Representation of Derived Units in UnitsML
Peter J. Linstrom∗
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FT
November 6, 2006
∗
phone: (301) 975-5422, e-mail: [email protected]
1 INTRODUCTION
11/6/06
Contents
1
2 Why this convention is needed
2
3 Information needed to define a unit
3
4 Proposed XML encoding
5 Important conventions
6 Potential problems
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7 Possible alternatives
FT
1 Introduction
4
5
7
8
A Prefixes from the SI
10
B SI units and units acceptable for use with the SI
11
C non-SI Units
16
1 Introduction
This document describes a proposed convention for defining derived units in terms of their base
units. This convention is intended for use in the UnitsML markup language to allow a precise
definition of a wide range of units. The goal of this convention is to improve interoperability
among applications and databases which use derived units based on commonly encountered base
units. It is understood that not all units can be represented using this convention. It is, however,
Representation of Derived Units in UnitsML
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2 WHY THIS CONVENTION IS NEEDED
11/6/06
anticipated that a wide range of scientific and engineering units of measure can be represented with
this convention.
The convention consists of representing the unit in terms of its base units and providing controlled
vocabulary of base units. For example the unit centimeter per second squared would be represented
in terms of the following:
1. The unit meter with the prefix centi raised to the power 1.
FT
2. The unit second raised to the power −1.
Please note that this convention seeks to address the problem of defining derived units, not to
define conversion factors. For this reason it will only support multiplication by constants which
have defined SI prefixes.
2
Why this convention is needed
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Without this convention, there is no easy way to reliably compare unit definitions from different
sources to see if they are the same. The proposed symbolic identifier can be used for this purpose,
but it is not parsable XML, so it requires a specialized parser and cannot be validated against an
XML schema. As will be noted later, other than syntax, this proposal is similar to the symbolic
identifier; the need to enumerate a set of base units and multiplicative prefixes is the same for both
approaches.
Other identifying data in the current XML schema lacks the qualities which would make them
useful for comparing unit definitions from different sources. Numeric identifiers are assigned by
the author of the definition and thus are only useful for comparison within the context in which
they were assigned. Names are obviously language specific. Even within a given language there
may be multiple names for a given unit, so names may not be unique identifiers.
Under this proposal, information about the definition is provided in a structured format based on
explicitly enumerated base units and multiplicative prefixes. This will allow comparison of unit
definitions from different sources; something essential for interoperability of applications with
different unit definition databases. Such comparison will be done by comparing base units, multiplicative prefixes, and exponents of units to see if they match.
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3 INFORMATION NEEDED TO DEFINE A UNIT
3
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Information needed to define a unit
In order to define a unit in terms of other units the following information is needed for each unit
which will be used to in the definition:
identifier A code or name which identifies the unit.
prefix The SI prefix which notes a factor to multiply the unit by.
FT
exponent numerator Numerator of the exponent to raise the unit and prefix to. The exponent
is expressed as a separate numerator and denominator to restrict it to rational numbers (by
restricting the numerator and denominator to integers). The exponent is applied to both the
unit and the prefix.
exponent denominator Denominator of the exponent to raise the unit and prefix to.
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Proposed codes for prefixes and units are provided in the appendix. It is important to note that
the codes for units are internal representations to be used by the markup language to denote specific units. They are not to be confused with symbols to be used in text documents or official
abbreviations for the units. In most applications, users should never see the codes defined in the
appendix.
It is proposed that only well defined units which are not explicitly derived units be included in the
set of units which may be used for definitions. This would mean that named derived units, such
as newtons, could be used, but explicitly derived units, such as acre-feet could not. Units such as
acre-feet can be defined as derived units.
Only those units and prefixes defined in the appendix should be used in definitions. If users are
allowed to add their own unit and prefix codes, interoperability will be lost. Because of this,
however, this representation scheme will not work for all units and, hence, must be an optional
part of the markup language.
There is one important and potentially controversial unit listed in table 23. The item unit refers to
a count of items and can be used to note derived units which included such counts (e.g. neutron
flux). This concept is at odds with the SI which assigns such counts a unit of 1. In this proposal
it was chosen to include counts as a named unit, because doing so provides additional semantic
clarity over the practice endorsed by the SI.
The units defined in the appendix have been taken from several sources [1, 2, 3, 4, 5, 6].
