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{{Short description|Measurement unit derived from basic metric value}}
{{Use dmy dates|date=August 2015}}

'''SI derived units''' are [[units of measurement]] [[derived unit|derived]] from the
seven [[SI base unit]]s 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 (mathematics)|power of exponentiation]] (see: [[Buckingham π theorem]]). Some are [[dimensionless quantity|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 factor]]s.

The SI has special names for 22 of these [[coherent derived unit]]s (for example, [[hertz]], the SI unit of measurement of frequency), but the rest merely reflect their derivation: for example, the [[square metre]] (m<sup>2</sup>), the SI derived unit of area; and the [[kilogram per cubic metre]] (kg/m<sup>3</sup> or kg⋅m<sup>−3</sup>), 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".<ref>{{cite journal|url=http://physics.nist.gov/Pubs/SP811/sec06.html|title=Special Publication 811|first=Curt|last=Suplee|journal=Nist |date=2 July 2009}}</ref>

==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).
{| class="wikitable sortable"
|+ style="font-size:larger;font-weight:bold;"|Named units derived from SI base units<ref>{{SIbrochure8th}}</ref>
|-
! Name
! [[Symbol]]
! [[Physical quantity|Quantity]]
! Equivalents
! [[SI base unit]]<br>Equivalents
|-
| [[hertz]]
| align = "center"| Hz
| [[frequency]]
| align = "center"| 1/s
| align = "center"| s<sup>−1</sup>
|-
| [[radian]]
| align = "center"| rad
| [[angle]]
| align = "center"| m/m
| align="center" | 1
|-
| [[steradian]]
| align = "center"| sr
| [[solid angle]]
| align = "center"| m<sup>2</sup>/m<sup>2</sup>
| align="center" | 1
|-
| [[newton (unit)|newton]]
| align = "center"| N
| [[force]], [[weight]]
| align = "center"| kg⋅m/s<sup>2</sup>
| align = "center"| kg⋅m⋅s<sup>−2</sup>
|-
| [[pascal (unit)|pascal]]
| align = "center"| Pa
| [[pressure]], [[Stress (physics)|stress]]
| align = "center"| N/m<sup>2</sup>
| align = "center"| kg⋅m<sup>−1</sup>⋅s<sup>−2</sup>
|-
| [[joule]]
| align = "center"| J
| [[energy]], [[Mechanical work|work]], [[heat]]
| align = "center"| m⋅N, C⋅V, W⋅s
| align = "center"| kg⋅m<sup>2</sup>⋅s<sup>−2</sup>
|-
| [[watt]]
| align = "center"| W
| [[Power (physics)|power]], [[radiant flux]]
| align = "center"| J/s, V⋅A
| align = "center"| kg⋅m<sup>2</sup>⋅s<sup>−3</sup>
|-
| [[coulomb]]
| align = "center"| C
| [[electric charge]] or [[quantity of electricity]]
| align = "center"| s⋅A, F⋅V
| align = "center"| s⋅A
|-
| [[volt]]
| align = "center"| V
| [[voltage]], [[electrical potential difference]], [[electromotive force]]
| align = "center"| W/A, J/C
| align = "center"| kg⋅m<sup>2</sup>⋅s<sup>−3</sup>⋅A<sup>−1</sup>
|-
| [[farad]]
| align = "center"| F
| [[capacitance|electrical capacitance]]
| align = "center"| C/V, s/Ω
| align = "center"| kg<sup>−1</sup>⋅m<sup>−2</sup>⋅s<sup>4</sup>⋅A<sup>2</sup>
|-
| [[ohm (unit)|ohm]]
| align = "center"| Ω
| [[electrical resistance and conductance|electrical resistance]], [[electrical impedance|impedance]], [[Reactance (electronics)|reactance]]
| align = "center"| 1/S, V/A
| align = "center"| kg⋅m<sup>2</sup>⋅s<sup>−3</sup>⋅A<sup>−2</sup>
|-
| [[Siemens (unit)|siemens]]
| align = "center"| S
| [[electrical conductance]]
| align = "center"| 1/Ω, A/V
| align = "center"| kg<sup>−1</sup>⋅m<sup>−2</sup>⋅s<sup>3</sup>⋅A<sup>2</sup>
|-
| [[Weber (unit)|weber]]
| align = "center"| Wb
| [[magnetic flux]]
| align = "center"| J/A, T⋅m<sup>2</sup>,V⋅s
| align = "center"| kg⋅m<sup>2</sup>⋅s<sup>−2</sup>⋅A<sup>−1</sup>
|-
| [[tesla (unit)|tesla]]
| align = "center"| T
| [[magnetic field|magnetic induction]], [[magnetic flux density]]
| align = "center"| V⋅s/m<sup>2</sup>, Wb/m<sup>2</sup>, N/(A⋅m) 
| align = "center"| kg⋅s<sup>−2</sup>⋅A<sup>−1</sup>
|-
| [[henry (unit)|henry]]
| align = "center"| H
| [[inductance|electrical inductance]]
| align = "center"| V⋅s/A, Ω⋅s, Wb/A
| align = "center"| kg⋅m<sup>2</sup>⋅s<sup>−2</sup>⋅A<sup>−2</sup>
|-
| [[Celsius|degree Celsius]]
| align = "center"| °C
| [[temperature]] relative to [[Absolute zero|273.15 K]]
| align = "center"| K
| align = "center"| K
|-
| [[lumen (unit)|lumen]]
| align = "center"| lm
| [[luminous flux]] 
| align = "center"| cd⋅sr
| align = "center"| cd
|-
| [[lux]]
| align = "center"| lx
| [[illuminance]]
| align = "center"| lm/m<sup>2</sup>
| align = "center"| cd⋅m<sup>−2</sup>
|-
| [[becquerel]]
| align = "center"| Bq
| [[radioactivity]] (decays per unit time)
| align = "center"| 1/s
| align = "center"| s<sup>−1</sup>
|-
| [[gray (unit)|gray]]
| align = "center"| Gy
| [[absorbed dose]] (of [[ionizing radiation]])
| align = "center"| J/kg
| align = "center"| m<sup>2</sup>⋅s<sup>−2</sup>
|-
| [[sievert]]
| align = "center"| Sv
| [[equivalent dose]] (of [[ionizing radiation]])
| align = "center"| J/kg
| align = "center"| m<sup>2</sup>⋅s<sup>−2</sup>
|-
| [[katal]]
| align = "center"| kat
| [[catalytic activity]]
| align = "center"| mol/s
| align = "center"| s<sup>−1</sup>⋅mol.
|}

