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 UNITS(1)                                                           UNITS(1)
                                 7 June 2013



 NAME
      units - unit conversion and calculation program

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

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

      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.

      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.

      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
      line.

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

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

         Currency exchange rates from 04/23/12
         2516 units, 85 prefixes, 65 nonlinear units

         You have:

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



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 UNITS(1)                                                           UNITS(1)
                                 7 June 2013



      tab key can be used to complete unit names. See Readline Support for
      more information about 'readline'.  To quit the program press Ctrl-C
      or Ctrl-D under Unix.  Under Windows press Ctrl-Z.

      The answer 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

      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




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      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
      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

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



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      'meter^radian' is not allowed.

      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 con-
      formable with the unit that you entered at the 'You have:' prompt
      above.  Conformable unit combinations will not appear on this list.

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

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

 USING UNITS NON-INTERACTIVELY
      The 'units' program can perform units conversions non-interactively
      from the command line.  To do this, type the command, type the 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
      characters.

      If you type

         units "2 liters" quarts

      then 'units' will print

             * 2.1133764
             / 0.47317647

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

      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-
      ment.

      When you invoke 'units' with only one argument, it will print out the
      definition of the specified unit.  It will return failure if the unit
      is not defined and success if the unit is defined.

 UNIT DEFINITIONS
      The conversion information is read from a units data file that is
      called 'definitions.units' and is usually located in the



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 UNITS(1)                                                           UNITS(1)
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      '/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 constants of nature are defined, including these:

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

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

      The 'pound' is a unit of mass.  To get force, multiply by the force
      conversion unit 'force' or use the shorthand 'lbf'.  (Note that 'g' is
      already taken as the standard abbreviation for the gram.)  The unit
      'ounce' is also a unit of mass.  The fluid ounce is 'fluidounce' or
      'floz'.  British capacity units that differ from their US counter-
      parts, such as the British Imperial gallon, are prefixed with 'br'.
      Currency is prefixed with its country name: 'belgiumfranc',
      'britainpound'.

      When searching for a unit, if the specified string does not appear
      exactly as a unit name, then the 'units' program will try to remove a
      trailing 's', 'es'.  Next units will replace a trailing 'ies' with
      'y'.  If that fails, 'units' will check for a prefix.  The database
      includes all of the standard metric prefixes.  Only one prefix is 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.



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 UNITS(1)                                                           UNITS(1)
                                 7 June 2013



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

      Before 1959, the value of a yard (and other units of measure defined
      in terms of it) differed slightly among English-speaking countries.
      In 1959, Australia, Canada, New Zealand, the United Kingdom, the
      United States, and South Africa adopted the Canadian value of 1 yard =
      0.9144 m (exactly), which was approximately halfway between the values
      used by the UK and the US; it had the additional advantage of making
      1 inch = 2.54 cm (exactly).  This new standard was termed the 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
      'USmile'.

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

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



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 UNITS(1)                                                           UNITS(1)
                                 7 June 2013



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

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

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

      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. An exponent like '2^3^2' is evaluated
      right to left as usual. The '^' operator has the second highest pre-
      cedence.  You can also use '**' as an exponent operator.

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

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

      You multiply units using a space or an asterisk ('*').  The example
      above shows both forms.  You can divide units using the slash ('/') or
      with 'per'.

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

      When a unit includes a prefix, exponent operators apply to the combi-
      nation, so 'centimeter^3' gives cubic centimeters.  If you separate
      the prefix from the unit with any multiplication operator, such as
      'centi meter^3', then the prefix is treated as a separate unit, so the
      exponent does not apply.  The second example would be a hundredth of a
      cubic meter, not a centimeter.



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      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: 'W / m^2 Hz'.  If you multiply with '*' then you must
      group the terms in the denominator with parentheses: 'W / (m^2 * Hz)'.

      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 '*' operator is
      convenient for multiplying a sequence of quotients.  With the '*'
      operator, the example above becomes 'm/s * s/day', which is equivalent
      to 'm/day'.  Similarly, you could write '1/2 * meter' to get half a
      meter.  Alternatively, parentheses can be used for grouping: you could
      write '(1/2) meter' to get half a meter.  See Complicated Unit Expres-
      sions for an illustration of the various options.

