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Unified Code for Units of Measure
System of codes for unambiguously representing measurement units

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. UCUM is used by different organizations like IEEE, and standards like DICOM, LOINC, HL7, and ISO 11240:2012.

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. There is also an OSGi-based implementation at Eclipse Foundation.

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Base units

Units are represented in UCUM with reference to a set of seven base units.7 The UCUM base units are the metre 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
NameSymbolMeasureDimensionsymbol8
metremlengthL
secondstimeT
gramgmassM
coulombCchargeQ
kelvinKthermodynamic temperatureC
candelacdluminous intensityF
radianradplane angleA

Metric and non-metric units

UCUM Metric prefixes
PrefixUCUM SymbolFactorPower
yottaY10000000000000000000000001024
zettaZ10000000000000000000001021
exaE10000000000000000001018
petaP10000000000000001015
teraT10000000000001012
gigaG1000000000109
megaM1000000106
kilok1000103
hectoh100102
decada10101
(none)(none)1100
decid0.110−1
centic0.0110−2
millim0.00110−3
microu0.00000110−6
nanon0.00000000110−9
picop0.00000000000110−12
femtof0.00000000000000110−15
attoa0.00000000000000000110−18
zeptoz0.00000000000000000000110−21
yoctoy0.00000000000000000000000110−24

Each unit represented in UCUM is identified as either "metric" or "non-metric".9 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.10

Binary prefixes are also supported.

UCUM Binary prefixes
PrefixUCUM SymbolFactorPower
tebiTi1099511627776240
gibiGi1073741824230
mebiMi1048576220
kibiKi1024210