==By field of application==

===Kinematics===
{| class="wikitable sortable"
|-
! Name
! Symbol
! Quantity
! Expression in terms<br> of SI base units
|-
| [[metre per second]] || m/s
| [[speed]], [[velocity]] || m⋅s<sup>−1</sup>
|-
| [[metre per second squared]] || m/s<sup>2</sup>
| [[acceleration]] || m⋅s<sup>−2</sup>
|-
| metre per second cubed || m/s<sup>3</sup>
| [[jerk (physics)|jerk, jolt]] || m⋅s<sup>−3</sup>
|-
| metre per second to the fourth || m/s<sup>4</sup>
| [[jounce|snap, jounce]] || m⋅s<sup>−4</sup>
|-
| kilogram metre per second to the third ||kg⋅m/s<sup>3</sup>
| [[Yank (physics)|yank]]|| m⋅kg⋅s<sup>−3</sup>
|-
| [[radian per second]] || rad/s
| [[angular velocity]] || s<sup>−1</sup>
|-
| [[radian per second squared]] || rad/s<sup>2</sup>
| [[angular acceleration]] || s<sup>−2</sup>
|-
| hertz per second || Hz/s
| [[frequency drift]] || s<sup>−2</sup>
|-
| [[cubic metre per second]] || m<sup>3</sup>/s
| [[volumetric flow]] || m<sup>3</sup>⋅s<sup>−1</sup>
|}

