Editing International System of Units (section)

== Definition ==

<!-- no wikilinks in this paragraph please -->
The International System of Units consists of a set of seven defining constants with seven corresponding base units, derived units, and a set of decimal-based multipliers that are used as prefixes.<ref name="SIBrochure9thEd"/>{{rp|page=125}}

=== SI defining constants ===

{| class="wikitable floatright" style="width: 400px; text-align:center;"
|+ SI defining constants
! scope="col" | Symbol
! scope="col" | Defining constant
! scope="col" | Exact value
|-
! scope="row" | {{math|Δ''ν''<sub>Cs</sub>}}
| [[Caesium standard|hyperfine transition frequency of <sup>133</sup>Cs]] || {{val|9192631770|u=Hz}}
|-
! scope="row" | {{mvar|c}}
| [[speed of light]] || {{val|299792458|u=m/s}}
|-
! scope="row" | {{mvar|h}}
| [[Planck constant]] || {{val|6.62607015|e=-34|u=J.s}}
|-
! scope="row" | {{mvar|e}}
| [[elementary charge]] || {{val|1.602176634|e=-19|u=C}}
|-
! scope="row" | {{mvar|k}}
| [[Boltzmann constant]] || {{val|1.380649|e=-23|u=J/K}}
|-
! scope="row" | {{Math|''N''<sub>A</sub>}}
| [[Avogadro constant]] || {{val|6.02214076|e=23|u=mol-1}}
|-
! scope="row" | {{Math|''K''<sub>cd</sub>}}
| [[luminous efficacy]] of {{val|540|u=THz}} radiation || {{val|683|u=lm/W}}
|}
The seven defining constants are the most fundamental feature of the definition of the system of units.<ref name="SIBrochure9thEd"/>{{rp|page=125}}
The magnitudes of all SI units are defined by declaring that seven constants have certain exact numerical values when expressed in terms of their SI units. These defining constants are the [[speed of light]] in vacuum {{Math|''c''}}, the [[caesium standard|hyperfine transition frequency of caesium]] {{math|Δ''ν''{{sub|Cs}}}}, the [[Planck constant]] {{Math|''h''}}, the [[elementary charge]] {{Math|''e''}}, the [[Boltzmann constant]] {{Math|''k''}}, the [[Avogadro constant]] {{Math|''N''<sub>A</sub>}}, and the [[luminous efficacy]] {{Math|''K''<sub>cd</sub>}}. The nature of the defining constants ranges from fundamental constants of nature such as {{Math|''c''}} to the purely technical constant {{Math|''K''<sub>cd</sub>}}. The values assigned to these constants were fixed to ensure continuity with previous definitions of the base units.<ref name="SIBrochure9thEd"/>{{rp|page=128}}

=== SI base units ===

{{Main|SI base unit}}

The SI selects seven units to serve as [[SI base unit|base unit]]s, corresponding to seven base physical quantities. They are the [[second]], with the symbol {{val|u=s}}, which is the SI unit of the physical quantity of [[time]]; the [[metre]], symbol {{val|u=m}}, the SI unit of [[length]]; [[kilogram]] ({{val|u=kg}}, the unit of [[mass]]); [[ampere]] ({{val|u=A}}, [[electric current]]); [[kelvin]] ({{val|u=K}}, [[thermodynamic temperature]]); [[Mole (unit)|mole]] ({{val|u=mol}}, [[amount of substance]]); and [[candela]] ({{val|u=cd}}, [[luminous intensity]]).<ref name="SIBrochure9thEd" />
The base units are defined in terms of the defining constants.  For example, the kilogram is defined by taking the Planck constant {{math|''h''}} to be {{val|6.62607015|e=-34|u=J.s}}, giving the expression in terms of the defining constants<ref name="SIBrochure9thEd" />{{rp|page=131}}
: {{nowrap|1={{val|1|u=kg}} = {{sfrac|({{val|299792458}}){{sup|2}}|({{val|6.62607015|e=-34}})({{val|9192631770}})}}{{sfrac|{{math|''h''}}{{thin space}}{{math|Δ''ν''{{sub|Cs}}}}|{{math|''c''}}{{sup|2}}}}.}}
All units in the SI can be expressed in terms of the base units, and the base units serve as a preferred set for expressing or analysing the relationships between units. The choice of which and even how many quantities to use as base quantities is not fundamental or even unique – it is a matter of convention.<ref name="SIBrochure9thEd" />{{rp|page=126|quote=[...] the choice of the base units was never unique, but grew historically and became familiar to users of the SI}}