      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'.  This operator
      has the highest precedence, so you can write the square root of two
      thirds '2|3^1|2'.  You cannot use the vertical bar to indicate divi-
      sion of non-numerical units (e.g., 'm|s' results in an error message).

         You have: 1|2 inch
         You want: cm
                 * 1.27
                 / 0.78740157

      You can use parentheses for grouping:

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

    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



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 UNITS(1)                                                           UNITS(1)
                                 7 June 2013



                 * 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 multiplica-
      tion has higher precedence than addition.  If you omit the
      parentheses, 'units' attempts to add '2' and '1|2 cups', and you get
      an error message:

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

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

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

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

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

         You have: $ 5 / yard
         You want: cents / inch
                 * 13.888889



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 UNITS(1)                                                           UNITS(1)
                                 7 June 2013



                 / 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', 'log2', 'exp', 'acos', 'atan' and 'asin'.  The 'sin', 'cos',
      and 'tan' functions require either a dimensionless argument or an
      argument with dimensions of angle.

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

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

         You have: sin(3 kg)
                           ^
         Unit not dimensionless

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

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

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

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

         You have: cuberoot(hectare)
                                   ^
         Unit not a root

    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




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 UNITS(1)                                                           UNITS(1)
                                 7 June 2013



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

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

           Delta P = A1 rho fLQ^2 / d^5

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

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

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

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

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

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

    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-
      culator.

      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



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                                 7 June 2013



      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-
      cessed.

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

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

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

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

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





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                                 7 June 2013



      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-
      ment.

    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
                 18.201919

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

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



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                                 7 June 2013



      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
                 * 147.92573
                 / 0.0067601492

 UNIT LISTS: CONVERSION TO SUMS OF
      Outside of the SI, it is sometimes desirable to convert a single unit
      to a sum of units-for example, feet to feet plus inches.  The 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
                 / 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



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                                 7 June 2013



      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

      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)





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                                 7 June 2013



      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 You have unit that you enter.

         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
      time:

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

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




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                                 7 June 2013



      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 * 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;



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                                 7 June 2013



                 20 g + 5 g + 2 g + 1 g + 0.34952312 * 1 g

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

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

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

      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
      conversions:

         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

      When you specify compact output with '--compact', '--terse' or '-t'
      and perform conversion to a unit list, 'units' lists the conversion
      factors for each unit in the list, separated by semicolons.

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



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                                 7 June 2013



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

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

 INVOKING UNITS
      You invoke 'units' like this:

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

      If the from-unit and to-unit are omitted, the program will use
      interactive prompts to determine which conversions to perform.  See
      Interactive Use.  If both from-unit and to-unit are given, 'units'
      will print the result of that single conversion and then exit. If only
      from-unit appears on the command line, 'units' will display the defin-
      ition 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.  See Command Line Use.

      The default behavior of 'units' can be changed by various options
      given on the command line.  In most cases, the options may be given in
      either short form (a single '-' followed by a single character) or
      long form ('--' followed by a word or hyphen-separated words).
      Short-form options are cryptic but require less typing; long-form
      options require more typing but are more explanatory and may be more
      mnemonic.  With long-form options you need only enter sufficient 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



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                                 7 June 2013



           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 max-
           imum, '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 preci-
           sion, the physically meaningful precision may be less than that
           shown.  The '--digits' option conflicts with the '--output-
           format' option.

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

      -o format, --output-format format
           This option affords complete control over the numeric output 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 '--



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                                 7 June 2013



           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'.

      -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.

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

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

      --compact
           Give compact output featuring only the conversion factor.  This
           turns off the '--verbose' option.

      -q, --quiet, --silent
           Suppress prompting of the user for units and the display of
           statistics about the number of units loaded.

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




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                                 7 June 2013



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

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

      -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
           seconds.

      -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 conver-
           sion'' line.

      -t, --terse
           Give terse output when converting units.  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'.

      -v, --verbose
           Give slightly more verbose output when converting units.  When
           combined with the '-c' option this gives the same effect as '--
           check-verbose'.

