
UNITS(1) UNITS(1)
NAME
units  unit conversion program
OVERVIEW OF `UNITS'
The `units' program converts quantities expressed in various scales to their equivalents
in other scales. The `units' program can handle multiplicative scale changes as well as
nonlinear conversions such as Fahrenheit to Celsius.
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 use the program interactively with prompts, or you can use it from the command
line.
INTERACTING WITH `UNITS'
To invoke units for interactive use, type `units' at your shell prompt. The program will
print something like this:
2131 units, 53 prefixes, 24 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 type of units you want to convert to. To convert
to feet, you would type `feet'.
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 output, which is marked with a `/' to indicate division, gives the
inverse of the conversion factor. If you convert 10 meters to feet, `units' will print
* 32.808399
/ 0.03048
which tells you that 10 meters equals about 32.8 feet. The second number gives the con
version 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 .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 .03048 dekameters. But the number given the other direction is inexact.
If you try to convert grains to pounds, you will see the following:
You have: grains
You want: pounds
* 0.00014285714
/ 7000
From the second line of the output you can immediately see that a grain is equal to a
seven thousandth of a pound. This is not so obvious from the first line of the output.
If you find the output format confusing, try using the `verbose' option:
You have: grain
You want: aeginamina
grain = 0.00010416667 aeginamina
grain = (1 / 9600) aeginamina
If you request a conversion between units which measure reciprocal dimensions, then
`units' will display the conversion results with an extra note indicating that reciprocal
conversion has been done:
You have: 6 ohms
You want: siemens
reciprocal conversion
* 0.16666667
/ 6
Reciprocal conversion can be suppressed by using the `strict' option. As usual, use the
`verbose' option to get more comprehensible output:
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
2.7777778e11 kg m^2 / sec^3
2.1166667e05 kg^2 m / sec
If you only want to find the reduced form or definition of a unit, simply press return at
the `You want:' prompt. Here is an example:
You have: jansky
You want:
Definition: fluxunit = 1e26 W/m^2 Hz = 1e26 kg / s^2
The output from `units' indicates that the jansky is defined to be equal to a fluxunit
which in turn is defined to be a certain combination of watts, meters, and hertz. The
fully reduced (and in this case somewhat more cryptic) form appears on the far right.
If you want a list of options you can type `?' at the `You want:' prompt. The program
will display a list of named units which are conformable with the unit that you entered at
the `You have:' prompt above. Note that conformable unit combinations will not appear on
this list.
Typing `help' at either prompt displays a short help message. You can also type `help'
followed by a unit name. This will invoke a pager on the units data base at the point
where that unit is defined. You can read the definition and comments that may give more
details or historical information about the unit.
USING `UNITS' NONINTERACTIVELY
The `units' program can perform units conversions noninteractively from the command line.
To do this, type the command, type the original units expression, and type the new units
you want. You will probably need to protect the units expressions from interpretation by
the shell using single 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(0) to the calling envi
ronment. If `units' is given nonconformable units to convert, it will print a message
giving the reduced form of each unit and it will return failure (nonzero) to the calling
environment.
When `units' is invoked 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 EXPRESSIONS
In order to enter more complicated units or fractions, you will need to use operations
such as powers, products and division. Powers of units can be specified using the `^'
character as shown in the following example, or by simple concatenation: `cm3' is equiva
lent 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. The `^' operator has the second highest prece
dence.
You have: cm^3
You want: gallons
* 0.00026417205
/ 3785.4118
You have: arabicfootarabictradepoundforce
You want: ft lbf
* 0.7296
/ 1.370614
Multiplication of units can be specified by using spaces, a hyphen (`') or an asterisk
(`*'). Division of units is indicated by the slash (`/') or by `per'.
