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units(n) Convert and manipulate quantities with units units(n)
____________________________________________________________________________________________________________
NAME
units - unit conversion
SYNOPSIS
package require Tcl 8.1
package require units ?2.1?
::units::convert value targetUnits
::units::reduce unitString
::units::new name baseUnits
____________________________________________________________________________________________________________
DESCRIPTION
This library provides a conversion facility from a variety of scientific and engineering shorthand
notations into floating point numbers. This allows application developers to easily convert values
with different units into uniformly scaled numbers.
The units conversion facility is also able to convert between compatible units. If, for example, a
application is expecting a value in ohms (Resistance), and the user specifies units of milliwe-bers/femtocoulomb, milliwebers/femtocoulomb,
bers/femtocoulomb, the conversion routine will handle it appropriately. An error will be generated
if an incorrect conversion is attempted.
Values are scaled from one set of units to another by dimensional analysis. Both the value units and
the target units are reduced into primitive units and a scale factor. Units are checked for compati-bility, compatibility,
bility, and the scale factors are applied by multiplication and division. This technique is
extremely flexible and quite robust.
New units and new unit abbreviations can be defined in terms of existing units and abbreviations. It
is also possible to define a new primitive unit, although that will probably be unnecessary. New
units will most commonly be defined to accommodate non-SI measurement systems, such as defining the
unit inch as 2.54 cm.
COMMANDS
::units::convert value targetUnits
Converts the value string into a floating point number, scaled to the specified targetUnits.
The value string may contain a number and units. If units are specified, then they must be
compatible with the targetUnits. If units are not specified for the value, then it will be
scaled to the target units. For example,
% ::units::convert "2.3 miles" km
3.7014912
% ::units::convert 300m/s miles/hour
671.080887616
% ::units::convert "1.0 m kg/s^2" newton
1.0
% ::units::convert 1.0 millimeter
1000.0
::units::reduce unitString
Returns a unit string consisting of a scale factor followed by a space separated list of
sorted and reduced primitive units. The reduced unit string may include a forward-slash (sep-arated (separated
arated from the surrounding primitive subunits by spaces) indicating that the remaining sub-units subunits
units are in the denominator. Generates an error if the unitString is invalid.
% ::units::reduce pascal
1000.0 gram / meter second second
::units::new name baseUnits
Creates a new unit conversion with the specified name. The new unit name must be only alpha-betic alphabetic
betic (upper or lower case) letters. The baseUnits string can consist of any valid units con-version conversion
version string, including constant factors, numerator and denominator parts, units with pre-fixes, prefixes,
fixes, and exponents. The baseUnits may contain any number of subunits, but it must reduce to
primitive units. BaseUnits could also be the string -primitive to represent a new kind of
quantity which cannot be derived from other units. But you probably would not do that unless
you have discovered some kind of new universal property.
% ::units::new furlong "220 yards"
% ::units::new fortnight "14 days"
% ::units::convert 100m/s furlongs/fortnight
601288.475303
UNIT STRING FORMAT
Value and unit string format is quite flexible. It is possible to define virtually any combination
of units, prefixes, and powers. Valid unit strings must conform to these rules.
• A unit string consists of an optional scale factor followed by zero or more subunits. The
scale factor must be a valid floating point number, and may or may not be separated from the
subunits. The scale factor could be negative.
• Subunits are separated form each other by one or more separator characters, which are space ("
"), hyphen ("-"), asterisk ("*"), and forward-slash ("/"). Sure, go ahead and complain about
using a minus sign ("-") to represent multiplication. It just isn't sound mathematics, and,
by rights, we should require everyone to use the asterisk ("*") to separate all units. But
the bottom line is that complex unit strings like m-kg/s^2 are pleasantly readable.
• The forward-slash seperator ("/") indicates that following subunits are in the denominator.
There can be at most one forward-slash separator.
• Subunits can be floating point scale factors, but with the exception of the leading scale fac-tor, factor,
tor, they must be surrounded by valid separators. Subunit scale factors cannot be negative.
(Remember that the hyphen is a unit separator.)
