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Unified Code for Units of Measure

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System of codes for unambiguously representing measurement units

TheUnified 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] UCUM is used by different organizations likeIEEE, and standards likeDICOM,LOINC,HL7, andISO 11240:2012.^[2]

The code set includes all units defined inISO 1000,ISO 2955-1983,^[3]^[a]ANSI X3.50-1986,^[4]^[b]HL7 andENV 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 bitASCII for machine-to-machine communication, with unambiguous mapping betweencase-sensitive and case-insensitive representations.

A referenceopen-source implementation is available as aJava applet. There is also anOSGi-based implementation atEclipse Foundation.

Base units

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Units are represented in UCUM with reference to a set of seven base units.^[5] The UCUM base units are themetre for measurement oflength, thesecond fortime, thegram formass, thecoulomb forcharge, thekelvin fortemperature, thecandela forluminous intensity, and theradian forplane angle. The UCUM base units form a set of mutually independent dimensions as required bydimensional analysis.

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

Thegram is the base unit ofmass instead of thekilogram, since in UCUM base units do not haveprefixes.
Electric charge is the base quantity for electromagnetic phenomena instead ofelectric current, since theelementary charge ofelectrons is more fundamental physically.
Themole is dimensionless in UCUM, since it can be defined in terms of theAvogadro number,
Theradian is a distinct base unit forplane angle, to distinguishangular velocity fromrotational frequency and to distinguish theradian from thesteradian forsolid angles.

UCUM base units
Name	Symbol	Measure	Dimension symbol^[6]
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

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UCUMMetric prefixes
Prefix	UCUM Symbol	Factor	Power
yotta	Y	1000000000000000000000000	10²⁴
zetta	Z	1000000000000000000000	10²¹
exa	E	1000000000000000000	10¹⁸
peta	P	1000000000000000	10¹⁵
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	u	0.000001	10⁻⁶
nano	n	0.000000001	10⁻⁹
pico	p	0.000000000001	10⁻¹²
femto	f	0.000000000000001	10⁻¹⁵
atto	a	0.000000000000000001	10⁻¹⁸
zepto	z	0.000000000000000000001	10⁻²¹
yocto	y	0.000000000000000000000001	10⁻²⁴

Each unit represented in UCUM is identified as either "metric" or "non-metric".^[5] Metric units can acceptmetric 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 thebel anddegree 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.^[5]

Binary prefixes are also supported.

UCUMBinary prefixes
Prefix	UCUM Symbol	Factor	Power
tebi	Ti	1099511627776	2⁴⁰
gibi	Gi	1073741824	2³⁰
mebi	Mi	1048576	2²⁰
kibi	Ki	1024	2¹⁰

Arbitrary units

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UCUM recognizes units that are defined by a particular measurement procedure, and which cannot be related to the base units.^[5] 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

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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	UCUM base unit Equivalents
hertz	Hz	frequency	s⁻¹
steradian	sr^{[n 1]}	solid angle	rad²
millinewton	mN	force,weight	g⋅m⋅s⁻²
millipascal	mPa	pressure,stress	g⋅m⁻¹⋅s⁻²
millijoule	mJ	energy,work,heat	g⋅m²⋅s⁻²
milliwatt	mW	power,radiant flux	g⋅m²⋅s⁻³
ampere	A^{[n 2]}	electric current	C⋅s⁻¹
millivolt	mV	voltage,electrical potential difference,electromotive force	g⋅m²⋅s⁻²⋅C⁻¹
kilofarad	kF	electrical capacitance	g⁻¹⋅m⁻²⋅s³⋅C²
milliohm	mΩ	electrical resistance,impedance,reactance	g⋅m²⋅s⁻¹⋅C⁻²
kilosiemens	kS	electrical conductance	g⁻¹⋅m⁻²⋅s¹⋅C²
milliweber	mWb	magnetic flux	g⋅m²⋅s⁻¹⋅C⁻¹
millitesla	mT	magnetic induction,magnetic flux density	g⋅s⁻¹⋅C⁻¹
millihenry	mH	electrical inductance	g⋅m²⋅C⁻²
degree Celsius	°C	Celsius temperature	K
lumen	lm	luminous flux	cd⋅rad²
lux	lx	illuminance	m⁻²⋅cd⋅rad²
becquerel	Bq	radioactivity (decays per unit time)	s⁻¹
gray	Gy	absorbed dose (ofionizing radiation)	m²⋅s⁻²
sievert	Sv	equivalent dose (ofionizing radiation)	m²⋅s⁻²
Notes ^In the SI, both the radian and steradian are dimensionless derived units. ^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 second	m/s	speed,velocity	m⋅s⁻¹
metre per second squared	m/s²	acceleration	m⋅s⁻²
metre per second cubed	m/s³	jerk, jolt	m⋅s⁻³
metre per second to the fourth	m/s⁴	snap, jounce	m⋅s⁻⁴
radian per second	rad/s	angular velocity	rad⋅s⁻¹
radian per second squared	rad/s²	angular acceleration	rad⋅s⁻²
hertz per second	Hz/s	frequency drift	s⁻²
cubic metre per second	m³/s	volumetric flow	m³⋅s⁻¹