You have: furlongs per fortnight
You want: m/s
* 0.00016630986
/ 6012.8727
Multiplication has a higher precedence than division and is evaluated left to right, so
`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 .5/meter, which
is probably not what you would intend if you entered that expression. You can indicate
division of numbers with the vertical dash (`'). This operator has the highest prece
dence so the square root of two thirds could be written `23^12'.
You have: 12 inch
You want: cm
* 1.27
/ 0.78740157
Parentheses can be used for grouping as desired.
You have: (1/2) kg / (kg/meter)
You want: league
* 0.00010356166
/ 9656.0833
Prefixes are defined separately from base units. In order to get centimeters, the units
database defines `centi' and `c' as prefixes. Prefixes can appear alone with no unit
following them. An exponent applies only to the immediately preceding unit and its prefix
so that `cm^3' or `centimeter^3' refer to cubic centimeters but `centimeter^3' refers to
hundredths of cubic meters. Only one prefix is permitted per unit, so `micromicrofarad'
will fail, but `micromicrofarad' will work.
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
which is 2 ft by 3 ft by 12 ft in steres, you could do the following:
You have: 2 ft 3 ft 12 ft
You want: stere
* 2.038813
/ 0.49048148
You have: $ 5 / yard
You want: cents / inch
* 13.888889
/ 0.072
And the second example shows how the dollar sign in the units conversion can precede the
five. Be careful: `units' will interpret `$5' with no space as equivalent to dollars^5.
Outside of the SI system, it is often desirable to add values of different units together.
Sums of conformable units are written with the `+' character.
You have: 2 hours + 23 minutes + 32 seconds
You want: seconds
* 8612
/ 0.00011611705
You have: 12 ft + 3 in
You want: cm
* 373.38
/ 0.0026782366
You have: 2 btu + 450 ftlbf
You want: btu
* 2.5782804
/ 0.38785542
The expressions which are added together must reduce to identical expressions in primitive
units, or an error message will be displayed:
You have: 12 printerspoint + 4 heredium
^
Illegal sum of nonconformable units
Because `' is used for products, it cannot also be used to form differences of units. If
a `' appears after `(' or after `+' then it will act as a negation operator. So you can
compute 20 degrees minus 12 minutes by entering `20 degrees + 12 arcmin'. The `+' char
acter is sometimes used 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 `+' as part of an exponent if possible.
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 dimen
sionless 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 trigonomet
ric 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. Higher roots can be
obtained 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
Nonlinear units are represented using functional notation. They make possible nonlinear
unit conversions such temperature. This is different from the linear units that convert
temperature differences. Note the difference below. The absolute temperature conversions
are handled by units starting with `temp', and you must use functional notation. The tem
perature differences 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
In this case, think of `tempF(x)' not as a function but as a notation which indicates that
`x' should have units of `tempF' attached to it. @xref{Nonlinear units}.
Some other examples of nonlinears units are ring size and wire gauge. There are numerous
different gauges and ring sizes. See the units database for more details. Note that 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
units database.
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
INVOKING `UNITS'
You invoke `units' like this:
units OPTIONS [FROMUNIT [TOUNIT]]
If the FROMUNIT and TOUNIT are omitted, then the program will use interactive prompts to
determine which conversions to perform. If both FROMUNIT and TOUNIT are given, `units'
will print the result of that single conversion and then exit. If only FROMUNIT appears
on the command line, `units' will display the definition of that unit and exit. Units
specified on the command line will need to be quoted to protect them from shell interpre
tation and to group them into two arguments. @xref{Command line use}.