• Subunits can be valid units or abbreviations. They may include a prefix. They may include a
plural suffix "s" or "es". They may also include a power string denoted by a circumflex
("^"), followed by a integer, after the unit name (or plural suffix, if there is one). Nega-tive Negative
tive exponents are not allowed. (Remember that the hyphen is a unit separator.)
EXAMPLE VALID UNIT STRINGS
Unit String Reduced Unit String
------------------------------------------------------------meter -----------------------------------------------------------meter
meter 1.0 meter
kilometer 1000.0 meter
km 1000.0 meter
km/s 1000.0 meter / second
/microsecond 1000000.0 / second
/us 1000000.0 / second
kg-m/s^2 1000.0 gram meter / second second
30second 30.0 second
30 second 30.0 second
30 seconds 30.0 second
200*meter/20.5*second 9.75609756098 meter / second
SI UNITS
The standard SI units are predefined according to NIST Special Publication 33_. Standard units for
both SI Base Units (Table 1) and SI Derived Units with Special Names (Tables 3a and 3b) are included
here for reference. Each standard unit name and abbreviation are included in this package.
SI BASE UNITS
Quantity Unit Name Abbr.
---------------------------------------------Length --------------------------------------------Length
Length meter m
Mass kilogram kg
Time second s
Current ampere A
Temperature kelvin K
Amount mole mol
Luminous Intensity candela cd
SI DERIVED UNITS WITH SPECIAL NAMES
Quantity Unit Name Abbr. Units Base Units
--------------------------------------------------------------------plane -------------------------------------------------------------------plane
plane angle radian rad m/m m/m
solid angle steradian sr m^2/m^2 m^2/m^2
frequency hertz Hz /s
force newton N m-kg/s^2
pressure pascal Pa N/m^2 kg/m-s^2
energy, work joule J N-m m^2-kg/s^2
power, radiant flux watt W J/s m^2-kg/s^3
electric charge coulomb C s-A
electric potential volt V W/A m^2-kg/s^3-A
capacitance farad F C/V s^4-A^2/m^2-kg
electric resistance ohm V/A m^2-kg/s^3-A^2
electric conductance siemens S A/V s^3-A^2/m^2-kg
magnetic flux weber Wb V-s m^2-kg/s^2-A
magnetic flux density tesla T Wb/m^2 kg/s^2-A
inductance henry H Wb/A m^2-kg/s^2-A^2
luminous flux lumen lm cd-sr
illuminance lux lx lm/m^2 cd-sr/m^2
activity (of a
radionuclide) becquerel Bq /s
absorbed dose gray Gy J/kg m^2/s^2
dose equivalent sievert Sv J/kg m^2/s^2
Note that the SI unit kilograms is actually implemented as grams because 1e-6 kilogram = 1 milligram,
not 1 microkilogram. The abbreviation for Electric Resistance (ohms), which is the omega character,
is not supported.
Also note that there is no support for Celsius or Farenheit temperature. The units conversion rou-tines routines
tines can only scale values with multiplication and division, so it is not possible to convert from
thermodynamic temperature (kelvins) to absolute degrees Celsius or Farenheit. Conversion of thermo-dynamic thermodynamic
dynamic quantities, such as thermal expansion (per unit temperature), however, are easy to add to the
units library.
SI Units can have a multiple or sub-multiple prefix. The prefix or its abbreviation should appear
before the unit, without spaces. Compound prefixes are not allowed, and a prefix should never be
used alone. These prefixes are defined in Table 5 of Special Publication 33_.
SI PREFIXES
Prefix Name Abbr. Factor
---------------------------------------yotta --------------------------------------yotta
yotta Y 1e24
zetta Z 1e21
exa E 1e18
peta P 1e15
tera T 1e12
giga G 1e9
mega M 1e6
kilo k 1e3
hecto h 1e2
deka da 1e1
deca 1e1
deci d 1e-1
centi c 1e-2
milli m 1e-3
micro u 1e-6
nano n 1e-9
pico p 1e-12
femto f 1e-15
atto a 1e-18
zepto z 1e-21
yocto y 1e-24
Note that we define the same prefix with both the USA ("deka") and non-USA ("deca") spellings. Also
note that we take the liberty of allowing "micro" to be typed as a "u" instead of the Greek character
mu.