{| class="wikitable" style="margin:1em auto 1em auto"
|+ <big>SI base units</big><ref name="SIBrochure9thEd"/>{{rp|page=136}}
|-
 ! scope="col" | Unit name
 ! scope="col" | Unit symbol
 ! scope="col" | [[Dimensional analysis#Definition|Dimension symbol]]
 ! scope="col" | [[Physical quantity|Quantity name]]
 ! scope="col" width=80 |Typical symbols
 ! scope="col" | Definition
|-
 ! scope="row" | [[second]]
 |style="text-align:center" |s
 |style="text-align:center" |<math>\mathsf{T}</math>
 | [[time]]
 |<math>t</math>
 |The duration of {{val|9192631770}} periods of the radiation corresponding to the transition between the two [[hyperfine structure|hyperfine]] levels of the [[ground state]] of the [[caesium-133]] atom.
|-
 ! scope="row" | [[metre]]
 |style="text-align:center" |m
 |style="text-align:center" |<math>\mathsf{L}</math>
 |[[length]]
 |<math>l</math>, <math>x</math>, <math>r</math>, etc.
 |The distance travelled by light in vacuum in {{sfrac|{{val|299792458}}}} second.
|-
 ! scope="row" | [[kilogram]]{{br}}<ref group="n">Despite the prefix "kilo-", the kilogram is the coherent base unit of mass, and is used in the definitions of derived units. Nonetheless, prefixes for the unit of mass are determined as if the gram were the base unit.</ref>
 |style="text-align:center" |kg
 |style="text-align:center" |<math>\mathsf{M}</math>
 |[[mass]]
 |<math>m</math>
 |The kilogram is defined by setting the [[Planck constant]] {{math|''h''}} to {{val|6.62607015|e=-34|u=J.s}} ({{nowrap|1=J = kg⋅m{{sup|2}}⋅s{{sup|−2}}}}), given the definitions of the metre and the second.<ref name="NIST 2018-11">{{cite news|url=https://www.nist.gov/news-events/news/2018/11/historic-vote-ties-kilogram-and-other-units-natural-constants|title=Historic Vote Ties Kilogram and Other Units to Natural Constants|last=Materese|first=Robin|date=16 November 2018|work=NIST|access-date=16 November 2018}}</ref>
|-
 ! scope="row" | [[ampere]]
 |style="text-align:center" |A
 |style="text-align:center" |<math>\mathsf{I}</math>
 |[[electric current]]
 |<math>I,\; i</math>
 |The flow of {{sfrac|1|{{val|1.602176634|e=-19}}}} times the [[elementary charge]] {{math|''e''}} per second, which is approximately {{val|6.2415090744|e=18}} elementary charges per second.
|-
 ! scope="row" | [[kelvin]]
 |style="text-align:center" |K
 |style="text-align:center" |<math>\mathsf{\Theta}</math>
 |[[thermodynamic temperature|thermodynamic{{br}}temperature]]
 |<math>T</math>
 |The kelvin is defined by setting the fixed numerical value of the [[Boltzmann constant]] {{math|''k''}} to {{val|1.380649|e=-23|u=J.K-1}}, ({{nowrap|1=J = kg⋅m<sup>2</sup>⋅s<sup>−2</sup>}}), given the definition of the kilogram, the metre, and the second.
|-
 ! scope="row" | [[mole (unit)|mole]]
 |style="text-align:center" |mol
 |style="text-align:center" |<math>\mathsf{N}</math>
 |[[amount of substance]]
 |<math>n</math>
 |The amount of substance of {{val|6.02214076|e=23}} elementary entities.<ref group="n">When the mole is used, the elementary entities must be specified and may be [[atom]]s, [[molecule]]s, [[ion]]s, [[electron]]s, other particles, or specified groups of such particles.</ref> This number is the fixed numerical value of the [[Avogadro constant]], {{math|''N''<sub>A</sub>}}, when expressed in the unit mol<sup>−1</sup>.
|-
 ! scope="row" | [[candela]]
 |style="text-align:center" |cd
 |style="text-align:center" |<math>\mathsf{J}</math>
 |[[luminous intensity]]
 |<math>I_{\rm v}</math>
 |The luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency {{val|5.4|e=14|u=hertz}} and that has a radiant intensity in that direction of {{sfrac|1|683}} watt per [[steradian]].
|-
 | colspan="6" |
; Notes
{{reflist|group="n"}}
|}

