' or
      'floz'.  When British capacity units differ from their US counter-
      parts, 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 coun-
      try 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 per-
      mitted 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

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 UNITS(1)                                                           UNITS(1)
                                19 March 2019

      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 Interna-
      tional 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.

      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

      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

      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.

      You can enter more complicated units by combining units with opera-
      tions such as multiplication, division, powers, addition, subtraction,
      and parentheses for grouping.  You can use the customary symbols for

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 UNITS(1)                                                           UNITS(1)
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      these operators when 'units' is invoked with its default options.
      Additionally, 'units' supports some extensions, including high prior-
      ity multiplication using a space, and a high priority numerical divi-
      sion operator ('|') that can simplify some expressions.

      You multiply units using a space or an asterisk ('*').  The next exam-
      ple 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

      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 advanta-
      geous.  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.

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 UNITS(1)                                                           UNITS(1)
                                19 March 2019

      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

         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 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 inter-
      nally 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 meaning-
      ful (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

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 UNITS(1)                                                           UNITS(1)
                                19 March 2019

      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 con-
      vert 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 out-
      side 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

         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

      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 multi-
      plication 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

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                                19 March 2019

      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

    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
                 * 13.888889
                 / 0.072

      And the second example shows how the dollar sign in the units conver-
      sion 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', 'ln',
      'log', 'exp', 'acos', 'atan', 'asin', 'cosh', 'sinh', 'tanh', 'acosh',
      'asinh', and 'atanh'.  The 'sin', 'cos', and 'tan' functions require
      either a dimensionless argument or an argument with dimensions of

         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

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 UNITS(1)                                                           UNITS(1)
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      The other functions on the list require dimensionless arguments.  The
      inverse trigonometric functions return arguments with dimensions of

      The 'ln' and 'log' functions give natural log and log base 10 respec-
      tively.  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

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

         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 under-
      score ('_').  It is useful when you want to convert the same input to
      several different units, for example

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 UNITS(1)                                                           UNITS(1)
                                19 March 2019

         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)
                                19 March 2019

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

      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

    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

                                   - 14 -           Formatted:  July 6, 2020

 UNITS(1)                                                           UNITS(1)
                                19 March 2019

      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

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

      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 sub-
      traction operator in general algebraic expressions, 'units' treats the
      binary '-' as a subtraction operator by default.  For backwards compa-
      tibility use the '--product' option, which causes 'units' to treat the
      binary '-' operator as a product operator.  When '-' is a multiplica-
      tion 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.  Regard-
      less 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 can-
      not know what options will be in force when your definition is pro-

      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 conver-
      sions are done using units starting with 'deg' and they do not require
      functional notation.

                                   - 15 -           Formatted:  July 6, 2020

 UNITS(1)                                                           UNITS(1)
                                19 March 2019

         You have: tempF(45)
         You want: tempC

         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 Non-
      linear 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 con-
      verting to a temperature rather than converting a temperature incre-

      The 'tempC()' and 'tempF()' definitions are limited to positive abso-
      lute 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

                                   - 16 -           Formatted:  July 6, 2020

 UNITS(1)                                                           UNITS(1)
                                19 March 2019

    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
                 / 2.8735632

         You have: 1 mm
         You want: wiregauge

         You have: grit_P(600)
         You want: grit_ansicoated

      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 cir-
      cleinch.  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

                                   - 17 -           Formatted:  July 6, 2020

 UNITS(1)                                                           UNITS(1)
                                19 March 2019

                 * 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

      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.

      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 conver-
      sion 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

                                   - 18 -           Formatted:  July 6, 2020

 UNITS(1)                                                           UNITS(1)
                                19 March 2019

                 / 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 typi-
      cally 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

      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

                                   - 19 -           Formatted:  July 6, 2020

 UNITS(1)                                                           UNITS(1)
                                19 March 2019

      in effect separating the integer and fractional parts of the coeffi-
      cient 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 conform-
      able 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

         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 disagree-
      ment 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

                                   - 20 -           Formatted:  July 6, 2020

 UNITS(1)                                                           UNITS(1)
                                19 March 2019

         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

      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

         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 cal-
      culations, 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 *

                                   - 21 -           Formatted:  July 6, 2020

 UNITS(1)                                                           UNITS(1)
                                19 March 2019

      3|4 cup' whether or not the '--show-factor' option is given.