Mechanical units
Name	Symbol	Quantity	Expression in terms of UCUM base units
square metre	m²	area	m²
cubic metre	m³	volume	m³
millinewton second	mN⋅s	momentum,impulse	m⋅g⋅s⁻¹
millijoule second per radian	mN⋅m⋅s/rad	angular momentum	m²⋅g⋅rad⋅s⁻¹
millijoule per radian	mN⋅m/rad = mJ/rad	torque	m²⋅g⋅rad⋅s⁻²
millinewton per second	mN/s	yank	m⋅g⋅s⁻³
reciprocal metre	m⁻¹	wavenumber,optical power,curvature,spatial frequency	m⁻¹
gram per square metre	g/m²	area density	m⁻²⋅g
gram per cubic metre	g/m³	density, mass density	m⁻³⋅g
cubic metre per gram	m³/g	specific volume	m³⋅g⁻¹
millijoule second	mJ⋅s	action	m²⋅g⋅s⁻¹
millijoule per gram	mJ/g	specific energy	m²⋅s⁻²
millijoule per cubic metre	mJ/m³	energy density	m⁻¹⋅g⋅s⁻²
millinewton per metre	mN/m = mJ/m²	surface tension,stiffness	g⋅s⁻²
milliwatt per square metre	mW/m²	heat flux density,irradiance	g⋅s⁻³
square metre per second	m²/s	kinematic viscosity,thermal diffusivity,diffusion coefficient	m²⋅s⁻¹
millipascal second	mPa⋅s = mN⋅s/m²	dynamicviscosity	m⁻¹⋅g⋅s⁻¹
gram per metre	g/m	linear mass density	m⁻¹⋅g
gram per second	g/s	mass flow rate	g⋅s⁻¹
milliwatt per steradian square metre	mW/(sr⋅m²)	radiance	g⋅rad⁻²⋅s⁻³
milliwatt per steradian cubic metre	mW/(sr⋅m³)	radiance	m⁻¹⋅g⋅rad⁻²⋅s⁻³
milliwatt per metre	mW/m	spectral power	m⋅g⋅s⁻³
gray per second	Gy/s	absorbed dose rate	m²⋅s⁻³
metre per cubic metre	m/m³	fuel efficiency	m⁻²
milliwatt per cubic metre	mW/m³	spectral irradiance,power density	m⁻¹⋅g⋅s⁻³
millijoule per square metre second	mJ/(m²⋅s)	energy flux density	g⋅s⁻³
reciprocal millipascal	mPa⁻¹	compressibility	m⋅g⁻¹⋅s²
millijoule per square metre	mJ/m²	radiant exposure	g⋅s⁻²
gram square metre per steradian	g⋅m²/sr	moment of inertia	m²⋅g⋅rad⁻²
millijoule second per radian per gram	mN⋅m⋅s/rad/g	specific angular momentum	m²⋅s⁻¹⋅rad⁻¹
milliwatt per steradian	mW/sr	radiant intensity	m²⋅g⋅rad⁻²⋅s⁻³
milliwatt per steradian metre	mW/(sr⋅m)	spectral intensity	m⋅g⋅rad⁻²⋅s⁻³