The following options allow you to read in an alternative units file, check your units
file, or change the output format:
c, check
Check that all units and prefixes defined in the units data file reduce to primi
tive units. Print a list of all units that cannot be reduced. Also display some
other diagnostics about suspicious definitions in the units data file. Note that
only definitions active in the current locale are checked.
checkverbose
Like the `check' option, this option prints a list of units that cannot be
reduced. But to help find unit definitions that cause endless loops, it lists the
units as they are checked. If `units' hangs, then the last unit to be printed has
a bad definition. Note that only definitions active in the current locale are
checked.
o format, outputformat format
Use the specified format for numeric output. Format is the same as that for the
printf function in the ANSI C standard. For example, if you want more precision
you might use `o %.15g'.
f filename, file filename
Use filename as the units data file rather than the default units data file. This
option overrides the `UNITSFILE' environment variable.
h, help
Print out a summary of the options for `units'.
q, quiet, silent
Suppress prompting of the user for units and the display of statistics about the
number of units loaded.
s, strict
Suppress conversion of units to their reciprocal units.
v, verbose
Give slightly more verbose output when converting units. When combined with the
`c' option this gives the same effect as `checkverbose'.
V, version
Print program version number, tell whether the readline library has been included,
and give the location of the default units data file.
UNIT DEFINITIONS
The conversion information is read from a units data file which is called `units.dat' and
is probably located in the `/usr/local/share' directory. If you invoke `units' with the
`V' option, it will print the location of this file. The default file includes defini
tions 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 permitivity of vacuum
G gravitational constant
mach speed of sound
The database 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 unit `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 counterparts,
such as the British Imperial gallon, are prefixed with `br'. Currency is prefixed with
its country name: `belgiumfranc', `britainpound'.
The US Survey foot, yard, and mile can be obtained by using the `US' prefix. These units
differ slightly from the international length units. They were in general use until 1959,
and are still used for geographic surveys. The acre is officially defined in terms of the
US Survey foot. If you want an acre defined according to the international foot, use
`intacre'. The difference between these units is about 4 parts per million. The British
also used a slightly different length measure before 1959. These can be obtained with the
prefix `UK'.
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' or a trailing `es'. If that
fails, `units' will check for a prefix. All of the standard metric prefixes are defined.
To find out what units and prefixes are available, read the standard units data file.
DEFINING NEW UNITS
All of the units and prefixes that `units' can convert are defined in the units data file.
If you want to add your own units, you can supply your own file.
A unit is specified on a single line by giving its name and an equivalence. Comments
start with a `#' character, which can appear anywhere in a line. The backslash character
(`') acts as a continuation character if it appears as the last character on a line, mak
ing it possible to spread definitions out over several lines if desired.
Unit names must not contain any of the operator characters `+', `', `*', `/', `', `^' or
the parentheses. They cannot begin with a digit or a decimal point (`.'), nor can they
end with a digit (except for zero). Be careful to define new units in terms of old ones
so that a reduction leads to the primitive units, which are marked with `!' characters.
When adding new units, be sure to use the `c' option to check that the new units reduce
properly. If you define any units which contain `+' characters, carefully check them
because the `c' option will not catch nonconformable sums. If you create a loop in the
units definitions, then `units' will hang when invoked with the `c' options. You will
need to use the `checkverbose' option which prints out each unit as it checks them.
The program will still hang, but the last unit printed will be the unit which caused the
infinite loop.
Here is an example of a short units file that defines some basic units:
m ! # The meter is a primitive unit
sec ! # The second is a primitive unit
micro 1e6 # 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 which ends with a `' character is a prefix. If a prefix definition contains any
`/' characters, be sure they are protected by parentheses. If you define `half 1/2' then
`halfmeter' would be equivalent to `1 / 2 meter'.
DEFINING NONLINEAR UNITS
Some units conversions of interest are nonlinear; for example, temperature conversions
between the Fahrenheit and Celsius scales cannot be done by simply multiplying by conver
sions factors.
When you give a linear unit definition such as `inch 2.54 cm' you are providing informa
tion that `units' uses to convert values in inches into primitive units of meters. For
nonlinear units, you give a functional definition that provides the same information.
Nonlinear units are represented using a functional notation. It is best to regard this
notation not as a function call but as a way of adding units to a number, much the same
way that writing a linear unit name after a number adds units to that number. Internally,
nonlinear units are defined by a pair of functions which convert to and from linear units
in the data file, so that an eventual conversion to primitive units is possible.