      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

      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

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

         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 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

                                   - 22 -           Formatted:  July 6, 2020

 UNITS(1)                                                           UNITS(1)
                                19 March 2019

      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

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

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

      The SI-an extension of the MKS (meter-kilogram-second) system-has
      largely supplanted the older CGS (centimeter-gram-second) 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 three different systems of CGS units: electrostatic
      units (ESU), electromagnetic units (EMU), and the Gaussian 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 dis-
      tance 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.

      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.

                                   - 23 -           Formatted:  July 6, 2020

 UNITS(1)                                                           UNITS(1)
                                19 March 2019

      The dimensions of electrical quantities in the various CGS systems are
      different from the SI dimensions for the same units; strictly, conver-
      sions 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 vari-
      ous systems.

    Specifying CGS Units
      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 cen-
      timeter 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 argu-
      ments to the '--units' option are 'gauss[ian]', 'esu', 'emu', and
      'si'; the argument is case insensitive.  The default mode for 'units'
      is SI units; the only effect of giving 'si' with the '--units' option
      is to prepend '(SI)' to the 'You have:' prompt.  Giving an unrecog-
      nized system generates a warning, and 'units' uses SI units.

      The changes resulting from the '--units' option are actually con-
      trolled 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' is case sensitive, so setting a value of 'EMU'
      will have no effect other than to give an error message and set SI

      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 sys-

    CGS Units Systems
      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 pre-
      fixed by 'stat-', e.g., 'statvolt' or 'statV'.  The prefix 'st-' is
      also recognized (e.g., 'stV').

                                   - 24 -           Formatted:  July 6, 2020

 UNITS(1)                                                           UNITS(1)
                                19 March 2019

      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 analo-
      gous 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 Sys-
      tem, 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.

    Conversions Between Different Systems
      The CGS systems define units that measure the same thing but may have
      conflicting dimensions.  Furthermore, the dimensions of the elec-
      tromagnetic CGS units are never compatible with SI.  But if you meas-
      ure charge in two different systems you have measured the same physi-
      cal thing, so there is a correspondence between the units in the dif-
      ferent 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 have

         (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

                                   - 25 -           Formatted:  July 6, 2020

 UNITS(1)                                                           UNITS(1)
                                19 March 2019

      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 dimen-
      sional 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 con-
      flict.  We cannot redefine the ampere to make this work because 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

    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,

         (Gaussian) You have: stC
                    You want:

                                   - 26 -           Formatted:  July 6, 2020

 UNITS(1)                                                           UNITS(1)
                                19 March 2019

                 Definition: statcoulomb = sqrt(dyne) cm = 1 sqrt_cm^3 sqrt_g / s

      You can suppressed the prefix by including a line


      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

      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.

      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 Expres-
      sions, 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

         ### 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, includ-
      ing lack of conformability of items in sums or differences or among
      items in a unit list.  For example, a conversion between zenith angle

                                   - 27 -           Formatted:  July 6, 2020

 UNITS(1)                                                           UNITS(1)
                                19 March 2019

      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.

      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 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.

                                   - 28 -           Formatted:  July 6, 2020

 UNITS(1)                                                           UNITS(1)
                                19 March 2019

      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 char-
      acters 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 defini-
           tion.  Only definitions active in the current locale are checked.

      -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 exponen-
           tial 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

                                   - 29 -           Formatted:  July 6, 2020

 UNITS(1)                                                           UNITS(1)
                                19 March 2019

           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'

      -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 for-
           mat using the specified format. The format is a single floating
           point numeric format for the 'printf()' function in the C pro-
           gramming 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 string ('-f ""'), the default units file (or that specified
           by 'UNITSFILE') will be loaded in addition to any others speci-
           fied 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

                                   - 30 -           Formatted:  July 6, 2020

 UNITS(1)                                                           UNITS(1)
                                19 March 2019

           other calculations that are to be used extensively or in a criti-
           cal 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 Cal-
           culations 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 sub-
           traction operator.

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

           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

      -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
           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 exam-
           ple, 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'.

                                   - 31 -           Formatted:  July 6, 2020

 UNITS(1)                                                           UNITS(1)
                                19 March 2019

           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.