Arbitrary units

UCUM recognizes units that are defined by a particular measurement procedure, and which cannot be related to the base units.11 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
NameSymbolQuantityUCUM base unitEquivalents
hertzHzfrequencys−1
steradiansr12solid anglerad2
millinewtonmNforce, weightg⋅m⋅s−2
millipascalmPapressure, stressg⋅m−1⋅s−2
millijoulemJenergy, work, heatg⋅m2⋅s−2
milliwattmWpower, radiant fluxg⋅m2⋅s−3
ampereA13electric currentC⋅s−1
millivoltmVvoltage, electrical potential difference, electromotive forceg⋅m2⋅s−2⋅C−1
kilofaradkFelectrical capacitanceg−1⋅m−2⋅s3⋅C2
milliohmmΩelectrical resistance, impedance, reactanceg⋅m2⋅s−1⋅C−2
kilosiemenskSelectrical conductanceg−1⋅m−2⋅s1⋅C2
milliwebermWbmagnetic fluxg⋅m2⋅s−1⋅C−1
milliteslamTmagnetic induction, magnetic flux densityg⋅s−1⋅C−1
millihenrymHelectrical inductanceg⋅m2⋅C−2
degree Celsius°CCelsius temperatureK
lumenlmluminous fluxcd⋅rad2
luxlxilluminancem−2⋅cd⋅rad2
becquerelBqradioactivity (decays per unit time)s−1
grayGyabsorbed dose (of ionizing radiation)m2⋅s−2
sievertSvequivalent dose (of ionizing radiation)m2⋅s−2
Notes
Kinematic units
NameSymbolQuantityExpression in terms of UCUM base units
metre per secondm/sspeed, velocitym⋅s−1
metre per second squaredm/s2accelerationm⋅s−2
metre per second cubedm/s3jerk, joltm⋅s−3
metre per second to the fourthm/s4snap, jouncem⋅s−4
radian per secondrad/sangular velocityrad⋅s−1
radian per second squaredrad/s2angular accelerationrad⋅s−2
hertz per secondHz/sfrequency drifts−2
cubic metre per secondm3/svolumetric flowm3⋅s−1
Mechanical units
NameSymbolQuantityExpression in terms of UCUM base units
square metrem2aream2
cubic metrem3volumem3
millinewton secondmN⋅smomentum, impulsem⋅g⋅s−1
millijoule second per radianmN⋅m⋅s/radangular momentumm2⋅g⋅rad⋅s−1
millijoule per radianmN⋅m/rad = mJ/radtorquem2⋅g⋅rad⋅s−2
millinewton per secondmN/syankm⋅g⋅s−3
reciprocal metrem−1wavenumber, optical power, curvature, spatial frequencym−1
gram per square metreg/m2area densitym−2⋅g
gram per cubic metreg/m3density, mass densitym−3⋅g
cubic metre per gramm3/gspecific volumem3⋅g−1
millijoule secondmJ⋅sactionm2⋅g⋅s−1
millijoule per grammJ/gspecific energym2⋅s−2
millijoule per cubic metremJ/m3energy densitym−1⋅g⋅s−2
millinewton per metremN/m = mJ/m2surface tension, stiffnessg⋅s−2
milliwatt per square metremW/m2heat flux density, irradianceg⋅s−3
square metre per secondm2/skinematic viscosity, thermal diffusivity, diffusion coefficientm2⋅s−1
millipascal secondmPa⋅s = mN⋅s/m2dynamic viscositym−1⋅g⋅s−1
gram per metreg/mlinear mass densitym−1⋅g
gram per secondg/smass flow rateg⋅s−1
milliwatt per steradian square metremW/(sr⋅m2)radianceg⋅rad−2⋅s−3
milliwatt per steradian cubic metremW/(sr⋅m3)radiancem−1⋅g⋅rad−2⋅s−3
milliwatt per metremW/mspectral powerm⋅g⋅s−3
gray per secondGy/sabsorbed dose ratem2⋅s−3
metre per cubic metrem/m3fuel efficiencym−2
milliwatt per cubic metremW/m3spectral irradiance, power densitym−1⋅g⋅s−3
millijoule per square metre secondmJ/(m2⋅s)energy flux densityg⋅s−3
reciprocal millipascalmPa−1compressibilitym⋅g−1⋅s2
millijoule per square metremJ/m2radiant exposureg⋅s−2
gram square metre per steradiang⋅m2/srmoment of inertiam2⋅g⋅rad−2
millijoule second per radian per grammN⋅m⋅s/rad/gspecific angular momentumm2⋅s−1⋅rad−1
milliwatt per steradianmW/srradiant intensitym2⋅g⋅rad−2⋅s−3
milliwatt per steradian metremW/(sr⋅m)spectral intensitym⋅g⋅rad−2⋅s−3
Electromagnetic units
NameSymbolQuantityExpression in terms of UCUM base units
coulomb per square metreC/m2electric displacement field, polarization densitym−2⋅C
coulomb per cubic metreC/m3electric charge densitym−3⋅C
ampere per square metreA/m2electric current densitym−2⋅s−1⋅C
kilosiemens per metrekS/melectrical conductivitym−3⋅g−1⋅s1⋅C2
kilofarad per metrekF/mpermittivitym−3⋅g−1⋅s2⋅C2
millihenry per metremH/mmagnetic permeabilitym⋅g⋅C−2
millivolt per metremV/melectric field strengthm⋅g⋅s−2⋅C−1
ampere per metreA/mmagnetization, magnetic field strengthm−1⋅s−1⋅C
coulomb per gramC/gexposure (X and gamma rays)g−1⋅C
milliohm metremΩ⋅mresistivitym3⋅g⋅s−1⋅C−2
coulomb per metreC/mlinear charge densitym−1⋅C
millijoule per milliteslamJ/mTmagnetic dipole momentm2⋅s−1⋅C
square metre per millivolt secondm2/(mV⋅s)electron mobilityg−1⋅s⋅C
reciprocal millihenrymH−1magnetic reluctancem−2⋅g−1⋅C2
milliweber per metremWb/mmagnetic vector potentialm⋅g⋅s−1⋅C−1
milliweber metremWb⋅mmagnetic momentm3⋅g⋅s−1⋅C−1
millitesla metremT⋅mmagnetic rigiditym⋅g⋅s−1⋅C−1
ampere radianA⋅radmagnetomotive forceC⋅rad⋅s−1
metre per millihenrym/mHmagnetic susceptibilitym−1⋅g−1⋅C2
Photometric units
NameSymbolQuantityExpression in terms of UCUM base units
lumen secondlm⋅sluminous energys⋅cd⋅rad2
lux secondlx⋅sluminous exposurem−2⋅s⋅cd⋅rad2
candela per square metrecd/m2luminancem−2⋅cd
lumen per milliwattlm/mWluminous efficacym−2⋅g−1⋅s3⋅cd⋅rad2
Thermodynamic units
NameSymbolQuantityExpression in terms of UCUM base units
millijoule per kelvinmJ/Kheat capacity, entropym2⋅g⋅s−2⋅K−1
millijoule per gram kelvinmJ/(K⋅g)specific heat capacity, specific entropym2⋅s−2⋅K−1
milliwatt per metre kelvinmW/(m⋅K)thermal conductivitym⋅g⋅s−3⋅K−1
kelvin per milliwattK/mWthermal resistancem−2⋅g−1⋅s3⋅K
reciprocal kelvinK−1thermal expansion coefficientK−1
kelvin per metreK/mtemperature gradientm−1⋅K

See also

Notes

Further reading

References

  1. "UCUM". The UCUM Organization. Retrieved May 1, 2019. https://unitsofmeasure.org ↩

  2. "Unified Code for Units of Measure (UCUM)". National Library of Medicine. Retrieved 2024-07-07. https://ucum.nlm.nih.gov/ ↩

  3. ISO 2955:1983 Information processing — Representation of SI and other units in systems with limited character sets [1] https://www.iso.org/standard/8005.html ↩

  4. Withdrawn without replacement. ↩

  5. FLOWCHART SYMBOLS AND THEIR USAGE IN INFORMATION PROCESSING https://global.ihs.com/doc_detail.cfm?document_name=ANSI%20X3%2E5&item_s_key=00009726 ↩

  6. Superseded by ISO 5807. /wiki/ISO_5807 ↩

  7. 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. http://unitsofmeasure.org/ucum.html ↩

  8. 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. http://unitsofmeasure.org/ucum-essence.xml ↩

  9. 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. http://unitsofmeasure.org/ucum.html ↩

  10. 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. http://unitsofmeasure.org/ucum.html ↩

  11. 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. http://unitsofmeasure.org/ucum.html ↩

  12. In the SI, both the radian and steradian are dimensionless derived units. ↩

  13. In the SI, the coulomb is derived from the ampere. 1 C = 1 A × 1 s. ↩