Here is an example nonlinear unit definition:
tempF(x) [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 specify the dimen
sions.
The definition begins with the unit name followed immediately (with no spaces) by a `('
character. In parentheses is the name of the parameter. Next is an optional specifica
tion of the units required by the functions in this definition. In the example above, the
`tempF' 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 argument conformable with `K'. In general the inverse
function will need units that match the quantity measured by your nonlinear unit. The
sole purpose of the expression in brackets to enable `units' to perform error checking on
function arguments.
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 tem
perature, 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 `;' charac
ter. 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 cor
rect inverse function to obtain proper conversions. The `check' option tests the
inverse at one point and print an error if it is not valid there, but this is not a guar
antee that your inverse is correct.
If you wish to make synonyms for nonlinear units, you still need to define both the for
ward and inverse functions. Inverse functions can be obtained using the `~' operator. So
to create a synonym for `tempF' you could write
fahrenheit(x) [1;K] tempF(x); ~tempF(fahrenheit)
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. Note that this definition requires a length as
input and produces an area as output, as indicated by the specification in brackets.
circlearea(r) [m;m^2] 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 `[' character. After the bracket, you should
indicate the units to be attached to the numbers in the table. No spaces can appear
before the `]' character, so a definition like `foo[kg meters]' is illegal; instead write
`foo[kg*meters]'. The definition of the unit consists of a list of pairs optionally sepa
rated 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 con
tinuation characters as
zincgauge[in] \
1 0.002 \
10 0.02 \
15 0.04 \
19 0.06 \
23 0.1
With the preceeding definition, the following conversion can be performed:
You have: zincgauge(10)
You want: in
* 0.02
/ 50
You have: .01 inch
You want: zincgauge
5
If you define a piecewise linear unit that is not strictly monotonic, then the inverse
will not be well defined. If the inverse is requested for such a unit, `units' will
return the smallest inverse. The `check' option will print a warning if a nonmonotonic
piecewise linear unit is encountered.
LOCALIZATION
Some units have different values in different locations. The localization feature accomo
dates this by allowing the units database to specify region dependent definitions. A
locale region in the units database begins with `!locale' followed by the name of the
locale. The leading `!' must appear in the first column of the units database. The
locale region is terminated by `!endlocale'. The following example shows how to define a
couple units in a locale.
!locale en_GB
ton brton
gallon brgallon
!endlocale
The current locale is specified by the `LOCALE' environment variable. Note that the `c'
option only checks the definitions which are active for the current locale.
ENVIRONMENT VARIABLES
The `units' programs uses the following environment variables.
LOCALE Specifies the locale. The default is `en_US'. Sections of the units database are
specific to certain locales.
PAGER Specifies the pager to use for help and for displaying the conformable units. The
help function browses the units database and calls the pager using the `+nn' syntax
for specifying a line number. The default pager is `more', but `less', `emacs', or
`vi' are possible alternatives.
UNITSFILE
Specifies the units database file to use (instead of the default). This will be
overridden by the `f' option.
READLINE SUPPORT
If the `readline' package has been compiled in, then when `units' is used interactively,
numerous command line editing features are available. To check if your version of `units'
includes the readline, invoke the program with the `version' option.
For complete information about readline, consult the documentation for the readline pack
age. 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 the `?' key then `units' will
display a list of all the units which start with the characters typed. For example, if
you type `metr' and then request completion, you will see something like this:
You have: metr
metre metriccup metrichorsepower metrictenth
metretes metricfifth metricounce metricton
metriccarat metricgrain metricquart metricyarncount
You have: metr
If there is a unique way to complete a 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.
FILES
/usr/share/units.dat  the standard units data file
AUTHOR
Adrian Mariano (adrian@cam.cornell.edu)
30 Jan 2001 UNITS(1) 