      -V, --version
           Print program version number, tell whether the 'readline' library
           has been included, and give the location of the default units
           data file.




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      -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 sys-
           tem settings or environment variables.  See Locale for a descrip-
           tion of locale format.

 ADDING YOUR OWN DEFINITIONS
    Units Data Files
      The units and prefixes that 'units' can convert are defined in the
      units data file, typically '/usr/share/units/definitions.units'.
      Although you can extend or modify this data file if you have appropri-
      ate user privileges, it's usually better to put extensions in separate
      files so that the definitions will be preserved when 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'.)

      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' and 'HOMEPATH'.  Running 'units -V' will
      display the location and name of your personal units file.

      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.

    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



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                                 7 June 2013



      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 the comment character '#'.

      Unit names must not contain any of the operator characters '+', '-',
      '*', '/', '|', '^', ';', '~', the comment character '#', or
      parentheses.  They cannot begin or end with an underscore ('_'), a
      comma (',') or a decimal point ('.').  The figure dash (U+2012), 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'
      would be valid names but 'foo2' or 'foo_a2' would be 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, 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 opera-
      tor, the '-' character can perform addition or multiplication depend-
      ing 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'.



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

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

      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 data file, so that an eventual conversion to prim-
      itive units is possible.

      Here is an example nonlinear unit definition:

         tempF(x) units=[1;K] (x+(-32)) degF + stdtemp ; \
                              (tempF+(-stdtemp))/degF + 32

      A nonlinear unit definition comprises a unit name, a dummy parameter
      name, two functions, and two corresponding units.  The functions tell
      'units' how to convert to and from the new unit.  In order to produce
      valid results, the arguments of these functions need to have the
      correct dimensions.  To facilitate error checking, you may optionally
      indicate units for these arguments.

      The definition begins with the unit name followed immediately (with no
      spaces) by a '(' character.  In parentheses is the name of the parame-
      ter.  Next is an optional specification of the units required by the
      functions in this definition.  In the example above, the 'tempF'



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      function requires an input argument conformable with '1'.  For normal
      nonlinear units definitions the forward function will always take a
      dimensionless argument. The inverse function requires an input argu-
      ment conformable with 'K'.  In general the inverse function will need
      units that match the quantity measured by your nonlinear unit. The
      purpose of the expression in brackets to enable 'units' to perform
      error checking on function arguments, and also to assign units to
      range and domain 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.

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

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

      This inverse definition takes an absolute temperature as its argument
      and converts it to the Fahrenheit temperature.  The inverse can be
      omitted by leaving out the ';' character, but then conversions to the
      unit will be impossible.  If the inverse is omitted then 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.

      If you wish to make synonyms for nonlinear units, you still need to
      define both the forward 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)

      You may define a function whose range and domain do not cover all of
      the real numbers.  In this case 'units' can handle errors better if
      you specify an appropriate range and domain.  You specify the range
      and domain as shown below.

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





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      In this example the domain is specified after the 'domain=' with the
      endpoints given in brackets.  One of the end points can be omitted to
      get an interval that goes to infinity.  So the range could be speci-
      fied as nonnegative by writing 'range=[0,]'.  Both the range and
      domain are optional and can appear independently and in any order
      along with the 'units' specification.  The values in the range and
      domain are attached to the units given in the 'units' specification.
      If you don't specify the units then the parameter inputs are reduced
      to primitive units for the numeric comparison to the values you give
      in the range or domain.  In this case you should only use 'range' or
      'domain' if the endpoints are zero and infinity.

      Specifying the range and domain allows 'units' to perform better error
      checking and give more helpful error messages when you invoke non-
      linear units conversions outside of their bounds. It also enables the
      '-c' option to find a point in the domain to use for its point check
      of your inverse definition.

      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
      messages.

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

      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 ']' char-
      acter, so a definition like 'foo[kg meters]' is illegal; 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




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                                 7 June 2013



         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-
      formed:

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

      If you define a piecewise linear unit that is not strictly monotonic,
      then the inverse will not be well defined.  If the inverse is
      requested for such a unit, 'units' will return the smallest inverse.
      The '--check' option will print a warning if a non-monotonic piecewise
      linear unit is encountered.