=== Derived units ===

{{Main|SI derived unit}}
The system allows for an unlimited number of additional units, called ''[[SI derived unit|derived units]]'', which can always be represented as products of powers of the base units, possibly with a nontrivial numeric multiplier. When that multiplier is one, the unit is called a ''[[coherence (units of measurement)|coherent]]'' derived unit. For example, the coherent derived SI unit of [[velocity]] is the [[metre per second]], with the symbol {{val|u=m/s}}.<ref name=SIBrochure9thEd/>{{rp|page=139}} The base and coherent derived units of the SI together form a coherent system of units (''the set of coherent SI units''). A useful property of a coherent system is that when the numerical values of physical quantities are expressed in terms of the units of the system, then the equations between the numerical values have exactly the same form, including numerical factors, as the corresponding equations between the physical quantities.<ref name="ISO80000-1">{{cite ISO standard|csnumber=30669|title=ISO 80000-1:2009 Quantities and units – Part 1: General}}</ref>{{rp|page=6}}

Twenty-two coherent derived units have been provided with special names and symbols as shown in the table below. The radian and steradian have no base units but are treated as derived units for historical reasons.<ref name=SIBrochure9thEd/>{{rp|page=137}}

{| class="wikitable floatleft" style="margin:1em auto 1em auto;line-height:1.4"
|+ <big>The 22 SI derived units with special names and symbols</big><ref name=SIBrochure9thEd/>{{rp|page=137}}
|-
! scope="col" | Name
! scope="col" | Symbol
! scope="col" | Quantity
! scope="col" | In SI base units
! scope="col" | In other SI units
|-
! scope="row" | [[radian]]<ref name=":0" group="nc">The radian and steradian are defined as dimensionless derived units.</ref>
| style="text-align:center;" | rad
| [[angle|plane angle]]
| style="text-align:center;" | <!-- intentionally left blank to reflect version 3.01 (2024) of the 9th SI brochure -->
| style="text-align:center;" | 1
|-
! scope="row" | [[steradian]]<ref name=":0" group="nc" />
| style="text-align:center;" | sr
| [[solid angle]]
| style="text-align:center;" | <!-- intentionally left blank to reflect version 3.01 (2024) of the 9th SI brochure -->
| style="text-align:center;" | 1
|-
! scope="row" | [[hertz]]
| style="text-align:center;" | Hz
| [[frequency]]
| style="text-align:center;" | s<sup>−1</sup>
| <!-- intentionally left blank -->
|-
! scope="row" | [[newton (unit)|newton]]
| style="text-align:center;" | N
| [[force]] 
| style="text-align:center;" | kg⋅m⋅s<sup>−2</sup>
| <!-- intentionally left blank -->
|-
! scope="row" | [[pascal (unit)|pascal]]
| style="text-align:center;" | Pa
| [[pressure]], [[stress (physics)|stress]]
| style="text-align:center;" | kg⋅m<sup>−1</sup>⋅s<sup>−2</sup>
| style="text-align:center;" | N/m<sup>2</sup> = J/m<sup>3</sup>
|-
! scope="row" | [[joule]]
| style="text-align:center;" | J
| [[energy]], [[mechanical work|work]], amount of [[heat]]
| style="text-align:center;" | kg⋅m<sup>2</sup>⋅s<sup>−2</sup>
| style="text-align:center;" | N⋅m = Pa⋅m<sup>3</sup>
|-
! scope="row" | [[watt]]
| style="text-align:center;" | W
| [[Power (physics)|power]], [[radiant flux]]
| style="text-align:center;" | kg⋅m<sup>2</sup>⋅s<sup>−3</sup>
| style="text-align:center;" | J/s
|-
! scope="row" | [[coulomb]]
