SI derived unit

SI derived units are units of measurement derived from the seven SI base units specified by the International System of Units (SI). They can be expressed as a product (or ratio) of one or more of the base units, possibly scaled by an appropriate power of exponentiation (see: Buckingham π theorem). Some are dimensionless, as when the units cancel out in ratios of like quantities. SI coherent derived units involve only a trivial proportionality factor, not requiring conversion factors.

The SI has special names for 22 of these coherent 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 coherent derived units, when written in full, are always 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", while the symbol for metre is "m".[1]

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 m⋅N, 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/Ω kg−1⋅m−2⋅s4⋅A2
ohm Ω electrical resistance, impedance, reactance 1/S, V/A kg⋅m2⋅s−3⋅A−2
siemens S electrical conductance 1/Ω, A/V kg−1⋅m−2⋅s3⋅A2
weber Wb magnetic flux J/A, T⋅m2,V⋅s kg⋅m2⋅s−2⋅A−1
tesla T magnetic induction, magnetic flux density V⋅s/m2, Wb/m2, N/(A⋅m) kg⋅s−2⋅A−1
henry H electrical inductance V⋅s/A, Ω⋅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 cd⋅m−2
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.

By field of application

Kinematics
Name Symbol Quantity Expression in terms
of SI base units
metre per secondm/s speed, velocitym⋅s−1
metre per second squaredm/s2 accelerationm⋅s−2
metre per second cubedm/s3 jerk, joltm⋅s−3
metre per second to the fourthm/s4 snap, jouncem⋅s−4
radian per secondrad/s angular velocitys−1
radian per second squaredrad/s2 angular accelerations−2
hertz per secondHz/s frequency drifts−2
cubic metre per secondm3/s volumetric flowm3⋅s−1

Mechanics
Name Symbol Quantity Expression in terms
of SI base units
square metrem2 aream2
cubic metrem3 volumem3
newton-secondN⋅s momentum, impulsem⋅kg⋅s−1
newton metre secondN⋅m⋅s angular momentumm2⋅kg⋅s−1
newton-metreN⋅m = J/rad torque, moment of forcem2⋅kg⋅s−2
newton per secondN/s yankm⋅kg⋅s−3
reciprocal metrem−1 wavenumber, optical power, curvature, spatial frequencym−1
kilogram per square metrekg/m2 area densitym−2⋅kg
kilogram per cubic metrekg/m3 density, mass densitym−3⋅kg
cubic metre per kilogramm3/kg specific volumem3⋅kg−1
joule-secondJ⋅s actionm2⋅kg⋅s−1
joule per kilogramJ/kg specific energym2⋅s−2
joule per cubic metreJ/m3 energy densitym−1⋅kg⋅s−2
newton per metreN/m = J/m2 surface tension, stiffnesskg⋅s−2
watt per square metreW/m2 heat flux density, irradiancekg⋅s−3
square metre per secondm2/s kinematic viscosity, thermal diffusivity, diffusion coefficient m2⋅s−1
pascal-secondPa⋅s = N⋅s/m2 dynamic viscositym−1⋅kg⋅s−1
kilogram per metrekg/m linear mass densitym−1⋅kg
kilogram per secondkg/s mass flow ratekg⋅s−1
watt per steradian square metreW/(sr⋅m2) radiancekg⋅s−3
watt per steradian cubic metreW/(sr⋅m3) radiancem−1⋅kg⋅s−3
watt per metreW/m spectral powerm⋅kg⋅s−3
gray per secondGy/s absorbed dose ratem2⋅s−3
metre per cubic metrem/m3 fuel efficiencym−2
watt per cubic metreW/m3 spectral irradiance, power densitym−1⋅kg⋅s−3
joule per square metre secondJ/(m2⋅s) energy flux densitykg⋅s−3
reciprocal pascalPa−1 compressibilitym⋅kg−1⋅s2
joule per square metreJ/m2 radiant exposurekg⋅s−2
kilogram square metrekg⋅m2 moment of inertiam2⋅kg
newton metre second per kilogramN⋅m⋅s/kg specific angular momentumm2⋅s−1
watt per steradianW/sr radiant intensitym2⋅kg⋅s−3
watt per steradian metreW/(sr⋅m) spectral intensitym⋅kg⋅s−3