===Mechanics===
{| class="wikitable sortable"
|-
! Name
! Symbol
! Quantity
! Expression in terms<br> of SI base units
|-
| [[square metre]] || m<sup>2</sup>
| [[area]] || m<sup>2</sup>
|-
| [[cubic metre]] || m<sup>3</sup>
| [[volume]] || m<sup>3</sup>
|-
| [[newton-second]] || N⋅s
| [[momentum]], [[Impulse (physics)|impulse]] || m⋅kg⋅s<sup>−1</sup>
|-
| newton metre second || N⋅m⋅s
| [[angular momentum]] || m<sup>2</sup>⋅kg⋅s<sup>−1</sup>
|-
| [[newton-metre]] || N⋅m = J/rad
| [[torque|torque, moment of force]] || m<sup>2</sup>⋅kg⋅s<sup>−2</sup>
|-
| newton per second || N/s
| [[Yank (physics)|yank]] || m⋅kg⋅s<sup>−3</sup>
|-
| [[reciprocal metre]] || m<sup>−1</sup>
| [[wavenumber]], [[optical power]], [[curvature]], [[spatial frequency]] || m<sup>−1</sup>
|-
| kilogram per square metre || kg/m<sup>2</sup>
| [[area density]] || m<sup>−2</sup>⋅kg
|-
| [[kilogram per cubic metre]] || kg/m<sup>3</sup>
| [[density]], mass density || m<sup>−3</sup>⋅kg
|-
| cubic metre per kilogram || m<sup>3</sup>/kg
| [[specific volume]] || m<sup>3</sup>⋅kg<sup>−1</sup>
|-
| [[joule-second]] || J⋅s
| [[Action (physics)|action]] || m<sup>2</sup>⋅kg⋅s<sup>−1</sup>
|-
| joule per kilogram || J/kg
| [[specific energy]] || m<sup>2</sup>⋅s<sup>−2</sup>
|-
| joule per cubic metre || J/m<sup>3</sup>
| [[energy density]] || m<sup>−1</sup>⋅kg⋅s<sup>−2</sup>
|-
| newton per metre || N/m = J/m<sup>2</sup>
| [[surface tension]], [[stiffness]] || kg⋅s<sup>−2</sup>
|-
| watt per square metre || W/m<sup>2</sup>
| heat flux density, [[irradiance]] || kg⋅s<sup>−3</sup>
|-
| square metre per second || m<sup>2</sup>/s
| [[kinematic viscosity]], [[thermal diffusivity]], [[diffusion]] coefficient
| m<sup>2</sup>⋅s<sup>−1</sup>
|-
| [[pascal-second]] || Pa⋅s = N⋅s/m<sup>2</sup>
| dynamic [[viscosity]] || m<sup>−1</sup>⋅kg⋅s<sup>−1</sup>
|-
| kilogram per metre || kg/m
| [[linear mass density]] || m<sup>−1</sup>⋅kg
|-
| kilogram per second || kg/s
| [[mass flow rate]] || kg⋅s<sup>−1</sup>
|-
| watt per steradian square metre || W/(sr⋅m<sup>2</sup>)
| [[radiance]] || kg⋅s<sup>−3</sup>
|-
| watt per steradian cubic metre || W/(sr⋅m<sup>3</sup>)
| [[radiance]] || m<sup>−1</sup>⋅kg⋅s<sup>−3</sup>
|-
| watt per metre || W/m
| [[spectral power]] || m⋅kg⋅s<sup>−3</sup>
|-
| gray per second || Gy/s
| [[absorbed dose]] rate || m<sup>2</sup>⋅s<sup>−3</sup>
|-
| metre per cubic metre  || m/m<sup>3</sup>
| [[fuel efficiency]] || m<sup>−2</sup>
|-
| watt per cubic metre || W/m<sup>3</sup>
| [[spectral irradiance]], [[power density]] || m<sup>−1</sup>⋅kg⋅s<sup>−3</sup>
|-
| joule per square metre second || J/(m<sup>2</sup>⋅s)
| [[energy flux density]] || kg⋅s<sup>−3</sup>
|-
| reciprocal pascal || Pa<sup>−1</sup>
| [[compressibility]] || m⋅kg<sup>−1</sup>⋅s<sup>2</sup>
|-
| joule per square metre || J/m<sup>2</sup>
| [[radiant exposure]] || kg⋅s<sup>−2</sup>
|-
| kilogram square metre || kg⋅m<sup>2</sup>
| [[moment of inertia]] || m<sup>2</sup>⋅kg
|-
| newton metre second per kilogram || N⋅m⋅s/kg
| [[specific angular momentum]] || m<sup>2</sup>⋅s<sup>−1</sup>
|-
| watt per steradian || W/sr
| [[radiant intensity]] || m<sup>2</sup>⋅kg⋅s<sup>−3</sup>
|-
| watt per steradian metre || W/(sr⋅m)
| [[spectral intensity]] || m⋅kg⋅s<sup>−3</sup>
|}

