Unified Code for Units of Measure

The Unified Code for Units of Measure (UCUM) is a system of codes for unambiguously representing measurement units. Its primary purpose is machine-to-machine communication rather than communication between humans.[1]

The code set includes all units defined in ISO 1000, ISO 2955-1983, ANSI X3.50-1986, HL7 and ENV 12435, and explicitly and verifiably addresses the naming conflicts and ambiguities in those standards to resolve them. It provides for representations of units in 7 bit ASCII for machine-to-machine communication, with unambiguous mapping between case-sensitive and case-insensitive representations.

A reference open-source implementation is available as a Java applet. Also an OSGi based implementation at Eclipse Foundation.

Base units

Units are represented in UCUM with reference to a set of seven base units.[2] The UCUM base units are the meter for measurement of length, the second for time, the gram for mass, the coulomb for charge, the kelvin for temperature, the candela for luminous intensity, and the radian for plane angle. The UCUM base units form a set of mutually independent dimensions as required by dimensional analysis.

Some of the UCUM base units are different from the SI base units. UCUM is compatible with, but not isomorphic with SI. There are four differences between the two sets of base units:

  1. The gram is the base unit of mass instead of the kilogram, since in UCUM base units do not have prefixes.
  2. Electric charge is the base quantity for electromagnetic phenomena instead of electric current, since the elementary charge of electrons is more fundamental physically.
  3. The mole is dimensionless in UCUM, since it can be defined in terms of the Avogadro number,
  4. The radian is a distinct base unit for plane angle, to distinguish angular velocity from rotational frequency and to distinguish the radian from the steradian for solid angles.
UCUM base units
Name Symbol Measure Dimension
symbol[3]
metre m length L
second s time T
gram g mass M
coulomb C charge Q
kelvin K thermodynamic temperature C
candela cd luminous intensity F
radian rad plane angle A

Metric and non-metric units
Metric prefixes in everyday use
Prefix Symbol Factor Power
tera T 1000000000000 1012
giga G 1000000000 109
mega M 1000000 106
kilo k 1000 103
hecto h 100 102
deca da 10 101
(none) (none) 1 100
deci d 0.1 10−1
centi c 0.01 10−2
milli m 0.001 10−3
micro μ 0.000001 10−6
nano n 0.000000001 10−9
pico p 0.000000000001 10−12

Each unit represented in UCUM is identified as either "metric" or "non-metric".[2] Metric units can accept metric prefixes as in SI. Non-metric units are not permitted to be used with prefixes. All of the base units are metric.

UCUM refers to units that are defined on non-ratio scales as "special units". Common examples include the bel and degree Celsius. While these are not considered metric units by UCUM, UCUM nevertheless allows metric prefixes to be used with them where this is common practice.[2]

Binary prefixes are also supported.

Arbitrary units

UCUM recognizes units that are defined by a particular measurement procedure, and which cannot be related to the base units.[2] These units are identified as "arbitrary units". Arbitrary units are not commensurable with any other unit; measurements in arbitrary units cannot be compared with or converted into measurements in any other units. Many of the recognized arbitrary units are used in biochemistry and medicine.

Derived units

Any metric unit in any common system of units can be expressed in terms of the UCUM base units

