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 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", 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 s1
radian rad angle m/m 1
steradian sr solid angle m2/m2 1
newton N force, weight kg⋅m/s2 kg⋅m⋅s2
pascal Pa pressure, stress N/m2 kg⋅m1⋅s2
joule J energy, work, heat m⋅N, C⋅V, W⋅s kg⋅m2⋅s2
watt W power, radiant flux J/s, V⋅A kg⋅m2⋅s3
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⋅s3⋅A1
farad F electrical capacitance C/V, s/Ω kg1⋅m2⋅s4⋅A2
ohm Ω electrical resistance, impedance, reactance 1/S, V/A kg⋅m2⋅s3⋅A2
siemens S electrical conductance 1/Ω, A/V kg1⋅m2⋅s3⋅A2
weber Wb magnetic flux J/A, T⋅m2 kg⋅m2⋅s2⋅A1
tesla T magnetic induction, magnetic flux density V⋅s/m2, Wb/m2, N/(A⋅m) kg⋅s2⋅A1
henry H electrical inductance V⋅s/A, Ω⋅s, Wb/A kg⋅m2⋅s2⋅A2
degree Celsius °C temperature relative to 273.15 K K K
lumen lm luminous flux cd⋅sr cd
lux lx illuminance lm/m2 cd⋅m2
becquerel Bq radioactivity (decays per unit time) 1/s s1
gray Gy absorbed dose (of ionizing radiation) J/kg m2⋅s2
sievert Sv equivalent dose (of ionizing radiation) J/kg m2⋅s2
katal kat catalytic activity mol/s s1⋅mol

Examples of derived quantities and units

Kinematic SI derived units
Name Symbol Quantity Expression in terms
of SI base units
metre per secondm/s speed, velocityms1
metre per second squaredm/s2 accelerationms2
metre per second cubedm/s3 jerk, joltms3
metre per second to the fourthm/s4 snap, jouncems4
radian per secondrad/s angular velocitys1
radian per second squaredrad/s2 angular accelerations2
hertz per secondHz/s frequency drifts2
cubic metre per secondm3/s volumetric flowm3s1
Mechanical SI derived units
Name Symbol Quantity Expression in terms
of SI base units
square metrem2 aream2
cubic metrem3 volumem3
newton secondNs momentum, impulsemkgs1
newton metre secondNms angular momentumm2kgs1
newton metreNm = J/rad torque, moment of forcem2kgs2
newton per secondN/s yankmkgs3
reciprocal metrem1 wavenumber, optical power, curvature, spatial frequencym1
kilogram per square metrekg/m2 area densitym2kg
kilogram per cubic metrekg/m3 density, mass densitym3kg
cubic metre per kilogramm3/kg specific volumem3kg1
joule secondJs actionm2kgs1
joule per kilogramJ/kg specific energym2s2
joule per cubic metreJ/m3 energy densitym1kgs2
newton per metreN/m = J/m2 surface tension, stiffnesskgs2
watt per square metreW/m2 heat flux density, irradiancekgs3
square metre per secondm2/s kinematic viscosity, thermal diffusivity, diffusion coefficient m2s1
pascal secondPas = Ns/m2 dynamic viscositym1kgs1
kilogram per metrekg/m linear mass densitym1kg
kilogram per secondkg/s mass flow ratekgs1
watt per steradian square metreW/(srm2) radiancekgs3
watt per steradian cubic metreW/(srm3) spectral radiancem1kgs3
watt per metreW/m spectral powermkgs3
gray per secondGy/s absorbed dose ratem2s3
metre per cubic metrem/m3 fuel efficiencym2
watt per cubic metreW/m3 spectral irradiance, power densitym1kgs3
joule per square metre secondJ/(m2s) energy flux densitykgs3
reciprocal pascalPa1 compressibilitymkg1s2
joule per square metreJ/m2 radiant exposurekgs2
kilogram square metrekgm2 moment of inertiam2kg
newton metre second per kilogramNms/kg specific angular momentumm2s1
watt per steradianW/sr radiant intensitym2kgs3
watt per steradian metreW/(srm) spectral intensitymkgs3
Molar SI derived units
Name Symbol Quantity Expression in terms
of SI base units
mole per cubic metremol/m3 molarity, amount of substance concentrationm3mol
cubic metre per molem3/mol molar volumem3mol1
joule per kelvin moleJ/(Kmol) molar heat capacity, molar entropy m2kgs2K1mol1
joule per moleJ/mol molar energym2kgs2mol1
siemens square metre per moleSm2/mol molar conductivitykg−1s3A2mol1
mole per kilogrammol/kg molalitykg1mol
kilogram per molekg/mol molar masskgmol1
cubic metre per mole secondm3/(mols) catalytic efficiencym3s1mol1
Electromagnetic SI derived units
Name Symbol Quantity Expression in terms
of SI base units
coulomb per square metreC/m2 electric displacement field, polarization densitym2sA
coulomb per cubic metreC/m3 electric charge densitym3sA
ampere per square metreA/m2 electric current densitym2A
siemens per metreS/m electrical conductivity m3kg1s3A2
farad per metreF/m permittivitym3kg1s4A2
henry per metreH/m magnetic permeabilitymkgs2A2
volt per metreV/m electric field strengthmkgs3A1
ampere per metreA/m magnetization, magnetic field strengthm1A
coulomb per kilogramC/kg exposure (X and gamma rays)kg1sA
ohm metreΩm resistivitym3kgs3A2
coulomb per metreC/m linear charge densitym1sA
joule per teslaJ/T magnetic dipole momentm2A
square metre per volt secondm2/(Vs) electron mobilitykg1s2A
reciprocal henryH1 magnetic reluctancem2kg1s2A2
weber per metreWb/m magnetic vector potentialmkgs2A1
weber metreWbm magnetic momentm3kgs2A1
tesla metreTm magnetic rigiditymkgs2A1
ampere radianArad magnetomotive forceA
metre per henrym/H magnetic susceptibilitym1kg1s2A2
Photometric SI derived units
Name Symbol Quantity Expression in terms
of SI base units
lumen secondlms luminous energyscd
lux secondlxs luminous exposurem2scd
candela per square metrecd/m2 luminancem2cd
lumen per wattlm/W luminous efficacym2kg1s3cd
Thermodynamic SI derived units
Name Symbol Quantity Expression in terms
of SI base units
joule per kelvinJ/K heat capacity, entropym2kgs2K1
joule per kilogram kelvinJ/(Kkg) specific heat capacity, specific entropy m2s2K1
watt per metre kelvinW/(mK) thermal conductivity mkgs3K1
kelvin per wattK/W thermal resistancem2kg1s3K
reciprocal kelvinK1 thermal expansion coefficientK1
kelvin per metreK/m temperature gradientm1K

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".
  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 14 August 2017
  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.CS1 maint: multiple names: authors list (link)
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