SI Derived Unit
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SI Derived Unit

SI derived units are units of measurement derived from the seven base units specified by the International System of Units (SI). They are either dimensionless or can be expressed as a product of one or more of the base units, possibly scaled by an appropriate power of exponentiation.

The SI has special names for 22 of these derived units (for example, hertz, the SI unit of measurement of frequency), but the rest merely reflect their derivation: for example, the square metre (m2), the SI derived unit of area; and the kilogram per cubic metre (kg/m3 or kg m-3), the SI derived unit of density.

The names of SI 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".[1]

## Derived units with special names

The International System of Units assigns special names to 22 derived units, which includes two dimensionless derived units, the radian (rad) and the steradian (sr).

Named units derived from SI base units[2]
Name Symbol Quantity Equivalents SI base unit
Equivalents
hertz Hz frequency 1/s s−1
radian rad angle m/m 1
steradian sr solid angle m2/m2 1
newton N force, weight kg?m/s2 kg?m?s−2
pascal Pa pressure, stress N/m2 kg?m−1?s−2
joule J energy, work, heat N?m
C?V
W?s
kg?m2?s−2
watt W power, radiant flux J/s
V?A
kg?m2?s−3
coulomb C electric charge or quantity of electricity s?A
F?V
s?A
volt V voltage, electrical potential difference, electromotive force W/A
J/C
kg?m2?s−3?A−1
farad F electrical capacitance C/V
s/?
kg−1?m−2?s4?A2
ohm ? electrical resistance, impedance, reactance 1/S
V/A
kg?m2?s−3?A−2
siemens S electrical conductance 1/?
A/V
kg−1?m−2?s3?A2
weber Wb magnetic flux J/A
T?m2
kg?m2?s−2?A−1
tesla T magnetic field strength, magnetic flux density V?s/m2
Wb/m2
N/(A?m)
kg?s−2?A−1
henry H electrical inductance V?s/A
s
Wb/A
kg?m2?s−2?A−2
degree Celsius °C temperature relative to 273.15 K K K
lumen lm luminous flux cd?sr cd
lux lx illuminance lm/m2 m−2?cd
becquerel Bq radioactivity (decays per unit time) 1/s s−1
gray Gy absorbed dose (of ionizing radiation) J/kg m2?s−2
sievert Sv equivalent dose (of ionizing radiation) J/kg m2?s−2
katal kat catalytic activity mol/s s−1?mol