      -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 pro-
           gram, 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 informa-
           tion 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

           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 defini-
           tions by default.  This overrides the locale determined from

                                   - 32 -           Formatted:  July 6, 2020

 UNITS(1)                                                           UNITS(1)
                                19 March 2019

           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 conver-
           sion, and will give an error if you attempt to convert hertz to

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

      -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.

           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 out-
           put 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
           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 com-
           mand line.

      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

                                   - 33 -           Formatted:  July 6, 2020

 UNITS(1)                                                           UNITS(1)
                                19 March 2019

         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
                 * 7.0104
                 / 0.14264521

         $ units 23ft m
                 * 7.0104
                 / 0.14264521

      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

         $ units --compact m 'ft;in'

         $ units --one-line 23ft m

                                   - 34 -           Formatted:  July 6, 2020

 UNITS(1)                                                           UNITS(1)
                                19 March 2019

                 * 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

         $ units --terse 23ft m

         $ units --terse m 'ft;in'

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

    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 this data file if you have appropriate user privileges, it's

                                   - 35 -           Formatted:  July 6, 2020

 UNITS(1)                                                           UNITS(1)
                                19 March 2019

      usually better to put extensions in separate files so that the defini-
      tions 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 defini-
      tions 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 stan-
      dard 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'.) Run-
      ning '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 Win-
      dows, 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 continua-
      tion 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 can-
      not contain spaces or the comment character '#'.

      Unit names must not contain any of the operator characters '+', '-',
      '*', '/', '|', '^', ';', '~', the comment character '#', or

                                   - 36 -           Formatted:  July 6, 2020

 UNITS(1)                                                           UNITS(1)
                                19 March 2019

      parentheses.  They cannot begin or end with an underscore ('_'), a
      comma (',') or a decimal point ('.').  The figure dash (U+2012), typo-
      graphical 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, 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.  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 reduc-
      tion leads to the primitive units, which are marked with '!' charac-
      ters.  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 defini-
      tions, 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 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

                                   - 37 -           Formatted:  July 6, 2020

 UNITS(1)                                                           UNITS(1)
                                19 March 2019

         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 defin-
      ition 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, tempera-
      ture 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 func-
      tional 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 primi-
      tive 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 func-
      tions tell 'units' how to convert to and from the new unit.  To pro-
      duce 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
      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

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 UNITS(1)                                                           UNITS(1)
                                19 March 2019

      dimensionless), and that the inverse function requires an input argu-
      ment conformable with 'K'.  For normal nonlinear units definition, the
      forward function will always take a dimensionless argument; in gen-
      eral, 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 defini-
      tion 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 defini-

         square(x)       x^2

      can have any arbitrary units, and can also take dimensionless argu-
      ments.  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.

      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:

                                   - 39 -           Formatted:  July 6, 2020

 UNITS(1)                                                           UNITS(1)
                                19 March 2019

         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 end-
      points given in brackets.  In accord with mathematical convention,
      square brackets indicate a closed interval (one that includes its end-
      points), 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 previ-
      ous example, 'units' can not tell whether you intend the lower end-
      point 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 for-
      ward and inverse functions; inverse functions can be obtained using
      the '~' operator.  So to create a synonym for 'tempF' you could write

         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 ori-
      ginal functions.  For example,

                                   - 40 -           Formatted:  July 6, 2020

 UNITS(1)                                                           UNITS(1)
                                19 March 2019

         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.  Specify-
      ing the range as the nonnegative numbers can prevent cryptic error

         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 '[' charac-
      ter.  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
      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 char-
      acters as

                                   - 41 -           Formatted:  July 6, 2020

 UNITS(1)                                                           UNITS(1)
                                19 March 2019

         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 per-

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

      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 warn-
      ing 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 piece-
      wise 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

      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

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                                19 March 2019

      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 con-
      firm that there are no actual errors before adding the 'noerror' key-

    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.

      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., scien-
      tific 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.

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                                19 March 2019

    Format Specification
      The format specification recognized with the '--output-format' option
      is 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 exponen-
      tial 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 fol-
      lowed 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.