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4 PROPOSED XML ENCODING
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It is important to remember that this is a working document and that the list of units
in the appendix is only an initial attempt at enumerating units to be defined. It is
envisioned that units will be added or removed from the list based on input from the
UnitsML developers. I addition, it should be recognized that the codes defined in this
document are solely for enumerating base units in the XML, schema; they are not
intended for use in any way outside of representing derived units in UnitsML.
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4 Proposed XML encoding
A noted above, derived units can be expressed as the product of base units with a multiplicative
prefix raised to a specified power. It is proposed that such definitions be contained an an element
named baseUnits. This element would contain elements for each base unit in the definition.
Each base unit would be noted in a baseUnit element. This element would have the following
attributes:
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prefix One of the codes for the multiplicative prefixes defined in table 1. If omitted there is no
prefix.
unit One of the unit codes defined in the appendix. This attribute is required.
numerator The numerator of the exponent to raise the unit and prefix to. The value should be an
integer. If this attribute is omitted the value is assumed to be one.
denominator The denominator of the exponent to raise the unit and prefix to. The value should
be an integer, but must not be zero. If this attribute is omitted the value assumed to be one.
The baseUnits element is a child of the unit element. Only one baseUnits element per
unit element would be allowed.
The proposed markup is best illustrated with a few examples. The text in figure 1 shows the
relevant markup for a cubic international foot. Another example (showing the use of rational
number exponents is the markup for centimeters to the three-halves power given in figure 2.
The advantages of the proposed markup can be seen by looking at an example. Figures 3 and 4
both show markup for kilojoules per cubic meter. The markup comes from different sources and
uses names in different languages. The elements defined in this proposal are in boldface text; all
other elements are present in the current definition of UnitsML. In the two figures, the existing
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5 IMPORTANT CONVENTIONS
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<baseUnits>
<baseUnit unit="foot" numerator="3" />
</baseUnits>
Figure 1: Representation for a cubic international foot.
<baseUnits>
<baseUnit unit="meter" prefix="c" numerator="3" denominator="2" />
</baseUnits>
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Figure 2: Representation for centimeters to the three-halves power.
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UnitsML provides names and a numeric identifier, neither of which can be used to compare the
units. The numeric identifier cannot be used because these are tied to a specific data sets, and
therefore cannot be relied on for inter-comparison. The names cannot be relied on because, in this
case, they are in different languages. Even if the same language is used, names are not reliable
identifiers because they may be constructed the differently for the same unit (e.g., foot-pounds
versus pound-feet. Without information provided in the baseUnits element, it would be impossible
to determine if the units are different or the same. In this case it can be seen that the units are the
same. Figure 5 shows another unit for energy per volume. Examination of the base units quickly
shows that this unit is quite different from that used noted in figures 3 and 4.
5 Important conventions
A problem arises when a unit can be expressed in terms of more than one set of base units. In such
cases it it possible that two identical units may not be recognized as such. There are two ways this
problem can occur:
1. Dimensionless base units such as radians or steradians are omitted.
2. There is a choice between representations which use SI special (named) derived units and
those which use the SI base units which correspond to the derived units.
In order to minimize these problems, the following conventions should be employed when developing a representation for a derived unit:
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5 IMPORTANT CONVENTIONS
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<unit numericID="En4324" />
<baseUnits>
<baseUnit unit="joule" prefix="k" />
<baseUnit unit="liter" numerator="-1" />
</baseUnits>
<name lang="en-US">kilojoules per liter</name>
...
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</unit>
Figure 3: XML markup for kilojoules per liter from an application with the name in English.
<unit numericID="ESP2421" />
<baseUnits>
<baseUnit unit="joule" prefix="k" />
<baseUnit unit="liter" numerator="-1" />
</baseUnits>
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<name lang="es">kilojoules por litro</name>
...
</unit>
Figure 4: XML markup for kilojoules per liter from an application with the name in Spanish.
<unit numericID="T3244" />
<baseUnits>
<baseUnit unit="thermo_btu" />
<baseUnit unit="foot" numerator="-3" />
</baseUnits>
<name lang="en-US">Thermochemical BTUs per cubic foot</name>
...
</unit>
Figure 5: XML markup for thermochemical BTUs per cubic foot.
Representation of Derived Units in UnitsML
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6 POTENTIAL PROBLEMS
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Don’t cancel units or omit dimensionless units. Canceling units (e.g. converting m · m−1 to 1)
causes information to be lost. Likewise, inclusion of base units such as radians retains information that would otherwise be lost.
