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.
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 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 .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:
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 return at the `You want:' prompt. Here is an example:
You have: jansky
You want:
Definition: fluxunit = 1e-26 W/m^2 Hz = 1e-26 kg / s^2
The output from units indicates that the jansky is defined to be
equal to a fluxunit which in turn is defined to be a certain combination
of watts, meters, and hertz. The fully reduced (and in this case
somewhat more cryptic) form appears on the far right.
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.
The units program can perform units conversions non-interactively
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 environment. If units is given non-conformable
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.
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 equivalent to
`cm^3'.
If the exponent is more than one digit, the `^' is required.
You have: cm^3
You want: gallons
* 0.00026417205
/ 3785.4118
You have: arabicfoot-arabictradepound-force
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 very high
precedence, higher even than the exponent operator.
You have: 1|2 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 `centi-meter^3' refers to hundredths of cubic meters. Only one
prefix is permitted per unit, so `micromicrofarad' will fail, but
`micro-microfarad' 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 ft-lbf
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 non-conformable 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 `+' character 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 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. 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 temperature 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. See section Defining 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
If the from-unit and to-unit are omitted, then the program
will use interactive prompts to determine which conversions to perform.
See section Interacting with units.
If both from-unit and to-unit are given, units will
print the result of that single conversion and then exit.
If only from-unit appears on the command line, units will
display the definition of that unit and exit.
Units specified on the command line will need
to be quoted to protect them from shell interpretation and to group
them into two arguments. See section Using units non-interactively.
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 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.
`--check-verbose'
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.
`-o format'
`--output-format 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
`--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.
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 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 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.
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, making 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 non-conformable 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 `--check-verbose' 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- 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 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'.
Some units conversions of interest are nonlinear; for
example, temperature conversions between the Fahrenheit and Celsius
scales cannot be done by simply multiplying by conversions factors.
When you give a linear unit definition such as `inch 2.54 cm' you
are providing information that units uses to convert values in
inches into primitive units of meters. For nonlinear units, you give
a functional definition that provides the same information.
Nonlinear units are represented using a functional notation.
It is best to regard this notation not as a function call but
as a way of adding units to a number, much the same way that
writing a linear unit name after a number adds units to that number.
Internally, nonlinear units are defined by a pair of functions
which convert to and from linear units in the data file, so that
an eventual conversion to primitive units is possible.
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 dimensions.
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 specification 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 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 print 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) [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
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 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 characters as
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
non-monotonic piecewise linear unit is encountered.
The units programs uses the following environment variables.
`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.
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 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 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.