      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

                                   - 44 -           Formatted:  July 6, 2020

 UNITS(1)                                                           UNITS(1)
                                19 March 2019

                 / 0.000000

      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 speci-
      fied 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 colum-
      nar output, but it may nonetheless assist in quickly assessing the
      relative magnitudes of results.  For example, with the format

         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

                                   - 45 -           Formatted:  July 6, 2020

 UNITS(1)                                                           UNITS(1)
                                19 March 2019

                 /     0.201168

      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 preci-
      sion (as indicated above, the '#' flag causes trailing zeros to be

      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 mean-
      ingful.  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

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

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 UNITS(1)                                                           UNITS(1)
                                19 March 2019

      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

      Some units have different values in different locations.  The locali-
      zation feature accommodates this by allowing a units data file to
      specify definitions that depend on the user's 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 for-
      matting of dates.  The 'units' program attempts to determine the
      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

      On systems running Microsoft Windows, the value returned by setlo-
      cale() 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'

      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

                                   - 47 -           Formatted:  July 6, 2020

 UNITS(1)                                                           UNITS(1)
                                19 March 2019


    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 vari-
      ables 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 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 defin-
      itions could be accommodated as follows:

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

                                   - 48 -           Formatted:  July 6, 2020

 UNITS(1)                                                           UNITS(1)
                                19 March 2019


      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
         !locale en_GB
         !set INCH_UNIT uk
         !locale en_CA
         !set INCH_UNIT canada
         !locale fr_FR
         !set INCH_UNIT france
         !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.

      If the variable given after '!var' or '!varnot' is undefined, then
      'units' prints an error message and ignores the definitions that fol-
      low.  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

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 UNITS(1)                                                           UNITS(1)
                                19 March 2019

      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 vari-
           ables; 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).

           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.

           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.

           Specifies the pager to use for help and for displaying the con-
           formable units.  The help function browses the units database and
           calls the pager using the '+n'n 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'.

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

           Specifies the units data file to use (instead of the default).
           You can only specify a single units data file using this environ-
           ment 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 ""').

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

                                   - 50 -           Formatted:  July 6, 2020

 UNITS(1)                                                           UNITS(1)
                                19 March 2019

           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'.

      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 sym-
      bolic 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 struc-
      ture 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

      If 'units' is obtained from the GNU Win32 Project
      (, 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' pro-
      gram; 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.

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

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 UNITS(1)                                                           UNITS(1)
                                19 March 2019

      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

      When Unicode support is not available, 'units' makes no assumptions
      about character encoding, except that characters in the range 00-7F
      hexadecimal correspond to ASCII encoding.  Non-ASCII characters are
      simply sequences of bytes, and have no special meanings; for defini-
      tions in supplementary units data files, you can use any encoding con-
      sistent 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 prop-
      erly.  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' ...
      '!endutf8' blocks-otherwise, they will be ignored.

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

      If the 'readline' package has been compiled in, then when 'units' is

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 UNITS(1)                                                           UNITS(1)
                                19 March 2019

      used interactively, numerous command line editing features are avail-
      able.  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 exam-
      ple, 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       definitions.units' on a Windows sys-
      tem.units program database iunits\s currency exchange rates and prices
      for some precious metacuGNU\cy.units' oneaeUnix-likehsystemvor time,
      'C:\ProgrameFilesn(x86)\and 'units' cannot provide real-time values.
      To update thcom/currency.units'uor'units_cur', which rewrites the file
      '/usr/local/its/urrency rates, typically
                                   - 53 -           Formatted:  July 6, 2020

 UNITS(1)                                                           UNITS(1)
                                19 March 2019

      This program requires Python (; 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 pro-
      gram on a different system.

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

       *  FloatRates (https://www/  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 (   The  base
          currency is always the euro ('EUR').  Exchange rates update daily.
          This source offers a more limited list of currencies than the oth-

       *  Fixer (  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 (  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 res-
          trictions 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
      (  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

      The following options are available:

                                   - 54 -           Formatted:  July 6, 2020

 UNITS(1)                                                           UNITS(1)
                                19 March 2019

      -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  sup-
           ported  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.

      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 key-
           words  '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

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 UNITS(1)                                                           UNITS(1)
                                19 March 2019

           End a block of definitions beginning with '!locale'

           End a block of definitions begun with '!utf8'

           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

      !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.

           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  environ-
           ment  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  environ-
           ment  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)
                                19 March 2019

      @DATAFILE@ - the standard units data file

      units was written by Adrian Mariano

                                   - 57 -           Formatted:  July 6, 2020