Chemistry
Name Symbol Quantity Expression in terms
of SI base units
mole per cubic metremol/m3 molarity, amount of substance concentrationm−3⋅mol
cubic metre per molem3/mol molar volumem3⋅mol−1
joule per kelvin moleJ/(K⋅mol) molar heat capacity, molar entropy m2⋅kg⋅s−2⋅K−1⋅mol−1
joule per moleJ/mol molar energym2⋅kg⋅s−2⋅mol−1
siemens square metre per moleS⋅m2/mol molar conductivitykg−1⋅s3⋅A2⋅mol−1
mole per kilogrammol/kg molalitykg−1⋅mol
kilogram per molekg/mol molar masskg⋅mol−1
cubic metre per mole secondm3/(mol⋅s) catalytic efficiencym3⋅s−1⋅mol−1

Electromagnetics
Name Symbol Quantity Expression in terms
of SI base units
coulomb per square metreC/m2 electric displacement field, polarization densitym−2⋅s⋅A
coulomb per cubic metreC/m3 electric charge densitym−3⋅s⋅A
ampere per square metreA/m2 electric current densitym−2⋅A
siemens per metreS/m electrical conductivity m−3⋅kg−1⋅s3⋅A2
farad per metreF/m permittivitym−3⋅kg−1⋅s4⋅A2
henry per metreH/m magnetic permeabilitym⋅kg⋅s−2⋅A−2
volt per metreV/m electric field strengthm⋅kg⋅s−3⋅A−1
ampere per metreA/m magnetization, magnetic field strengthm−1⋅A
coulomb per kilogramC/kg exposure (X and gamma rays)kg−1⋅s⋅A
ohm metreΩ⋅m resistivitym3⋅kg⋅s−3⋅A−2
coulomb per metreC/m linear charge densitym−1⋅s⋅A
joule per teslaJ/T magnetic dipole momentm2⋅A
square metre per volt secondm2/(V⋅s) electron mobilitykg−1⋅s2⋅A
reciprocal henryH−1 magnetic reluctancem−2⋅kg−1⋅s2⋅A2
weber per metreWb/m magnetic vector potentialm⋅kg⋅s−2⋅A−1
weber metreWb⋅m magnetic momentm3⋅kg⋅s−2⋅A−1
tesla metreT⋅m magnetic rigiditym⋅kg⋅s−2⋅A−1
ampere radianA⋅rad magnetomotive forceA
metre per henrym/H magnetic susceptibilitym−1⋅kg−1⋅s2⋅A2

Photometry
Name Symbol Quantity Expression in terms
of SI base units
lumen secondlm⋅s luminous energys⋅cd
lux secondlx⋅s luminous exposurem−2⋅s⋅cd
candela per square metrecd/m2 luminancem−2⋅cd
lumen per wattlm/W luminous efficacym−2⋅kg−1⋅s3⋅cd

Thermodynamics
Name Symbol Quantity Expression in terms
of SI base units
joule per kelvinJ/K heat capacity, entropym2⋅kg⋅s−2⋅K−1
joule per kilogram kelvinJ/(K⋅kg) specific heat capacity, specific entropy m2⋅s−2⋅K−1
watt per metre kelvinW/(m⋅K) thermal conductivity m⋅kg⋅s−3⋅K−1
kelvin per wattK/W thermal resistancem−2⋅kg−1⋅s3⋅K
reciprocal kelvinK−1 thermal expansion coefficientK−1
kelvin per metreK/m temperature gradientm−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]

See also

References
  1. Suplee, Curt (2 July 2009). "Special Publication 811". Nist.
  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 4 June 2021, retrieved 16 December 2021
  3. "Resolution 8 of the CGPM at its 20th Meeting (1995)". Bureau International des Poids et Mesures. Retrieved 23 September 2014.

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.{{cite book}}: CS1 maint: multiple names: authors list (link)
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