===Chemistry===
{| class="wikitable sortable"
|-
! Name
! Symbol
! Quantity
! Expression in terms<br> of SI base units
|-
| mole per cubic metre || mol/m<sup>3</sup>
| [[molarity]], amount of substance concentration || m<sup>−3</sup>⋅mol
|-
| [[cubic metre per mole]] || m<sup>3</sup>/mol
| [[molar volume]] || m<sup>3</sup>⋅mol<sup>−1</sup>
|-
| joule per kelvin mole || J/(K⋅mol)
| [[molar heat capacity]], molar entropy
| m<sup>2</sup>⋅kg⋅s<sup>−2</sup>⋅K<sup>−1</sup>⋅mol<sup>−1</sup>
|-
| [[joule per mole]] || J/mol
| molar energy || m<sup>2</sup>⋅kg⋅s<sup>−2</sup>⋅mol<sup>−1</sup>
|-
| siemens square metre per mole || S⋅m<sup>2</sup>/mol
| [[molar conductivity]] || kg<sup>−1</sup>⋅s<sup>3</sup>⋅A<sup>2</sup>⋅mol<sup>−1</sup>
|-
| mole per kilogram || mol/kg
| [[molality]] || kg<sup>−1</sup>⋅mol
|-
| kilogram per mole || kg/mol
| [[molar mass]] || kg⋅mol<sup>−1</sup>
|-
| cubic metre per mole second || m<sup>3</sup>/(mol⋅s)
| [[catalytic efficiency]] || m<sup>3</sup>⋅s<sup>−1</sup>⋅mol<sup>−1</sup>
|}

===Electromagnetics===
{| class="wikitable sortable"
|-
! Name
! Symbol
! Quantity
! Expression in terms<br> of SI base units
|-
| coulomb per square metre || C/m<sup>2</sup>
| [[electric displacement field]], [[polarization density]] || m<sup>−2</sup>⋅s⋅A
|-
| coulomb per cubic metre || C/m<sup>3</sup>
| electric [[charge density]] || m<sup>−3</sup>⋅s⋅A
|-
| ampere per square metre || A/m<sup>2</sup>
| electric [[current density]] || m<sup>−2</sup>⋅A
|-
| [[siemens per metre]] || S/m
| [[electrical conductivity]]
| m<sup>−3</sup>⋅kg<sup>−1</sup>⋅s<sup>3</sup>⋅A<sup>2</sup>
|-
| farad per metre || F/m
| [[permittivity]] || m<sup>−3</sup>⋅kg<sup>−1</sup>⋅s<sup>4</sup>⋅A<sup>2</sup>
|-
| henry per metre || H/m
| [[magnetic permeability]] || m⋅kg⋅s<sup>−2</sup>⋅A<sup>−2</sup>
|-
| volt per metre || V/m
| [[electric field]] strength || m⋅kg⋅s<sup>−3</sup>⋅A<sup>−1</sup>
|-
| ampere per metre || A/m
| [[magnetization]], [[magnetic field]] strength || m<sup>−1</sup>⋅A
|-
| coulomb per kilogram || C/kg
| [[ionizing radiation|exposure]] ([[x-ray|X]] and [[gamma ray]]s) || kg<sup>−1</sup>⋅s⋅A
|-
| [[ohm metre]] || Ω⋅m
| [[resistivity]] || m<sup>3</sup>⋅kg⋅s<sup>−3</sup>⋅A<sup>−2</sup>
|-
| coulomb per metre || C/m
| [[linear density|linear charge density]] || m<sup>−1</sup>⋅s⋅A
|-
| joule per tesla || J/T
| [[magnetic dipole moment]] || m<sup>2</sup>⋅A
|-
| square metre per volt second || m<sup>2</sup>/(V⋅s)
| [[electron mobility]] || kg<sup>−1</sup>⋅s<sup>2</sup>⋅A
|-
| reciprocal henry || H<sup>−1</sup>
| [[magnetic reluctance]] || m<sup>−2</sup>⋅kg<sup>−1</sup>⋅s<sup>2</sup>⋅A<sup>2</sup>
|-
| weber per metre || Wb/m
| [[magnetic vector potential]] || m⋅kg⋅s<sup>−2</sup>⋅A<sup>−1</sup>
|-
| weber metre || Wb⋅m
| [[magnetic moment]] || m<sup>3</sup>⋅kg⋅s<sup>−2</sup>⋅A<sup>−1</sup>
|-
| tesla metre || T⋅m
| [[magnetic rigidity]] || m⋅kg⋅s<sup>−2</sup>⋅A<sup>−1</sup>
|-
| ampere radian || A⋅rad
| [[magnetomotive force]] || A
|-
| metre per henry || m/H
| [[magnetic susceptibility]] || m<sup>−1</sup>⋅kg<sup>−1</sup>⋅s<sup>2</sup>⋅A<sup>2</sup>
|}