| style="text-align:center;" | C
| [[electric charge]]
| style="text-align:center;" | s⋅A
| <!-- intentionally left blank -->
|-
! scope="row" | [[volt]]
| style="text-align:center;" | V
| [[electric potential difference]]{{efn|Electric potential difference is also called "voltage" in many countries, as well as "electric tension" or simply "tension" in some countries.}}
| style="text-align:center;" | kg⋅m<sup>2</sup>⋅s<sup>−3</sup>⋅A<sup>−1</sup>
| style="text-align:center;" | W/A = J/C
|-
! scope="row" | [[farad]]
| style="text-align:center;" | F
| [[capacitance]]
| style="text-align:center;" | kg<sup>−1</sup>⋅m<sup>−2</sup>⋅s<sup>4</sup>⋅A<sup>2</sup>
| style="text-align:center;" | C/V = C<sup>2</sup>/J
|-
! scope="row" | [[ohm (unit)|ohm]]
| style="text-align:center;" | Ω
| [[electrical resistance]]
| style="text-align:center;" | kg⋅m<sup>2</sup>⋅s<sup>−3</sup>⋅A<sup>−2</sup>
| style="text-align:center;" | V/A = J⋅s/C<sup>2</sup>
|-
! scope="row" | [[siemens (unit)|siemens]]
| style="text-align:center;" | S
| [[electrical conductance]]
| style="text-align:center;" | kg<sup>−1</sup>⋅m<sup>−2</sup>⋅s<sup>3</sup>⋅A<sup>2</sup>
| style="text-align:center;" | Ω<sup>−1</sup>
|-
! scope="row" | [[weber (unit)|weber]]
| style="text-align:center;" | Wb
| [[magnetic flux]]
| style="text-align:center;" | kg⋅m<sup>2</sup>⋅s<sup>−2</sup>⋅A<sup>−1</sup>
| style="text-align:center;" | V⋅s
|-
! scope="row" | [[tesla (unit)|tesla]]
| style="text-align:center;" | T
| [[magnetic flux density]]
| style="text-align:center;" | kg⋅s<sup>−2</sup>⋅A<sup>−1</sup>
| style="text-align:center;" | Wb/m<sup>2</sup>
|-
! scope="row" | [[henry (unit)|henry]]
| style="text-align:center;" | H
| [[inductance]]
| style="text-align:center;" | kg⋅m<sup>2</sup>⋅s<sup>−2</sup>⋅A<sup>−2</sup>
| style="text-align:center;" | Wb/A
|-
! scope="row" | [[degree Celsius]]
| style="text-align:center;" | °C
| [[Celsius temperature]]
| style="text-align:center;" | K
| <!-- intentionally left blank -->
|-
! scope="row" | [[lumen (unit)|lumen]]
| style="text-align:center;" | lm
| [[luminous flux]]
| style="text-align:center;" | cd⋅sr<ref name="keep-sr" group="nc">In photometry, the steradian is usually retained in expressions for units.</ref>
| style="text-align:center;" | cd⋅sr
|-
! scope="row" | [[lux]]
| style="text-align:center;" | lx
| [[illuminance]]
| style="text-align:center;" | cd⋅sr⋅m<sup>−2</sup><ref name="keep-sr" group="nc"/>
| style="text-align:center;" | lm/m<sup>2</sup>
|-
! scope="row" | [[becquerel]]
| style="text-align:center;" | Bq
| [[Radioactive decay|activity referred to a radionuclide]]
| style="text-align:center;" | s<sup>−1</sup>
| <!-- intentionally left blank -->
|-
! scope="row" | [[gray (unit)|gray]]
| style="text-align:center;" | Gy
| [[absorbed dose]], [[kerma (physics)|kerma]]
| style="text-align:center;" | m<sup>2</sup>⋅s<sup>−2</sup>
| style="text-align:center;" | J/kg
|-
! scope="row" | [[sievert]]
| style="text-align:center;" | Sv
| [[dose equivalent]]
| style="text-align:center;" | m<sup>2</sup>⋅s<sup>−2</sup>
| style="text-align:center;" | J/kg
|-
! scope="row" | [[katal]]
| style="text-align:center;" | kat
| [[catalytic activity]]
| style="text-align:center;" | mol⋅s<sup>−1</sup>
| <!-- intentionally left blank -->
|-
<!-- Note: there are exactly 22 entries in the ref -->
| colspan="5" | '''Notes'''
<references group="nc" />
|}
{{Clear}}