Units derived from UCUM base units
Name Symbol Quantity Equivalents UCUM base unit
Equivalents
hertz Hz frequency 1/s s−1
steradian sr[n 1] solid angle rad2 rad2
millinewton mN force, weight g⋅m/s2 g⋅m⋅s−2
millipascal mPa pressure, stress mN/m2 g⋅m−1⋅s−2
millijoule mJ energy, work, heat mN⋅m
C⋅mV
mW⋅s		 g⋅m2⋅s−2
milliwatt mW power, radiant flux mJ/s
mV⋅A		 g⋅m2⋅s−3
ampere A[n 2] electric current C/s
mV/mΩ
mW/mV
mJ/mWb		 C⋅s−1
millivolt mV voltage, electrical potential difference, electromotive force mW/A
mJ/C		 g⋅m2⋅s−2⋅C−1
kilofarad kF electrical capacitance C/mV
s/mΩ		 g−1⋅m−2⋅s3⋅C2
milliohm mΩ electrical resistance, impedance, reactance 1/kS
mV/A		 g⋅m2⋅s−1⋅C−2
kilosiemens kS electrical conductance 1/mΩ
A/mV		 g−1⋅m−2⋅s1⋅C2
milliweber mWb magnetic flux C⋅mΩ
mJ/A
mT⋅m2		 g⋅m2⋅s−1⋅C−1
millitesla mT magnetic induction, magnetic flux density mV⋅s/m2
mWb/m2
mN/(A⋅m)		 g⋅s−1⋅C−1
millihenry mH electrical inductance mV⋅s/A
mΩ⋅s
mWb/A		 g⋅m2⋅C−2
degree Celsius °C temperature relative to 273.15 K K K
lumen lm luminous flux cd⋅sr cd⋅rad2
lux lx illuminance lm/m2 m−2⋅cd⋅rad2
becquerel Bq radioactivity (decays per unit time) 1/s s−1
gray Gy absorbed dose (of ionizing radiation) mJ/g m2⋅s−2
sievert Sv equivalent dose (of ionizing radiation) mJ/g m2⋅s−2
Notes
  1. In the SI, both the radian and steradian are dimensionless derived units.
  2. In the SI, the coulomb is derived from the ampere. 1 C = 1 A ⋅ 1 s
Kinematic units
Name Symbol Quantity Expression in terms
of UCUM base units
metre per secondm/s speed, velocitym⋅s−1
metre per second squaredm/s2 accelerationm⋅s−2
metre per second cubedm/s3 jerk, joltm⋅s−3
metre per second to the fourthm/s4 snap, jouncem⋅s−4
radian per secondrad/s angular velocityrad⋅s−1
radian per second squaredrad/s2 angular accelerationrad⋅s−2
hertz per secondHz/s frequency drifts−2
cubic metre per secondm3/s volumetric flowm3⋅s−1
Mechanical units
Name Symbol Quantity Expression in terms
of UCUM base units
square metrem2 aream2
cubic metrem3 volumem3
millinewton secondmN⋅s momentum, impulsem⋅g⋅s−1
millijoule second per radianmN⋅m⋅s/rad angular momentumm2⋅g⋅rad⋅s−1
millijoule per radiannN⋅m/rad = mJ/rad torquem2⋅g⋅rad⋅s−2
millinewton per secondmN/s yankm⋅g⋅s−3
reciprocal metrem−1 wavenumber, optical power, curvature, spatial frequencym−1
gram per square metreg/m2 area densitym−2⋅g
gram per cubic metreg/m3 density, mass densitym−3⋅g
cubic metre per gramm3/g specific volumem3⋅g−1
millijoule secondmJ⋅s actionm2⋅g⋅s−1
millijoule per grammJ/g specific energym2⋅s−2
millijoule per cubic metremJ/m3 energy densitym−1⋅g⋅s−2
millinewton per metremN/m = mJ/m2 surface tension, stiffnessg⋅s−2
milliwatt per square metremW/m2 heat flux density, irradianceg⋅s−3
square metre per secondm2/s kinematic viscosity, thermal diffusivity, diffusion coefficient m2⋅s−1
millipascal secondmPa⋅s = mN⋅s/m2 dynamic viscositym−1⋅g⋅s−1
gram per metreg/m linear mass densitym−1⋅g
gram per secondg/s mass flow rateg⋅s−1
milliwatt per steradian square metremW/(sr⋅m2) radianceg⋅rad−2⋅s−3
milliwatt per steradian cubic metremW/(sr⋅m3) spectral radiancem−1⋅g⋅rad−2⋅s−3