## Examples of derived quantities and units

Kinematic SI derived units
Name Symbol Quantity Expression in terms
of SI 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 s−1
radian per second squared rad/s2 angular acceleration s−2
hertz per second Hz/s frequency drift s−2
cubic metre per second m3/s volumetric flow m3⋅s−1
Mechanical SI derived units
Name Symbol Quantity Expression in terms
of SI base units
square metre m2 area m2
cubic metre m3 volume m3
newton second N⋅s momentum, impulse m⋅kg⋅s−1
newton metre second N⋅m⋅s angular momentum m2⋅kg⋅s−1
newton metre N⋅m = J/rad torque, moment of force m2⋅kg⋅s−2
newton per second N/s yank m⋅kg⋅s−3
reciprocal metre m−1 wavenumber, optical power, curvature, spatial frequency m−1
kilogram per square metre kg/m2 area density m−2⋅kg
kilogram per cubic metre kg/m3 density, mass density m−3⋅kg
cubic metre per kilogram m3/kg specific volume m3⋅kg−1
joule second J⋅s action m2⋅kg⋅s−1
joule per kilogram J/kg specific energy m2⋅s−2
joule per cubic metre J/m3 energy density m−1⋅kg⋅s−2
newton per metre N/m = J/m2 surface tension, stiffness kg⋅s−2
watt per square metre W/m2 heat flux density, irradiance kg⋅s−3
square metre per second m2/s kinematic viscosity, thermal diffusivity, diffusion coefficient m2⋅s−1
pascal second Pa⋅s = N⋅s/m2 dynamic viscosity m−1⋅kg⋅s−1
kilogram per metre kg/m linear mass density m−1⋅kg
kilogram per second kg/s mass flow rate kg⋅s−1
watt per steradian square metre W/(sr⋅m2) radiance kg⋅s−3
watt per steradian cubic metre W/(sr⋅m3) spectral radiance m−1⋅kg⋅s−3
watt per metre W/m spectral power m⋅kg⋅s−3
gray per second Gy/s absorbed dose rate m2⋅s−3
metre per cubic metre m/m3 fuel efficiency m−2
watt per cubic metre W/m3 spectral irradiance, power density m−1⋅kg⋅s−3
joule per square metre second J/(m2⋅s) energy flux density kg⋅s−3
reciprocal pascal Pa−1 compressibility m⋅kg−1⋅s2
joule per square metre J/m2 radiant exposure kg⋅s−2
kilogram square metre kg⋅m2 moment of inertia m2⋅kg
newton metre second per kilogram N⋅m⋅s/kg specific angular momentum m2⋅s−1
watt per steradian W/sr radiant intensity m2⋅kg⋅s−3
watt per steradian metre W/(sr⋅m) spectral intensity m⋅kg⋅s−3
Molar SI derived units
Name Symbol Quantity Expression in terms
of SI base units
mole per cubic metre mol/m3 molarity, amount of substance concentration m−3⋅mol
cubic metre per mole m3/mol molar volume m3⋅mol−1
joule per kelvin mole J/(K⋅mol) molar heat capacity, molar entropy m2⋅kg⋅s−2⋅K−1⋅mol−1
joule per mole J/mol molar energy m2⋅kg⋅s−2⋅mol−1
siemens square metre per mole S⋅m2/mol molar conductivity kg-1⋅s3⋅A2⋅mol−1
mole per kilogram mol/kg molality kg−1⋅mol
kilogram per mole kg/mol molar mass kg⋅mol−1
cubic metre per mole second m3/(mol⋅s) catalytic efficiency m3⋅s−1⋅mol−1
Electromagnetic SI derived units
Name Symbol Quantity Expression in terms
of SI base units
coulomb per square metre C/m2 electric displacement field, polarization density m−2⋅s⋅A
coulomb per cubic metre C/m3 electric charge density m−3⋅s⋅A
ampere per square metre A/m2 electric current density m−2⋅A
siemens per metre S/m electrical conductivity m−3⋅kg−1⋅s3⋅A2
farad per metre F/m permittivity m−3⋅kg−1⋅s4⋅A2
henry per metre H/m magnetic permeability m⋅kg⋅s−2⋅A−2
volt per metre V/m electric field strength m⋅kg⋅s−3⋅A−1
ampere per metre A/m magnetization, magnetic field strength m−1⋅A
coulomb per kilogram C/kg exposure (X and gamma rays) kg−1⋅s⋅A
ohm metre ?⋅m resistivity m3⋅kg⋅s−3⋅A−2
coulomb per metre C/m linear charge density m−1⋅s⋅A
joule per tesla J/T magnetic dipole moment m2⋅A
square metre per volt second m2/(V⋅s) electron mobility kg−1⋅s2⋅A
reciprocal henry H−1 magnetic reluctance m−2⋅kg−1⋅s2⋅A2
weber per metre Wb/m magnetic vector potential m⋅kg⋅s−2⋅A−1
weber metre Wb⋅m magnetic moment m3⋅kg⋅s−2⋅A−1
tesla metre T⋅m magnetic rigidity m⋅kg⋅s−2⋅A−1
ampere radian A⋅rad magnetomotive force A
metre per henry m/H magnetic susceptibility m−1⋅kg−1⋅s2⋅A2
Photometric SI derived units
Name Symbol Quantity Expression in terms
of SI base units
lumen second lm⋅s luminous energy s⋅cd⋅sr
lux second lx⋅s luminous exposure m−2⋅s⋅cd⋅sr
candela per square metre cd/m2 luminance m−2⋅cd
lumen per watt lm/W luminous efficacy m−2⋅kg−1⋅s3⋅cd⋅sr
Thermodynamic SI derived units
Name Symbol Quantity Expression in terms
of SI base units
joule per kelvin J/K heat capacity, entropy m2⋅kg⋅s−2⋅K−1
joule per kilogram kelvin J/(K⋅kg) specific heat capacity, specific entropy m2⋅s−2⋅K−1
watt per metre kelvin W/(m⋅K) thermal conductivity m⋅kg⋅s−3⋅K−1
kelvin per watt K/W thermal resistance m−2⋅kg−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 SI

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

## Supplementary units

Until 1995, the SI classified the radian and the steradian as supplementary units, but this designation was abandoned and the units were grouped as derived units.[3]

## References

1. ^ Suplee, Curt (2 July 2009). "Special Publication 811".
2. ^ International Bureau of Weights and Measures (2006), The International System of Units (SI) (PDF) (8th ed.), ISBN 92-822-2213-6, archived (PDF) from the original on 2017-08-14
3. ^

## 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.

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