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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 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".

Contents

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
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
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 N force m⋅kg⋅s−2
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
pressure P Force per area m−1⋅kg⋅s−2
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
reciprocal mole mol−1 Avogadro constant 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 Ω⋅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
lux second lx⋅s luminous exposure m−2⋅s⋅cd
candela per square metre cd/m2 luminance m−2⋅cd
lumen per watt lm/W luminous efficacy m−2⋅kg−1⋅s3⋅cd
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

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.

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.

  • 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)

SI derived unit
SI derived unit Language Watch Edit 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 Contents 1 Derived units with special names 2 Examples of derived quantities and units 3 Other units used with SI 4 Supplementary units 5 See also 6 References 7 Bibliography 8 External linksDerived units with special names EditThe 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 Equivalentshertz Hz frequency 1 s s 1radian rad angle m m 1steradian sr solid angle m2 m2 1newton N force weight kg m s2 kg m s 2pascal Pa pressure stress N m2 kg m 1 s 2joule J energy work heat m N C V W s kg m2 s 2watt W power radiant flux J s V A kg m2 s 3coulomb C electric charge or quantity of electricity s A F V s Avolt V voltage electrical potential difference electromotive force W A J C kg m2 s 3 A 1farad F electrical capacitance C V s W kg 1 m 2 s4 A2ohm W electrical resistance impedance reactance 1 S V A kg m2 s 3 A 2siemens S electrical conductance 1 W A V kg 1 m 2 s3 A2weber Wb magnetic flux J A T m2 V s kg m2 s 2 A 1tesla T magnetic induction magnetic flux density V s m2 Wb m2 N A m kg s 2 A 1henry H electrical inductance V s A W s Wb A kg m2 s 2 A 2degree Celsius C temperature relative to 273 15 K K Klumen lm luminous flux cd sr cdlux lx illuminance lm m2 cd m 2becquerel Bq radioactivity decays per unit time 1 s s 1gray Gy absorbed dose of ionizing radiation J kg m2 s 2sievert Sv equivalent dose of ionizing radiation J kg m2 s 2katal kat catalytic activity mol s s 1 molExamples of derived quantities and units EditKinematic SI derived units Name Symbol Quantity Expression in terms of SI base unitsmetre per second m s speed velocity m s 1metre per second squared m s2 acceleration m s 2metre per second cubed m s3 jerk jolt m s 3metre per second to the fourth m s4 snap jounce m s 4radian per second rad s angular velocity s 1radian per second squared rad s2 angular acceleration s 2hertz per second Hz s frequency drift s 2cubic metre per second m3 s volumetric flow m3 s 1Mechanical SI derived units Name Symbol Quantity Expression in terms of SI base unitssquare metre m2 area m2cubic metre m3 volume m3newton N force m kg s 2newton second N s momentum impulse m kg s 1newton metre second N m s angular momentum m2 kg s 1newton metre N m J rad torque moment of force m2 kg s 2newton per second N s yank m kg s 3reciprocal metre m 1 wavenumber optical power curvature spatial frequency m 1kilogram per square metre kg m2 area density m 2 kgkilogram per cubic metre kg m3 density mass density m 3 kgcubic metre per kilogram m3 kg specific volume m3 kg 1joule second J s action m2 kg s 1joule per kilogram J kg specific energy m2 s 2joule per cubic metre J m3 energy density m 1 kg s 2newton per metre N m J m2 surface tension stiffness kg s 2watt per square metre W m2 heat flux density irradiance kg s 3square metre per second m2 s kinematic viscosity thermal diffusivity diffusion coefficient m2 s 1pascal second Pa s N s m2 dynamic viscosity m 1 kg s 1pressure P Force per area m 1 kg s 2kilogram per metre kg m linear mass density m 1 kgkilogram per second kg s mass flow rate kg s 