The derived units in the SI are formed by powers, products, or quotients of the base units and are unlimited in number.<ref name=SIBrochure9thEd/>{{rp|page=138}}<ref name="NIST330"/>{{rp|pages=14,16}}

[[File:Physics measurements SI units.png|thumb|Arrangement of the principal measurements in physics based on the mathematical manipulation of length, time, and mass]]

[[Derived unit]]s apply to some [[derived quantity|derived quantities]], which may by definition be expressed in terms of [[base quantity|base quantities]], and thus are not independent; for example, [[electrical conductance]] is the inverse of [[electrical resistance]], with the consequence that the siemens is the inverse of the ohm, and similarly, the ohm and siemens can be replaced with a ratio of an ampere and a volt, because those quantities bear a defined relationship to each other.{{efn|Ohm's law: {{nowrap|1=1 Ω = 1 V/A}} from the relationship {{nowrap|1=''E'' = ''I'' × ''R''}}, where ''E'' is electromotive force or voltage (unit: volt), ''I'' is current (unit: ampere), and ''R'' is resistance (unit: ohm).}} Other useful derived quantities can be specified in terms of the SI base and derived units that have no named units in the SI, such as acceleration, which has the SI unit m/s<sup>2</sup>.<ref name="SIBrochure9thEd" />{{rp|page=139}}

A combination of base and derived units may be used to express a derived unit. For example, the SI unit of [[force]] is the [[newton (unit)|newton]] (N), the SI unit of [[pressure]] is the [[Pascal (unit)|pascal]] (Pa) – and the pascal can be defined as one newton per square metre (N/m<sup>2</sup>).<ref>{{cite web |title=Units & Symbols for Electrical & Electronic Engineers |url=http://www.theiet.org/students/resources/units-symbols.cfm |publisher=Institution of Engineering and Technology |date=1996 |pages=8–11 |access-date=19 August 2013 |archive-url=https://web.archive.org/web/20130628212624/http://www.theiet.org/students/resources/units-symbols.cfm |archive-date=28 June 2013}}</ref>

=== Prefixes ===

{{Main|Metric prefix}}

Like all metric systems, the SI uses [[metric prefix]]es to systematically construct, for the same physical quantity, a set of units that are decimal multiples of each other over a wide range. For example, driving distances are normally given in [[kilometre]]s (symbol {{val|u=km}}) rather than in metres. Here the metric prefix '[[kilo-]]' (symbol 'k') stands for a factor of 1000; thus, {{val|1|u=km}} = {{val|1000|u=m}}.