Use SI units for dimensionless ratios. A dimensionless ratio (e.g. length divided by length) can
be expressed equally well with many different units. By standardizing on non-prefixed SI
units for such ratios, there will only be one way of expressing a given ratio.
FT
When possible, use SI derived units instead of base units. The derived units provide more information because they provide a logical grouping of the base units. It is more meaningful
to express torque units as a force unit times a distance unit than the SI base units which make
of the force unit and distance unit.
Use the appropriate SI derived units for the area of endeavor. When representing torque (force
times distance), one should use newton meters, while energy should be represented by joules
6
Potential problems
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This proposal may provide two implementation problems: lack of specificity in unit definitions,
and conflict with the symbolic identifier.
A potential drawback of this approach is that it may be confused with a code list for units. Although
codes are used to represent common base units, it should be noted that these are only intended for
use within the proposed convention; they should not be used in other applications. Despite this
fact, it may appear that this approach is defining a new code list for units.
Another drawback of this proposal is that it does not support version numbers. Version numbers
may be used by a units database to distinguish between different definitions of a unit that used over
time. This means, for example, that this convention cannot distinguish between different versions
of the meter. This drawback is particularly significant in the case units based on experimental
values (such as the electron-volt). Conversions between such units and the corresponding SI units
may change over time as better experiments or theory provide more accurate measurements of
the unit. This drawback is inherent in this proposal because version numbers are tied to a specific
database – this proposal seeks to provide interoperability so it cannot be tied to a single data source.
It should be noted that this proposal supports well known changes in unit definitions such as the
difference between survey feet and international feet.
This proposal attempts to do much of what the proposed symbolic identifier intended to do. There
is a strong argument that both this proposal is almost redundant with the symbolic identifier since
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7 POSSIBLE ALTERNATIVES
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they both define units in terms base of base units. This proposal is arguably better for the following
reasons:
• All data is marked up in XML, so no specialized parser is needed to extract the data.
• Because prefix and unit codes are XML attributes they can be validated using XML schema.
XML schema can also be used to require that exponent numerators and denominators be
integers.
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• There is no pressure to reduce the size of unit codes, so more readable codes can be used.
Since the symbolic identifier is a single string, long codes could result in unmanageable
string lengths.
As noted above the symbolic identifier has the advantage of being able to specify a version number.
It also has the advantage of being readily used as a query string.
Possible alternatives
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7
In addition to the approach outlined above, it is useful to consider possible alternative approaches.
Alternatives include the proposed symbolic identifier, referring users to a pre-defined set of base
units in a public database, or mapping ID codes from one database to another.
As noted above, this proposal is arguably superior to the proposed symbolic identifier for UnitsML
because it uses XML syntax. There are, however, some advantages to the symbolic identifier.
These advantages include a compact format and the ability to use the identifier in non-XML aware
applications. The symbolic identifier, for example, could be readily encoded into a URL while the
proposed representation scheme could not.
Another alternative could be to refer to a recommended set of base units in the UnitsML documentation and providing a mechanism for referring to these units in UnitsML markup. For example,
one could state that base units should be taken from the NIST UnitsDB whenever possible. This
approach would have the advantage of not requiring the UnitsML language enumerate base units.
However, without such an enumeration, it would be impossible for XML validators to detect erroneous base unit specifications in documents.
A third alternative is to do nothing at all and allow users and organizations to construct lists which
map from units from one database to another. The goal of this proposal is to reduce the need for
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REFERENCES
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such maps, but it should be assessed if the reduction if effort in mapping one unit set to anther is
worth the effort required by this proposal.
References
[1] Barry N. Taylor, editor. Guide to the SI, with a focus on usage and unit conversions: NIST
Special Publication 811. U.S. Government Printing Office, Washington, DC, 1995.
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[2] Tina Butcher, Linda Crown, Richard Suiter, and Juana Williams, editors. Specifications, Tolerances, and Other Technical Requirements for Weighing and Measuring Devices as adopted by
the 88th National Conference on Weights and Measures 2003. National Institute of Standards
and Technology, Gaithersburg, MD, 2004.
[3] Louis E. Barbrow and Lewis V. Judson. Weights and Measures Standards of the United States:
A brief history. U.S. Government Printing Office, Washington, DC, 1976.
