UCUM derived unit

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UCUM derived units are units of measurement derived from the seven base units specified by the Unified Code for Units of Measure (UCUM). They can be expressed as a product of one or more of the base units, possibly scaled by an appropriate power of exponentiation.

The UCUM has special names for 20 of these derived units (for example, hertz, the UCUM unit of measurement of frequency), but the rest merely reflect their derivation: for example, the square metre (m²), the UCUM derived unit of area; and the gram per cubic metre (g/m³ or g m⁻³), the UCUM derived unit of density.

The names of UCUM derived units, when written in full, are in lowercase. However, the symbols for units named after persons are written with an uppercase initial letter. For example, the symbol for hertz is "Hz"; but the symbol for metre is "m".

Derived units

The Unified Code for units of measure retains the names of all the SI derived units. However, the switch from the kilogram to the gram affects many of the derived units.

Units derived from UCUM base units

Name	Symbol	Quantity	Equivalents	UCUM base unit Equivalents
hertz	Hz	frequency	1/s	s−1
steradian	sr	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	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

Examples of derived quantities and units

Kinematic UCUM derived 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 UCUM derived 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	nN⋅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)	spectral 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 UCUM derived 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 UCUM derived 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 UCUM derived 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

Other units used with UCUM

Some other units such as the hour, litre, tonne, bar and electronvolt are not UCUM units, but are widely used in conjunction with UCUM units.

See also

• International Vocabulary of Metrology
• Metric prefix
• Metric system
• Planck units

Bibliography

• I. Mills, Tomislav Cvitas, Klaus Homann, Nikola Kallay, IUPAC (June 1993). Quantities, Units and Symbols in Physical Chemistry (2nd ed.). Blackwell Science Inc. p. 72.CS1 maint: Multiple names: authors list (link) Search this book on

External Links

https://docs.rs/dimensioned/0.6.0/i686-pc-windows-gnu/dimensioned/unit_systems/ucum/index.html

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