The SI provides twenty-four metric prefixes that signify decimal powers ranging from 10<sup>−30</sup> to 10<sup>30</sup>, the most recent being adopted in 2022.<ref name="SIBrochure9thEd" />{{rp|pages=143–144}}<ref>{{cite web |first1=Daniel|last1=Lawler|title=Earth now weighs six ronnagrams: New metric prefixes voted in |url=https://phys.org/news/2022-11-earth-ronnagrams-metric-prefixes-voted.html |publisher=phys.org |date=18 November 2022}}</ref><ref>{{cite web |date=18 November 2022 |title=List of Resolutions for the 27th meeting of the General Conference on Weights and Measures |url=https://www.bipm.org/documents/20126/64811223/Resolutions-2022.pdf |publisher=BIPM|url-status=dead |access-date=18 November 2022 |archive-date=18 November 2022 |archive-url=https://web.archive.org/web/20221118153958/https://www.bipm.org/documents/20126/64811223/Resolutions-2022.pdf}}</ref><ref>{{cite web |title=New prefixes for the SI adopted by the General Conference on Weights and Measures |url=https://www.bipm.org/en/-/2022-12-19-si-prefixes |access-date=11 January 2023 |website=BIPM }}</ref> Most prefixes correspond to integer powers of 1000; the only ones that do not are those for 10, 1/10, 100, and 1/100.
The conversion between different SI units for one and the same physical quantity is always through a power of ten. This is why the SI (and metric systems more generally) are called ''decimal systems of measurement units''.<ref name="DecimalSystem">{{cite web |url=https://usma.org/decimal-nature-of-the-metric-system |title=Decimal Nature of the Metric System |publisher=[[US Metric Association]] | date=2015 |access-date=15 April 2020 |archive-url=https://web.archive.org/web/20200415225727/https://usma.org/decimal-nature-of-the-metric-system/ |archive-date=15 April 2020 |url-status=live}}</ref>

{{Anchor|Compound unit}}The grouping formed by a prefix symbol attached to a unit symbol (e.g. '{{val|u=km}}', '{{val|u=cm}}') constitutes a new inseparable unit symbol. This new symbol can be raised to a positive or negative power. It can also be combined with other unit symbols to form ''compound unit'' symbols.<ref name="SIBrochure9thEd" />{{rp|page=143}} For example, {{val|u=g/cm3}} is an SI unit of [[density]], where {{val|u=cm3}} is to be interpreted as ({{val|u=cm}}){{sup|3}}.

Prefixes are added to unit names to produce multiples and [[submultiple]]s of the original unit. All of these are integer powers of ten, and above a hundred or below a hundredth all are integer powers of a thousand. For example, ''kilo-'' denotes a multiple of a thousand and ''milli-'' denotes a multiple of a thousandth, so there are one thousand millimetres to the metre and one thousand metres to the kilometre. The prefixes are never combined, so for example a millionth of a metre is a ''micrometre'', not a ''millimillimetre''. Multiples of the kilogram are named as if the gram were the base unit, so a millionth of a kilogram is a ''milligram'', not a ''microkilogram''.<ref name="SIBrochure">{{SIbrochure8th}}</ref>{{rp|page=122}}<ref name="NIST811"/>{{rp|page=14}}

The BIPM specifies 24 prefixes for the International System of Units (SI):

{{SI prefixes (infobox)}}

=== Coherent and non-coherent SI units <span class="anchor" id="Coherent SI units"></span> ===

{{Further|Coherent unit}}

The base units and the derived units formed as the product of powers of the base units with a numerical factor of one form a [[coherent system of units]]. Every physical quantity has exactly one coherent SI unit. For example, {{nowrap|1=1 m/s = (1 m) / (1 s)}} is the coherent derived unit for velocity.<ref name="SIBrochure9thEd" />{{rp|page=139}} With the exception of the kilogram (for which the prefix kilo- is required for a coherent unit), when prefixes are used with the coherent SI units, the resulting units are no longer coherent, because the prefix introduces a numerical factor other than one.<ref name="SIBrochure9thEd" />{{rp|page=137}} For example, the metre, kilometre, centimetre, nanometre, etc. are all SI units of length, though only the metre is a {{em|coherent}} SI unit. The complete set of SI units consists of both the coherent set and the multiples and sub-multiples of coherent units formed by using the SI prefixes.<ref name="SIBrochure9thEd" />{{rp|page=138}}