[4] The nist reference on constants, units, and uncertainty. http://physics.nist.gov/
cuu/index.html.
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[5] Gunther Schadow and Clement J. McDonald. The unified code for units of measure. http:
//aurora.rg.iupui.edu/˜schadow/units/UCUM/.
[6] I. M. Mills, B. N. Taylor, and A. J. Thor. Defnitions of the units radian, neper, bel and decibel.
Metrologia, 38(4):353–361, 2001.
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A PREFIXES FROM THE SI
A
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Prefixes from the SI
The SI defines prefixes for powers of ten. These prefixes and their symbols are noted in table 1.
Under this proposal the listed symbols will be used to identify the prefix.
Code
Y
Z
E
P
T
G
M
k
h
da
d
c
m
u
n
p
f
a
z
y
Factor
1024
1021
1018
1015
1012
109
106
103
102
101
10−1
10−2
10−3
10−6
10−9
10−12
10−15
10−18
10−21
10−24
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Symbol
Y
Z
E
P
T
G
M
k
h
da
d
c
m
µ
n
p
f
a
z
y
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Prefix
yotta
zetta
exa
peta
tera
giga
mega
kilo
hecto
deka
deci
centi
milli
micro
nano
pico
femto
atto
zepto
yocto
Table 1: SI prefixes
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B SI UNITS AND UNITS ACCEPTABLE FOR USE WITH THE SI
B
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SI units and units acceptable for use with the SI
This proposal will support all SI units and those deemed acceptable for use with the SI. The tables
noted below provide information on units and their proposed representation.
SI units and those which can be used with the SI fall into categories:
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base units These are units which are used to define other units. Proposed representations for these
units are given in table 2. Please note that the gram is listed in place of the kilogram as the
base unit. This deviation from the SI was done to make prefixes apply in a rational manner
(since the kilogram already has a prefix applied).
special derived units These are derived units which have been given a special name. These units
are noted in table 3.
derived units for human health These units are included in the SI for purposes of protecting
human health. They are listed in table 4
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units accepted for use with the SI These units, noted in table 5, are not part of the SI but can be
used with the SI.
units accepted for use with the SI in specific fields These units can only be used with the SI in
specific fields of endeavor. They are noted in table 6.
units temporarily accepted for use with the SI These units, listed in table 7 are allowed to be
used with the SI on a temporary basis.
Representation of Derived Units in UnitsML
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Code
meter
gram
second
ampere
second
ampere
kelvin
kelvin
Quantity
length
mass
Comment
This is not an SI unit; it is used
here in place of the kilogram to
make prefixes work as expected.
time
electric current
thermodynamic
temperature
amount
of
substance
luminous
intensity
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Unit name
meter
gram
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B SI UNITS AND UNITS ACCEPTABLE FOR USE WITH THE SI
mole
mole
candela
candela
Table 2: SI base units
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B SI UNITS AND UNITS ACCEPTABLE FOR USE WITH THE SI
farad
ohm
farad
ohm
siemens
siemens
weber
tesla
weber
tesla
henry
degree Celsius
lumen
lux
katal
henry
celsius
lumen
lux
katal
Quantity
plane angle
solid angle
frequency
force
pressure
energy
power
electric charge
electric potential
capacitance
electric resistance
electric conductance
magnetic flux
magnetic flux
density
inductance
temperature
luminous flux
illuminance
catalytic activity
Comment
m · m−1
m2 · m−2
s−1
m · kg · s−2
kg · m−1 · s−2 or N · m−2
kg · m2 · s−2 or N · m
kg · m2 · s−3 or J · s−1
s·A
kg · m2 · A−1 · s−3 or W/A
FT
Code
radian
steradian
hertz
newton
pascal
joule
watt
coulomb
volt
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Unit name
radian
steradian
hertz
newton
pascal
joule
watt
coulomb
volt
11/6/06
A2 · s4 · kg −1 · m−2 or C/V
kg · m2 · A−2 · s−3 or V · A−1
A2 · s3 · kg −1 · m−2 or A · V −1
kg · m2 · s−2 · A−1 or V · s
kg · A−1 · s−2 or W b · m−2
kg · m2 · s−2 · A−2 or W b · A−1
K − 273.15
cd · sr
cd · sr · m−2 or lm · m2
mol · s−1
Table 3: SI special derived units
Unit name
becquerel
Code
becquerel
gray
sievert
gray
sievert
Quantity
radionucleotide
activity
absorbed dose
dose equivalent
Comment
s−1
m2 · s−2 or J · kg −1
m2 · s−2 or J · kg −1
Table 4: SI derived units for human health
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B SI UNITS AND UNITS ACCEPTABLE FOR USE WITH THE SI
Code
minute
hour
day
arc degree
arc minute
arc second
liter
metric ton
Quantity
time
time
time
plane angle
plane angle
plane angle
volume
mass
Comment
60 seconds
60 minutes
24 hours
(π/180) radians
1/60 of a degree
1/60 of a minute
1dm3
103 kg, also called tonne
FT
Unit name
minute
hour
day
degree
minute
second
liter
metric ton
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Table 5: Units accepted for use with the SI
Unit name
electron volt
Code
electron volt
unified
atomic atomic mass unit
mass unit
astronomical unit
astronomical unit
Quantity
energy
mass
length
Comment
The kinetic energy acquired by an
electron in passing through a potential difference of 1 volt in a vacuum.