Electromagnetic units
Name	Symbol	Quantity	Expression in terms of UCUM base units
coulomb per square metre	C/m²	electric displacement field,polarization density	m⁻²⋅C
coulomb per cubic metre	C/m³	electriccharge density	m⁻³⋅C
ampere per square metre	A/m²	electriccurrent density	m⁻²⋅s⁻¹⋅C
kilosiemens per metre	kS/m	electrical conductivity	m⁻³⋅g⁻¹⋅s¹⋅C²
kilofarad per metre	kF/m	permittivity	m⁻³⋅g⁻¹⋅s²⋅C²
millihenry per metre	mH/m	magnetic permeability	m⋅g⋅C⁻²
millivolt per metre	mV/m	electric field strength	m⋅g⋅s⁻²⋅C⁻¹
ampere per metre	A/m	magnetization,magnetic field strength	m⁻¹⋅s⁻¹⋅C
coulomb per gram	C/g	exposure (X andgamma rays)	g⁻¹⋅C
milliohm metre	mΩ⋅m	resistivity	m³⋅g⋅s⁻¹⋅C⁻²
coulomb per metre	C/m	linear charge density	m⁻¹⋅C
millijoule per millitesla	mJ/mT	magnetic dipole moment	m²⋅s⁻¹⋅C
square metre per millivolt second	m²/(mV⋅s)	electron mobility	g⁻¹⋅s⋅C
reciprocal millihenry	mH⁻¹	magnetic reluctance	m⁻²⋅g⁻¹⋅C²
milliweber per metre	mWb/m	magnetic vector potential	m⋅g⋅s⁻¹⋅C⁻¹
milliweber metre	mWb⋅m	magnetic moment	m³⋅g⋅s⁻¹⋅C⁻¹
millitesla metre	mT⋅m	magnetic rigidity	m⋅g⋅s⁻¹⋅C⁻¹
ampere radian	A⋅rad	magnetomotive force	C⋅rad⋅s⁻¹
metre per millihenry	m/mH	magnetic susceptibility	m⁻¹⋅g⁻¹⋅C²

Photometric units
Name	Symbol	Quantity	Expression in terms of UCUM base units
lumen second	lm⋅s	luminous energy	s⋅cd⋅rad²
lux second	lx⋅s	luminous exposure	m⁻²⋅s⋅cd⋅rad²
candela per square metre	cd/m²	luminance	m⁻²⋅cd
lumen per milliwatt	lm/mW	luminous efficacy	m⁻²⋅g⁻¹⋅s³⋅cd⋅rad²

Thermodynamic units
Name	Symbol	Quantity	Expression in terms of UCUM base units
millijoule per kelvin	mJ/K	heat capacity,entropy	m²⋅g⋅s⁻²⋅K⁻¹
millijoule per gram kelvin	mJ/(K⋅g)	specific heat capacity, specific entropy	m²⋅s⁻²⋅K⁻¹
milliwatt per metre kelvin	mW/(m⋅K)	thermal conductivity	m⋅g⋅s⁻³⋅K⁻¹
kelvin per milliwatt	K/mW	thermal resistance	m⁻²⋅g⁻¹⋅s³⋅K
reciprocal kelvin	K⁻¹	thermal expansion coefficient	K⁻¹
kelvin per metre	K/m	temperature gradient	m⁻¹⋅K

Notes

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^Withdrawn without replacement.
^Superseded byISO 5807.

References

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^"UCUM". The UCUM Organization. RetrievedMay 1, 2019.
^"Unified Code for Units of Measure (UCUM)".National Library of Medicine. Retrieved2024-07-07.
^ISO 2955:1983 Information processing — Representation of SI and other units in systems with limited character sets[1]
^FLOWCHART SYMBOLS AND THEIR USAGE IN INFORMATION PROCESSING
^^a ^b ^c ^dSchadow, Gunther; McDonald, Clement J. (November 21, 2017)."The Unified Code for Units of Measure, version 2.1". Regenstrief Institute and the UCUM Organization. Archived fromthe original on 2013-11-05. Retrieved2019-05-13.
^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. Retrieved2019-12-20.

External links

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Media related toUnified Code for Units of Measure at Wikimedia Commons
unitsofmeasure.org Archived 2012-10-17 at theWayback Machine - The official UCUM web site. The UCUM Organization
Unified Code for Units of Measure (UCUM) at Lister Hill National Center for Biomedical Communications (LHNCBC), U.S. National Library of Medicine (NLM)
dimensioned::unit_systems::ucum - Rust
- The UCUM-LHC Validator and Converter
- UCUM Web Service (API)
"UOMo", Eclipse Foundation (2010)
"UCUM", Regenstrief Institute (2008)

Systems of measurement

Current

General	International System of Units (SI) UK imperial system US customary units (USCS/USC)
Specific	Apothecaries' Avoirdupois Troy Astronomical Electrical English Engineering Units (US)
Natural	Atomic Geometrised Heaviside–Lorentz Planck Quantum chromodynamical Stoney

Background

Metric	Overview Outline History Metrication
UK/US	Overview Comparison Foot–pound–second (FPS)

Historic

Metric	metre–kilogram–second (MKS) metre–tonne–second (MTS) centimetre–gram–second (CGS) gravitational
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South America	Argentine Bolivian Brazilian Chilean Colombian Paraguayan Peruvian Uruguayan Venezuelan