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

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

      Unit list aliases are only for unit lists, so the definition must
      include a ';'.  Unit list aliases can never be combined with units or
      other unit list aliases, so the definition of 'time' shown above could
      not have been shortened to 'year;day;hms'.  As usual, be sure to run
      'units --check' to ensure that the units listed in unit list aliases
      are conformable.

 NUMERIC OUTPUT FORMAT
      By default, 'units' shows results to eight significant digits. You can
      change this with the '--exponential', '--digits', and '--output-
      format' options.  The first sets an exponential format (i.e., scien-
      tific notation) like that used in the original Unix 'units' program,
      the second allows you to specify a different number of significant



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                                 7 June 2013



      digits, and the last allows you to control the output appearance using
      the format for the 'printf()' function in the C programming language.
      If you only want to change the number of significant digits or specify
      exponential format type, use the '--digits' and '--exponential'
      options.  The '--output-format' option affords the greatest control of
      the output appearance, but requires at least rudimentary knowledge of
      the 'printf()' format syntax. See Invoking Units for descriptions of
      these options.

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

    Flags
      The '+' flag causes the output to have a sign ('+' or '-').  The space
      flag ' ' is similar to the '+' flag, except that when the value is
      positive, it is prefixed with a space rather than a plus sign; this
      flag is ignored if the '+' flag is also given.  The '+' or ' ' flag
      could be useful if conversions might include positive and negative
      results, and you wanted to align the decimal points in exponential
      notation.  The '#' flag causes the output value to contain a decimal
      point in all cases; by default, the output contains a decimal point
      only if there are digits (which can be trailing zeros) to the right of



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                                 7 June 2013



      the point.  With the 'g' or 'G' types, the '#' flag also prevents the
      suppression of trailing zeros.  The digit-grouping flag ''' shows a
      thousands separator in digits to the left of the decimal point.  This
      can be useful when displaying large numbers in fixed-point decimal;
      for example, with the format '%f',

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

      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
      '%12.6f',

         You have: km
         You want: in



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                                 7 June 2013



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

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

      With the 'g' and 'G' format types, trailing zeros are suppressed, so
      the results may sometimes have fewer digits than the specified preci-
      sion (as indicated above, the '#' flag causes trailing zeros to be
      displayed).

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

      The C 'printf()' function allows a precision of arbitrary size,
      whether or not all of the digits are meaningful.  With most compilers,
      the maximum internal precision with 'units' is 15 decimal digits (or
      13 hexadecimal digits).  With the '--digits' option, you are limited
      to the maximum internal precision; with the '--output-format' option,
      you may specify a precision greater than this, but it may not be 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



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                                 7 June 2013



      affects only the display of numbers; if a result relies on physical
      constants that are not known to the specified precision, the number of
      physically meaningful digits may be less than the number of digits
      shown.

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

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

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

    Locale
      A locale is a subset of a user's environment that indicates the user's
      language and country, and some attendant preferences, such as the 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
      'en_GB'.

      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' in the same directory, typically
      '/usr/local/share/units', as the default units data files.  The file
      includes entries for many combinations of language and country, and
      can be extended to include other combinations.  The 'locale.map'
      comprises two tab-separated columns; each entry is of the form

         Windows-locale   POSIX-locale

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

         English_United States   en_US

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





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

         !locale en_GB
         gallon       4.54609 liter
         !endlocale

    Additional Localization
      Sometimes the locale isn't sufficient to determine unit preferences.
      There could be regional preferences, or a company could have specific
      preferences.  Though probably uncommon, such differences could arise
      with the choice of English customary units outside of English-speaking
      countries.  To address this, 'units' allows specifying definitions
      that depend on environment variable settings.  The environment 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
         !endvar
         !var INCH_UNIT canada
         yard          0.9144 meter
         !endvar
         !var INCH_UNIT uk
         yard          0.91439841 meter
         !endvar
         !var INCH_UNIT canada uk usa
         foot          1|3 yard



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                                 7 June 2013



         inch          1|12 foot
         !endvar
         !var INCH_UNIT france
         foot          144|443.296 m
         inch          1|12 foot
         line          1|12 inch
         !endvar
         !varnot INCH_UNIT usa uk france canada
         !message Unknown value for INCH_UNIT
         !endvar

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

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

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

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

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




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      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
      definitions.