1/12 of the mass of an atom of carbon 12.
Based on the mean earth
sun distance,
approximately
11
1.49597870 meters
Table 6: Units accepted for use with the SI in specific fields
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B SI UNITS AND UNITS ACCEPTABLE FOR USE WITH THE SI
Quantity
length
length
length
area
area
area
pressure
velocity
radionucleotide
activity
radiation
exposure
absorbed dose
dose equivalent
roentgen
roentgen
rad
rem
rad
rem
Comment
1852 meters
One nautical mile per hour.
10−10 meters
100 square meters
100 are or 104 square meters
10−28 square meters
105 pascals
1cm · s−2
3.7 × 1010 becquerels
FT
Code
nautical mile
knot
angstrom
are
hectare
barn
bar
gal
curie
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Unit name
nautical mile
knot
ångström
are
hectare
barn
bar
gal
curie
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2.58 × 10−4 coulombs per kilogram of air
10−2 grays
10−2 sieverts
Table 7: Units temporarily accepted for use with the SI
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C NON-SI UNITS
C
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non-SI Units
Several types of non-SI units are supported. Types of units supported include CGS (tables 8, 9,
and 10), U.S. customary (tables 11, 12, 13, and 14) imperial (table 14), nutrition (tables 15, 16),
and other (tables 17, 18, 19, 20, 21, 22, and 23)
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FT
The intent is not to support all such units, but to support ones widely used in current and historical
practice. Units such as the perm which have poorly defined or conflicting definitions are omitted
from these tables.
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C NON-SI UNITS
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stoke
stoke
darcy
darcy
Quantity
energy
force
pressure
viscosity
inverse viscosity
kinematic viscosity
permeability
Comment
10−7 joules
10−5 newtons
1 dyne per square centimeter
0.1 pascal seconds
10 inverse pascal seconds
energy
10−4 square meters per second,
also known as stokes
The permeability of a one centimeter thick solid with a cross
section of one square centimeter
through which one cubic centimeter of fluid, having a viscosity of
one centipoise, will flow in one
second when exposed to a pressure difference of one atmosphere.
The number of wavelengths per
centimeter.
The luminance of a surface that
emits or reflects one lumen per
square centimeter.
1 lumen per square centimeter or
104 lux
4.184 joules
energy
4.1868 joules
FT
Code
erg
dyne
barye
poise
rhe
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Unit name
erg
dyne
barye
poise
rhe
kayser
kayser
wavenumber
lambert
lambert
luminance
phot
phot
illumination
thermochemical
thermo calorie
calorie
international steam table calorie
table calorie
debye
debye
dipole
ment
mo- 10−18 statcoulomb centimeters
Table 8: Some CGS units
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C NON-SI UNITS
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abcoulomb
abfarad
abhenry
abohm
abcoulomb
abfarad
abhenry
abohm
abmho
abmho
abvolt
abvolt
abwatt
maxwell
abwatt
maxwell
gauss
gauss
Quantity
electric current
electric charge
capacitance
inductance
electric resistance
electric conductance
electric potential
power
magnetic flux
Comment
10 amperes also known as the biot
10 coulombs
109 farads
10−9 henrys
10−9 ohms
FT
Code
abampere
magnetic flux
density
magnetic potential difference
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Unit name
abampere
gilbert
gilbert
oersted
oersted
magnetic field
strength
stilb
stilb
luminance
109 siemens
10−8 volts
10−7 watt
10−8 webers, also known as an abweber, previously known as a line
10−4 teslas, also known as an
abtesla
Defined as magnetic potential difference around a closed path enclosing a surface through which
flows a current of 1/4π abamperes.
