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. 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.

Base units

Units are represented in UCUM with reference to a set of seven base units. 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

Name	Symbol	Measure	Dimension symbol
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

UCUM Metric 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". 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.

Binary prefixes are also supported.

UCUM Binary prefixes

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

Arbitrary units

UCUM recognizes units that are defined by a particular measurement procedure, and which cannot be related to the base units. 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	UCUM base unit Equivalents
hertz	Hz	frequency	s−1
steradian	sr	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	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 (of ionizing radiation)	m2⋅s−2
sievert	Sv	equivalent dose (of ionizing radiation)	m2⋅s−2
Notes

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	dynamic viscosity	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	electric charge density	m−3⋅C
ampere per square metre	A/m2	electric current 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 and gamma 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

See also

• Outline of metrology and measurement
• GNU Units
• International vocabulary of metrology

Further reading

• Schadow, Gunther; McDonald, Clement J.; Jeffrey G., Suico; Föhring, Ulrich; Tolxdorff, Thomas (1999-03-01). "Units of Measure in Clinical Information Systems". Journal of the American Medical Informatics Association. 6 (2): 151–162. doi:10.1136/jamia.1999.0060151. PMC 61354. PMID 10094068.

External links

• Media related to Unified Code for Units of Measure at Wikimedia Commons
• unitsofmeasure.org - 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)