The kilogram is the only coherent SI unit whose name and symbol include a prefix. For historical reasons, the names and symbols for multiples and sub-multiples of the unit of mass are formed as if the [[gram]] were the base unit. Prefix names and symbols are attached to the unit name ''gram'' and the unit symbol g respectively. For example, {{val|e=-6|u=kg}} is written ''milligram'' and {{val|u=mg}}, not ''microkilogram'' and {{val|u=μkg}}.<ref name="SIBrochure9thEd" />{{rp|page=144}}

Several different quantities may share the same coherent SI unit. For example, the joule per kelvin (symbol {{val|u=J/K}}) is the coherent SI unit for two distinct quantities: [[heat capacity]] and [[entropy]]; another example is the ampere, which is the coherent SI unit for both [[electric current]] and [[magnetomotive force]]. This illustrates why it is important not to use the unit alone to specify the quantity. As the ''SI Brochure'' states,<ref name="SIBrochure9thEd" />{{rp|page=140}} "this applies not only to technical texts, but also, for example, to measuring instruments (i.e. the instrument read-out needs to indicate both the unit and the quantity measured)".

Furthermore, the same coherent SI unit may be a base unit in one context, but a coherent derived unit in another. For example, the ampere is a base unit when it is a unit of electric current, but a coherent derived unit when it is a unit of magnetomotive force.<ref name="SIBrochure9thEd" />{{rp|page=140}}

{| class="wikitable floatleft" style="margin:1em auto 1em auto;line-height:1.4"
|+ <big>Examples of coherent derived units in terms of base units</big><ref name="NIST330" />{{rp|page=17}}
|-
! scope="col" | Name
! scope="col" | Symbol
! scope="col" | Derived quantity
! scope="col" | Typical symbol
|-
! scope="row" | [[square metre]]
| style="text-align:center;" | {{val|u=m2}}
| [[area]]
| style="text-align:center;" | {{math|''A''}}
|-
! scope="row" | [[cubic metre]]
| style="text-align:center;" | {{val|u=m3}}
| [[volume]]
| style="text-align:center;" | {{math|''V''}}
|-
! scope="row" | [[metre per second]]
| style="text-align:center;" | {{val|u=m/s}}
| [[speed]], [[velocity]]
| style="text-align:center;" | {{math|''v''}}
|-
! scope="row" | [[metre per second squared]]
| style="text-align:center;" | {{val|u=m/s2}}
| [[acceleration]]
| style="text-align:center;" | {{math|''a''}}
|-
! scope="row" rowspan="2" | [[reciprocal metre]]
| rowspan="2" style="text-align:center;" | {{val|u=m-1}}
| [[wavenumber]]
| style="text-align:center;" | {{math|''σ''}}, {{math|''ṽ''}}
|-
| [[vergence (optics)]]
| style="text-align:center;" | {{math|''V''}}, 1/{{math|''f''}}
|-
! scope="row" | [[kilogram per cubic metre]]
| style="text-align:center;" | {{val|u=kg/m3}}
| [[density]]
| style="text-align:center;" | {{math|''ρ''}}
|-
! scope="row" | kilogram per square metre
| style="text-align:center;" | {{val|u=kg/m2}}
| [[surface density]]
| style="text-align:center;" | {{math|''ρ''{{smallsub|A}}}}
|-
! scope="row" | cubic metre per kilogram
| style="text-align:center;" | {{val|u=m3/kg}}
| [[specific volume]]
| style="text-align:center;" | {{math|''v''}}
|-
! scope="row" | ampere per square metre
| style="text-align:center;" | {{val|u=A/m<sup>2</sup>}}
| [[current density]]
| style="text-align:center;" | {{math|''j''}}
|-
! scope="row" | [[amperes per metre|ampere per metre]]
| style="text-align:center;" | {{val|u=A/m}}
| [[magnetic field strength]]
| style="text-align:center;" | {{math|''H''}}
|-
! scope="row" | mole per cubic metre
| style="text-align:center;" | {{val|u=mol/m3}}
| [[concentration]]
| style="text-align:center;" | {{math|''c''}}
|-
! scope="row" | [[kilogram per cubic metre]]
| style="text-align:center;" | {{val|u=kg/m3}}
| [[Mass concentration (chemistry)|mass concentration]]
| style="text-align:center;" | {{math|''ρ''}}, {{math|''γ''}}
|-
! scope="row" | [[candela per square metre]]
| style="text-align:center;" | {{val|u=cd/m<sup>2</sup>}}
| [[luminance]]
| style="text-align:center;" | {{math|''L''<sub>v</sub>}}
|}