Many non-SI units are commonly used in applications. Appendix B.8 of NIST Special Publication 811
lists many non-SI conversion factors. It is not possible to include all possible unit definitions in
this package. In some cases, many different conversion factors exist for a given unit, depending on
the context. (The appendix lists over 40 conversions for British thermal units!) Application spe-cific specific
cific conversions can always be added using the new command, but some well known and often used con-versions conversions
versions are included in this package.
NON-SI UNITS
Unit Name Abbr. Base Units
--------------------------------------------------angstrom -------------------------------------------------angstrom
angstrom 1.0E-10 m
astronomicalUnit AU 1.495979E11 m
atmosphere 1.01325E5 Pa
bar 1.0E5 Pa
calorie 4.1868 J
curie 3.7E10 Bq
day 8.64E4 s
degree 1.745329E-2 rad
erg 1.0E-7 J
faraday 9.648531 C
fermi 1.0E-15 m
foot ft 3.048E-1 m
gauss 1.0E-4 T
gilbert 7.957747E-1 A
grain gr 6.479891E-5 kg
hectare ha 1.0E4 m^2
hour h 3.6E3 s
inch in 2.54E-2 m
lightYear 9.46073E15 m
liter L 1.0E-3 m^3
maxwell Mx 1.0E-8 Wb
mho 1.0 S
micron 1.0E-6 m
mil 2.54E-5 m
mile mi 1.609344E3 m
minute min 6.0E1 s
parsec pc 3.085E16 m
pica 4.233333E-3 m
pound lb 4.535924E-1 kg
revolution 6.283185 rad
revolutionPerMinute rpm 1.047198E-1 rad/s
yard yd 9.144E-1 m
year 3.1536E7 s
QUANTITIES AND DERIVED UNITS WITH SPECIAL NAMES
This units conversion package is limited specifically to unit reduction, comparison, and scaling.
This package does not consider any of the quantity names for either base or derived units. A similar
implementation or an extension in a typed or object-oriented language might introduce user defined
types for the quantities. Quantity type checking could be used, for example, to ensure that all
length values properly reduced to meters, or that all velocity values properly reduced to meters/sec-ond. meters/second.
ond.
A C implementation of this package has been created to work in conjunction with the Simplified Wrap-per Wrapper
per Interface Generator (http://www.swig.org/). That package (units.i) exploits SWIG's typemap sys-tem system
tem to automatically convert script quantity strings into floating point quantities. Function argu-ments arguments
ments are specified as quantity types (e.g., typedef float Length), and target units (expected by the
C application code) are specified in an associative array. Default units are also defined for each
quantity type, and are applied to any unit-less quantity strings.
A units system enhanced with quantity type checking might benefit from inclusion of other derived
types which are expressed in terms of special units, as illustrated in Table 2 of NIST Publication
33_. The quantity area, for example, could be defined as units properly reducing to meter^2,
although the utility of defining a unit named square meter is arguable.
REFERENCES
The unit names, abbreviations, and conversion values are derived from those published by the United
States Department of Commerce Technology Administration, National Institute of Standards and Technol-ogy Technology
ogy (NIST) in NIST Special Publication 33_: The International System of Units (SI) and NIST Special
Publication 811: Guide for the Use of the International System of Units (SI). Both of these publica-tions publications
tions are available (as of December 2000) from http://physics.nist.gov/cuu/Reference/contents.html
The ideas behind implementation of this package is based in part on code written in 1993 by Adrian
Mariano which performed dimensional analysis of unit strings using fixed size tables of C structs.
After going missing in the late 1990's, Adrian's code has reappeared in the GNU Units program at
http://www.gnu.org/software/units/
AUTHORS
Robert W. Techentin
BUGS, IDEAS, FEEDBACK
This document, and the package it describes, will undoubtedly contain bugs and other problems.
Please report such in the category units of the Tcllib SF Trackers [http://source -
forge.net/tracker/? group_id=12883]. Please also report any ideas for enhancements you may have for
either package and/or documentation.
KEYWORDS
angle, constants, conversion, distance, radians, unit
COPYRIGHT
Copyright (c) 2000-2005 Mayo Foundation
units 1.2 units(n)
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