Defined as the strength of the magnetic field at a distance of 1 centimeter from a straight conductor
of infinite length and negligible
circular cross section which carries a current of 0.5 abamperes.
1 candela per square centimeter
Table 9: Units from the CGS electromagnetic system
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C NON-SI UNITS
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Code
statampere
statcoulomb
statcoulomb
Quantity
electric current
electric charge
statfarad
statfarad
capacitance
stathenry
stathenry
statohm
statohm
Comment
1 statcoulomb per second. Also
called an esampre
The point charge which repels an
equal point charge at a distance of
1 centimeter with a force of one
dyne. Also called an escoulomb or
a franklin.
The capacitance such that a charge
of 1 statcoulomb results in a potential increase of 1 statvolt.
The self inductance of a circuit
with a potential of 1 statvolt when
subjected produced by a current
change of one statampere per second.
The amount of electrical resistance such that 1 statvolt of potential across the circuit produces 1
statampere of current.
The amount of electrical conductance such that 1 statvolt of potential across the circuit produces 1
statampere of current.
The potential such that the amount
of work needed to move 1 statcoulomb of electric charge is 1
erg.
10−7 watts
The magnetic flux which when
linearly reduced to zero in a single turn circuit results in a e.m.f.
of one statvolt.
1 statweber per square centimeter.
FT
Unit name
statampere
inductance
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electric resistance
statmho
statmho
electric conductance
statvolt
statvolt
electric potential
statwatt
statweber
statwatt
statweber
power
magnetic flux
stattesla
stattesla
magnetic flux
density
Table 10: Units from the CGS electrostatic system
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C NON-SI UNITS
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Code
long ton
short ton
gross hundredweight
troy ounce
troy ounce
pennyweight
apothecaries dram
pennyweight
apothecaries dram
scruple
grain
scruple
grain
mass
mass
slug
slug
mass
mass
mass
mass
mass
mass
mass
mass
mass
D
RA
hundredweight
pound
ounce
dram
troy pound
Quantity
mass
mass
mass
Comment
2240 avoirdupois pounds
2000 avoirdupois pounds
112 avoirdupois pounds
FT
Unit name
long ton
short ton
gross
hundredweight
hundredweight
avoirdupois pound
avoirdupois ounce
avoirdupois dram
troy pound
100 avoirdupois pounds
4.5359237 × 10−01 kilograms
1/16 of an avoirdupois pound
1/16 of an avoirdupois ounce
144/175 of an avoirdupois pound,
same as an apothecaries pound
1/12 of a troy pound, same as an
apothecaries ounce
1/20 of a troy ounce
1/8 of a troy or apothecaries
ounce.
1/3 of an apothecaries dram
1/24 of a pennyweight or 1/5760
of a troy pound or 1/7000 of an
avoirdupois pound; grains are the
same in the avoirdupois, troy, and
apothecaries systems
The mass that one pound force accelerates at one foot per second.
Table 11: Customary units for mass
Representation of Derived Units in UnitsML
Page 20
11/6/06
Code
pound force
poundal
poundal
kip
ton-force
kilogram-force
kip
ton force
kilogram force
Quantity
force
force
force
force
force
D
RA
Unit name
pound-force
FT
C NON-SI UNITS
Comment
The force exerted by an
avoirdupois pound when subjected to the standard acceleration
of earth’s gravity (9.80665m·s−2 ).
The force required to accelerate
and avoirdupois pound at 1 foot
per second.
1000 pounds-force
2000 pounds-force
The force exerted by a kilogram when subjected to the standard acceleration of earth’s gravity
(9.80665m · s−2 ).
Table 12: Customary units for force
Representation of Derived Units in UnitsML
Page 21
C NON-SI UNITS
11/6/06
Code
inch
foot
yard
mile
survey
survey
survey
survey
survey
U.S. survey chain
survey chain
length
D
RA
inch
foot
yard
fathom
rod
Quantity
length
length
length
length
length
length
length
length
length
U.S. survey link
survey link
length
U.S. survey furlong survey furlong
U.S. survey mile
survey mile
length
length
acre
area
acre
Comment
1/12 of an international foot
0.3048 meters
3 international feet
5280 international feet
1/12 of a U.S. survey foot
1200/3937 meters
3 U.S. survey feet
6 U.S. survey feet
16.5 U.S. survey feet, also known
as a pole or perch
4 U.S. survey rods; also known as
Gunter’s chain
1/100 U.S. survey chain; also
known as Gunter’s link
40 rods or 660 U.S. survey feet
5280 U.S. survey feet or 8 furlongs; also known as a statue mile
in the U.S.
