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# UCUM derived unit

UCUM derived units are units of measurement derived from the seven base units specified by the Unified Code for Units of Measure (UCUM).[dubious ] 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[disputed ] (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 with special names

The Unified Code for units of measure assigns special names to 20 derived units.[disputed ] There are many SI derived units like the Newton that are defined in terms of the kilogram, the SI unit of mass. But the UCUM unit of mass is the gram, not the kilogram. So there are many units in the UCUM with prefixes like the millinewton.

Named 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 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

## 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.[citation needed]

## 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 