milliwatt per metremW/m spectral powerm⋅g⋅s−3
gray per secondGy/s absorbed dose ratem2⋅s−3
metre per cubic metrem/m3 fuel efficiencym−2
milliwatt per cubic metremW/m3 spectral irradiance, power densitym−1⋅g⋅s−3
millijoule per square metre secondmJ/(m2⋅s) energy flux densityg⋅s−3
reciprocal millipascalmPa−1 compressibilitym⋅g−1⋅s2
millijoule per square metremJ/m2 radiant exposureg⋅s−2
gram square metre per steradiang⋅m2/sr moment of inertiam2⋅g⋅rad−2
millijoule second per radian per grammN⋅m⋅s/rad/g specific angular momentumm2⋅s−1⋅rad−1
milliwatt per steradianmW/sr radiant intensitym2⋅g⋅rad−2⋅s−3
milliwatt per steradian metremW/(sr⋅m) spectral intensitym⋅g⋅rad−2⋅s−3
Electromagnetic units
Name Symbol Quantity Expression in terms
of UCUM base units
coulomb per square metreC/m2 electric displacement field, polarization densitym−2⋅C
coulomb per cubic metreC/m3 electric charge densitym−3⋅C
ampere per square metreA/m2 electric current densitym−2⋅s−1⋅C
kilosiemens per metrekS/m electrical conductivity m−3⋅g−1⋅s1⋅C2
kilofarad per metrekF/m permittivitym−3⋅g−1⋅s2⋅C2
millihenry per metremH/m magnetic permeabilitym⋅g⋅C−2
millivolt per metremV/m electric field strengthm⋅g⋅s−2⋅C−1
ampere per metreA/m magnetization, magnetic field strengthm−1⋅s−1⋅C
coulomb per gramC/g exposure (X and gamma rays)g−1⋅C
milliohm metremΩ⋅m resistivitym3⋅g⋅s−1⋅C−2
coulomb per metreC/m linear charge densitym−1⋅C
millijoule per milliteslamJ/mT magnetic dipole momentm2⋅s−1⋅C
square metre per millivolt secondm2/(mV⋅s) electron mobilityg−1⋅s⋅C
reciprocal millihenrymH−1 magnetic reluctancem−2⋅g−1⋅C2
milliweber per metremWb/m magnetic vector potentialm⋅g⋅s−1⋅C−1
milliweber metremWb⋅m magnetic momentm3⋅g⋅s−1⋅C−1
millitesla metremT⋅m magnetic rigiditym⋅g⋅s−1⋅C−1
ampere radianA⋅rad magnetomotive forceC⋅rad⋅s−1
metre per millihenrym/mH magnetic susceptibilitym−1⋅g−1⋅C2
Photometric units
Name Symbol Quantity Expression in terms
of UCUM base units
lumen secondlm⋅s luminous energys⋅cd⋅rad2
lux secondlx⋅s luminous exposurem−2⋅s⋅cd⋅rad2
candela per square metrecd/m2 luminancem−2⋅cd
lumen per milliwattlm/mW luminous efficacym−2⋅g−1⋅s3⋅cd⋅rad2
Thermodynamic units
Name Symbol Quantity Expression in terms
of UCUM base units
millijoule per kelvinmJ/K heat capacity, entropym2⋅g⋅s−2⋅K−1
millijoule per gram kelvinmJ/(K⋅g) specific heat capacity, specific entropy m2⋅s−2⋅K−1
milliwatt per metre kelvinmW/(m⋅K) thermal conductivity m⋅g⋅s−3⋅K−1
kelvin per milliwattK/mW thermal resistancem−2⋅g−1⋅s3⋅K
reciprocal kelvinK−1 thermal expansion coefficientK−1
kelvin per metreK/m temperature gradientm−1⋅K

See also

References
  1. "UCUM". The UCUM Organization. Retrieved May 1, 2019.
  2. Schadow, Gunther; McDonald, Clement J. (November 21, 2017). "The Unified Code for Units of Measure, version 2.1". Regenstrief Institute and the UCUM Organization. Retrieved 2019-05-13.
  3. Schadow, Gunther; McDonald, Clement J. (November 21, 2017). "The Unified Code for Units of Measure (XML specification), version 2.1". Regenstrief Institute and the UCUM Organization. Retrieved 2019-12-20.

Further reading
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