43560 square U.S. survey feet
FT
Unit name
international inch
international foot
international yard
international mile
U.S. survey inch
U.S. survey foot
U.S. survey yard
U.S. survey fathom
U.S. survey rod
Table 13: Customary units for length and area
Representation of Derived Units in UnitsML
Page 22
C NON-SI UNITS
gallon
quart
pint
gill
ounce
gallon
quart
pint
cup
gill
fluid ounce
fluid dram
minim
tablespoon
teaspoon
bushel
peck
dry quart
dry pint
Quantity
volume
volume
volume
volume
volume
Comment
4.54609−3 cubic meters
1/4 of an imperial gallon
1/2 of an imperial quart
1/4 of an imperial pint
1/5 of an imperial gill
volume
volume
volume
volume
volume
volume
volume
volume
volume
volume
dry volume
dry volume
dry volume
dry volume
231 cubic international inches
1/4 of a U.S. liquid gallon
1/2 of a U.S. liquid quart
1/2 of a U.S. liquid pint
1/4 of a U.S. liquid pint
1/8 of a U.S. cup
1/8 of a U.S. fluid ounce
1/60 of a U.S. fluid ounce
1/2 of a U.S. fluid ounce
1/3 of a U.S. tablespoon
2150.42 cubic international inches
1/4 of a U.S. bushel
1/8 of a U.S. peck
1/2 of a U.S. dry quart
FT
Code
imperial
imperial
imperial
imperial
imperial
D
RA
Unit name
imperial gallon
imperial quart
imperial pint
imperial gill
imperial
fluid
ounce
U.S. liquid gallon
U.S. liquid quart
U.S. liquid pint
U.S. cup
U.S. gill
U.S. fluid ounce
U.S. fluid dram
U.S. minim
U.S. tablespoon
U.S. teaspoon
U.S. bushel
U.S. peck
U.S. dry quart
U.S. dry pint
11/6/06
Table 14: Imperial and customary units for volume
Unit name
Code
thermochemical
thermo kg calorie
kilogram calorie
international steam table kg calorie
table
kilogram
calorie
Quantity
energy
Comment
4184 joules
energy
4186.8 joules
Table 15: Units used in nutrition.
Representation of Derived Units in UnitsML
Page 23
C NON-SI UNITS
Unit name
label teaspoon
label tablespoon
label cup
label fluid ounce
label ounce
11/6/06
Code
label teaspoon
label tablespoon
label cup
label fluid ounce
label ounce
Quantity
volume
volume
volume
volume
mass
Comment
5 ml
15 ml
240 ml
30 ml
28 g
Code
horsepower
electric horsepower
boiler horsepower
metric horsepower
water horsepower
uk horsepower
Quantity
power
power
power
power
power
power
D
RA
Unit name
horsepower
electric horsepower
boiler horsepower
metric horsepower
water horsepower
U.K. horsepower
FT
Table 16: Units specified in U.S. regulations for food labels (21CFR101.9 b 5 viii).
Comment
550 pound-force per second
746 watts
defined by ASME
Table 17: Miscellaneous units for power
Unit name
degree Fahrenheit
degree Rankine
Code
fahrenheit
rankine
Quantity
temperature
temperature
Comment
9/5 × K − 459.67
9/5 × K
Table 18: Miscellaneous units for temperature
Representation of Derived Units in UnitsML
Page 24
C NON-SI UNITS
Code
atmosphere
Quantity
pressure
Comment
technical atmosphere pressure
pressure
cm Hg
pressure
0C cm Hg
in Hg
32F in Hg
60F in Hg
ft Hg
mm water
FT
mm Hg
pressure
pressure
pressure
pressure
pressure
pressure
D
RA
Unit name
standard
atmosphere
technical
atmosphere
millimeter of Hg
(conventional)
centimeter of Hg
(conventional)
0o C centimeter of
Hg
inch of Hg (conventional)
32o F inch of Hg
60o F inch of Hg
foot of Hg (conventional)
millimeter of water
(conventional)
centimeter of water
(conventional)
4o C centimeter of
water
inch of water (conventional)
39.2o F inch of water
60o F inch of water
foot of water (conventional)
39.2o F foot of water
11/6/06
cm water
pressure
4C cm water
pressure
in water
pressure
39F in water
pressure
60F in water
ft water
pressure
pressure
39F ft water
pressure
Table 19: Miscellaneous units for pressure.