===Photometry===
{| class="wikitable sortable"
|-
! Name
! Symbol
! Quantity
! Expression in terms<br> of SI base units
|-
| [[lumen second]] || lm⋅s
| [[luminous energy]] || s⋅cd
|-
| [[lux second]] || lx⋅s
| [[luminous exposure]] || m<sup>−2</sup>⋅s⋅cd
|-
| [[candela per square metre]] || cd/m<sup>2</sup>
| [[luminance]] || m<sup>−2</sup>⋅cd
|-
| lumen per watt || lm/W
| [[luminous efficacy]] || m<sup>−2</sup>⋅kg<sup>−1</sup>⋅s<sup>3</sup>⋅cd
|}

===Thermodynamics===
{| class="wikitable sortable"
|-
! Name
! Symbol
! Quantity
! Expression in terms<br> of SI base units
|-
| joule per kelvin || J/K
| [[heat capacity]], [[entropy]] || m<sup>2</sup>⋅kg⋅s<sup>−2</sup>⋅K<sup>−1</sup>
|-
| joule per kilogram kelvin || J/(K⋅kg)
| [[specific heat capacity]], specific entropy
| m<sup>2</sup>⋅s<sup>−2</sup>⋅K<sup>−1</sup>
|-
| watt per metre kelvin || W/(m⋅K)
| [[thermal conductivity]]
| m⋅kg⋅s<sup>−3</sup>⋅K<sup>−1</sup>
|-
| kelvin per watt || K/W
| [[thermal resistance]] || m<sup>−2</sup>⋅kg<sup>−1</sup>⋅s<sup>3</sup>⋅K
|-
| reciprocal kelvin || K<sup>−1</sup>
| [[thermal expansion coefficient]] || K<sup>−1</sup>
|-
| kelvin per metre || K/m
| [[temperature gradient]] || m<sup>−1</sup>⋅K
|}

==Other units used with SI==
Some other units such as the [[hour]], [[litre]], [[tonne]], [[Bar (unit)|bar]], and [[electronvolt]] are [[Non-SI units accepted for use with SI|not SI units]], but are widely used in conjunction with SI units.

==Supplementary units{{anchor|SI supplementary unit}}==
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.<ref>{{cite web | title = Resolution 8 of the CGPM at its 20th Meeting (1995) | url = http://www.bipm.org/en/CGPM/db/20/8/ | access-date = 2014-09-23 | publisher = [[Bureau International des Poids et Mesures]]}}</ref>

==See also==
* [[Coherent derived unit]]
* [[International System of Quantities]] (ISQ)
* [[International Vocabulary of Metrology]]
* [[List of physical quantities]]
* [[Metric prefix]]
* [[Metric system]]

==References==
{{reflist}}

==Bibliography==
* {{cite book|author=I. Mills, Tomislav Cvitas, Klaus Homann, Nikola Kallay, IUPAC|title=Quantities, Units and Symbols in Physical Chemistry|edition= 2nd|date=June 1993|publisher= Blackwell Science Inc |page=72}}

==External links==
* {{Commonscatinline}}

{{SI units}}
{{Portal bar|Physics}}

[[Category:SI units|Derived]]
[[Category:SI derived units| ]]

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