 ENVIRONMENT VARIABLES
      The 'units' program uses the following environment variables:

      HOME Specifies the location of your home directory; it is used by
           'units' to find a personal units data file '.units'.  On systems
           running Microsoft Windows, 'units' tries to determine your home
           directory from the 'HOMEDRIVE' and 'HOMEPATH' environment vari-
           ables if 'HOME' does not exist.

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

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

      PAGER
           Specifies the pager to use for help and for displaying the 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'.

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

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

 UNICODE SUPPORT
      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



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                                 7 June 2013



      blocks beginning with '!utf8' and ending with '!endutf8'.

      When 'units' starts, it checks the locale to determine the character
      set.  If 'units' is compiled with Unicode support and if the character
      set is UTF-8, 'units' reads the UTF-8 definitions; otherwise these
      definitions are ignored.  When Unicode support is active, 'units' will
      check every line of 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.

      At present, 'units' does not support Unicode under Microsoft Windows.
      The UTF-16 and UTF-32 encodings are not supported on any systems.

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

      When Unicode support is not active, 'units' makes no assumptions about
      character encoding, except that characters in the range 00-7F hexade-
      cimal correspond to ASCII encoding.  Non-ASCII characters are simply
      sequences of bytes, and have no special meanings; for definitions in
      supplementary units data files, you can use any encoding consistent
      with this assumption.  For example, if you wish to use non-ASCII char-
      acters 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).  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
      active, 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.

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



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      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 char-
      acters typed.  For example, if you type 'metr' and then request com-
      pletion, 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 unitname, 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.

 UPDATING CURRENCY EXCHANGE RATES
      The units program includes currency exchange rates and prices for some
      precious metals in the database.  Of course, these values change over
      time, sometimes very rapidly, and 'units' cannot provide real time
      values.  To update the exchange rates run the 'units_cur', which
      rewrites the files containing the currency rates, typically
      '/usr/local/share/units/currency.units'.  This program must be run
      with suitable permissions to write the file.  To keep the rates
      updated automatically, it could be run by a cron job on a Unix-like
      system, or a similar scheduling program on a different system.
      Currency exchange rates are taken from Time Genie
      (http://www.timegenie.com) and precious metals pricing from Packetizer
      (www.packetizer.com).  These sites update once per day, so there is no
      benefit in running the update script more often than daily.  You can
      run 'units_cur' with a filename specified on the command line and it
      will write the data to that file.  If you give '-' for the file it
      will write to standard output.

 DATABASE COMMAND SYNTAX
      unit definition
           Define a regular unit.

      prefix- definition
           Define a prefix.

 definition(var) ; inverse(funcname)
      funcname(var) units=[in-units,out-units] domain=[x1,x2] range=[y1,y2]
           Define a nonlinear unit or unit function.  The three optional



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           keywords 'units=', 'range=' and 'domain=' can appear in any
           order.  The definition of the inverse is optional.

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

      !endlocale
           End a block of definitions beginning with '!locale'

      !endutf8
           End a block of definitions begun with '!utf8'

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

      !include file
           Include the specified file.

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

      !message text
           Display text when the database is read unless the quiet option
           ('-q') is enabled.

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

      !unitlist alias definition
           Define a unit list alias.

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

      !var variable value-list
           Load the following definitions only if the environment variable,
           variable is set to one of the values listed on the space
           separated value list. If variable is not set then 'units' prints
           an error message and ignores the following definitions.

      !varnot variable value-list
           Load the following definitions only if the environment variable,
           variable is not set to one of the values listed on the space
           separated value list.  If variable is not set then 'units' prints
           an error message and ignores the following definitions.





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 GNU FREE DOCUMENTATION LICENSE
 FILES
      @DATAFILE@ - the standard units data file

 AUTHOR














































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