Representation of Derived Units in UnitsML
Page 25
C NON-SI UNITS
Unit name
light year
parsec
printer’s pica
computer pica
printer’s point
computer point
11/6/06
Code
light year
parsec
printers pica
computer pica
printers point
computer point
Quantity
length
length
length
length
length
length
Comment
1/6 of an inch
1/72.27 of an inch
1/72 of an inch
Table 20: Miscellaneous length units.
table btu
mean btu
Quantity
energy
Comment
energy
1.05505585262 joules
energy
1/180 of the quantity of heat
needed to raise the temperature of
one avoirdupois pound of water
from 32o to 212o Fahrenheit.
The amount of heat needed to
raise the temperature of one
avoirdupois pound by one degree
Fahrenheit at 39o Fahrenheit.
The amount of heat needed to
raise the temperature of one
avoirdupois pound by one degree
Fahrenheit at 59o Fahrenheit.
The amount of heat needed to
raise the temperature of one
avoirdupois pound by one degree
Fahrenheit at 60o Fahrenheit.
4.184 × 109 joules
105 international steam table
BTUs.
105 59o F BTUs.
FT
Code
thermo btu
D
RA
Unit name
thermochemical
British thermal unit
international steam
table British thermal unit
mean BTU
39o F British ther- 39F btu
mal unit
energy
59o F British ther- 59F btu
mal unit
energy
60o F British ther- 60F btu
mal unit
energy
tons of TNT
E.C. therm
tons of tnt
ec therm
energy
energy
U.S. therm
us therm
energy
Table 21: Miscellaneous energy units.
Representation of Derived Units in UnitsML
Page 26
C NON-SI UNITS
11/6/06
sidereal year
sidereal year
sidereal day
sidereal day
sidereal hour
sidereal minute
sidereal second
shake
sidereal hour
sidereal minute
sidereal second
shake
Quantity
time
time
Comment
365 days
The time for the Earth to complete
one revolution of its orbit, as measured in the frame defined by the
intersection of the ecliptic and the
equator.
The time for the Earth to complete
one revolution of its orbit, as measured in a fixed frame of reference.
The time for the Earth to complete one rotation, as measured in
a fixed frame of reference.
FT
Code
year
tropical year
time
time
D
RA
Unit name
year
tropical year
time
time
time
time
10−8 seconds
Table 22: Miscellaneous time units.
Representation of Derived Units in UnitsML
Page 27
C NON-SI UNITS
11/6/06
Quantity
count
denier
tex
gon
denier
tex
gon
mil (NATO)
NATO mil
pound mole
pound mole
ton of refrigeration
ton refrigeration
Comment
Used to note cases where discrete
items are counted. The SI does not
recognize a unit for this purpose.
linear density grams per 9000 meters
linear density 10−6 kilograms per meter
plane angle
1/400 of a revolution; also known
as a grade or gradian
plane angle
1/6400 of a revolution; also
known as a angular mil. Other
militaries have used other definitions for the mil.
amount
of The amount of substance such that
substance
its mass in avoirdupois pounds is
equal to its molecular (or atomic
weight) in unified atomic mass
units.
heat flow rate 12000 international steam table
BTUs per hour
area
the area of a circle that is 1 mil
(1/1000 of an inch) in diameter
ratio
Common logarithm of an intensity
or power ratio.
ratio
Natural logarithm of an amplitude
ratio.
concentration Negative common logarithm of
moles per liter.
volume
42 U.S. gallons
luminance
1/π candela per square foot
illuminance
the illuminance at 1 foot from a 1
candela point source of light
mass
0.2 grams
FT
Code
item
D
RA
Unit name
item
circular mil
circular mil
bel
bel
neper
neper
pH
ph
petroleum barrel
footlambert
footcandle
petro barrel
footlambert
footcandle
metric carat
carat
Table 23: Miscellaneous units.
Representation of Derived Units in UnitsML
Page 28