1watt per steradian square metre W sr m2 radiance kg s 3watt per steradian cubic metre W sr m3 spectral radiance m 1 kg s 3watt per metre W m spectral power m kg s 3gray per second Gy s absorbed dose rate m2 s 3metre per cubic metre m m3 fuel efficiency m 2watt per cubic metre W m3 spectral irradiance power density m 1 kg s 3joule per square metre second J m2 s energy flux density kg s 3reciprocal pascal Pa 1 compressibility m kg 1 s2joule per square metre J m2 radiant exposure kg s 2kilogram square metre kg m2 moment of inertia m2 kgnewton metre second per kilogram N m s kg specific angular momentum m2 s 1watt per steradian W sr radiant intensity m2 kg s 3watt per steradian metre W sr m spectral intensity m kg s 3Molar SI derived units Name Symbol Quantity Expression in terms of SI base unitsmole per cubic metre mol m3 molarity amount of substance concentration m 3 molcubic metre per mole m3 mol molar volume m3 mol 1joule per kelvin mole J K mol molar heat capacity molar entropy m2 kg s 2 K 1 mol 1joule per mole J mol molar energy m2 kg s 2 mol 1siemens square metre per mole S m2 mol molar conductivity kg 1 s3 A2 mol 1mole per kilogram mol kg molality kg 1 molkilogram per mole kg mol molar mass kg mol 1cubic metre per mole second m3 mol s catalytic efficiency m3 s 1 mol 1reciprocal mole mol 1 Avogadro constant mol 1Electromagnetic SI derived units Name Symbol Quantity Expression in terms of SI base unitscoulomb per square metre C m2 electric displacement field polarization density m 2 s Acoulomb per cubic metre C m3 electric charge density m 3 s Aampere per square metre A m2 electric current density m 2 Asiemens per metre S m electrical conductivity m 3 kg 1 s3 A2farad per metre F m permittivity m 3 kg 1 s4 A2henry per metre H m magnetic permeability m kg s 2 A 2volt per metre V m electric field strength m kg s 3 A 1ampere per metre A m magnetization magnetic field strength m 1 Acoulomb per kilogram C kg exposure X and gamma rays kg 1 s Aohm metre W m resistivity m3 kg s 3 A 2coulomb per metre C m linear charge density m 1 s Ajoule per tesla J T magnetic dipole moment m2 Asquare metre per volt second m2 V s electron mobility kg 1 s2 Areciprocal henry H 1 magnetic reluctance m 2 kg 1 s2 A2weber per metre Wb m magnetic vector potential m kg s 2 A 1weber metre Wb m magnetic moment m3 kg s 2 A 1tesla metre T m magnetic rigidity m kg s 2 A 1ampere radian A rad magnetomotive force Ametre per henry m H magnetic susceptibility m 1 kg 1 s2 A2Photometric SI derived units Name Symbol Quantity Expression in terms of SI base unitslumen second lm s luminous energy s cdlux second lx s luminous exposure m 2 s cdcandela per square metre cd m2 luminance m 2 cdlumen per watt lm W luminous efficacy m 2 kg 1 s3 cdThermodynamic SI derived units Name Symbol Quantity Expression in terms of SI base unitsjoule per kelvin J K heat capacity entropy m2 kg s 2 K 1joule per kilogram kelvin J K kg specific heat capacity specific entropy m2 s 2 K 1watt per metre kelvin W m K thermal conductivity m kg s 3 K 1kelvin per watt K W thermal resistance m 2 kg 1 s3 Kreciprocal kelvin K 1 thermal expansion coefficient K 1kelvin per metre K m temperature gradient m 1 KOther units used with SI EditSome 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 EditUntil 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 EditInternational System of Quantities ISQ International Vocabulary of Metrology Metric prefix Metric systemReferences Edit Suplee Curt 2 July 2009 Special Publication 811 International Bureau of Weights and Measures 2006 The International System of Units SI PDF 8th ed ISBN 92 822 2213 6 archived from the original PDF on 14 August 2017 Resolution 8 of the CGPM at its 20th Meeting 1995 Bureau International des Poids et Mesures Retrieved 23 September 2014 Bibliography EditI 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 External links Edit Media related to SI derived units at Wikimedia Commons Physics portal Retrieved from https en wikipedia org w index php title SI derived unit amp oldid 1045266543, wikipedia, wiki, book,

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