{| class="wikitable floatleft" style="margin:1em auto 1em auto;line-height:1.4"
|+ <big>Examples of derived units that include units with special names</big><ref name="NIST330" />{{rp|page=18}}
|-
! scope="col" | Name
! scope="col" | Symbol
! scope="col" | Quantity
! scope="col" | In SI base units
|-
! scope="row" | [[pascal-second]]
| style="text-align:center;" | Pa⋅s
| [[dynamic viscosity]]
| style="text-align:center;" | m<sup>−1</sup>⋅kg⋅s<sup>−1</sup>
|-
! scope="row" | [[newton-metre]]
| style="text-align:center;" | N⋅m
| [[moment of force]]
| style="text-align:center;" | m<sup>2</sup>⋅kg⋅s<sup>−2</sup>
|-
! scope="row" | newton per metre
| style="text-align:center;" | N/m
| [[surface tension]]
| style="text-align:center;" | kg⋅s<sup>−2</sup>
|-
! scope="row" | [[radian per second]]
| style="text-align:center;" | rad/s
| [[angular velocity]], [[angular frequency]]
| style="text-align:center;" | s<sup>−1</sup>
|-
! scope="row" | [[radian per second squared]]
| style="text-align:center;" | rad/s<sup>2</sup>
| [[angular acceleration]]
| style="text-align:center;" | s<sup>−2</sup>
|-
! scope="row" | [[watt per square metre]]
| style="text-align:center;" | W/m<sup>2</sup>
| heat flux density, [[irradiance]]
| style="text-align:center;" | kg⋅s<sup>−3</sup>
|-
! scope="row" | [[joule per kelvin]]
| style="text-align:center;" | J/K
| [[entropy]], [[heat capacity]]
| style="text-align:center;" | m<sup>2</sup>⋅kg⋅s<sup>−2</sup>⋅K<sup>−1</sup>
|-
! scope="row" | joule per kilogram-kelvin
| style="text-align:center;" | J/(kg⋅K)
| [[specific heat capacity]], [[specific entropy]]
| style="text-align:center;" | m<sup>2</sup>⋅s<sup>−2</sup>⋅K<sup>−1</sup>
|-
! scope="row" | joule per kilogram
| style="text-align:center;" | J/kg
| [[specific energy]]
| style="text-align:center;" | m<sup>2</sup>⋅s<sup>−2</sup>
|-
! scope="row" | watt per metre-kelvin
| style="text-align:center;" | W/(m⋅K)
| [[thermal conductivity]]
| style="text-align:center;" | m⋅kg⋅s<sup>−3</sup>⋅K<sup>−1</sup>
|-
! scope="row" | joule per cubic metre
| style="text-align:center;" | J/m<sup>3</sup>
| [[energy density]]
| style="text-align:center;" | m<sup>−1</sup>⋅kg⋅s<sup>−2</sup>
|-
! scope="row" | volt per metre
| style="text-align:center;" | V/m
| [[electric field strength]]
| style="text-align:center;" | m⋅kg⋅s<sup>−3</sup>⋅A<sup>−1</sup>
|-
! scope="row" | coulomb per cubic metre
| style="text-align:center;" | C/m<sup>3</sup>
| [[electric charge density]]
| style="text-align:center;" | m<sup>−3</sup>⋅s⋅A
|-
! scope="row" | coulomb per square metre
| style="text-align:center;" | C/m<sup>2</sup>
| [[surface charge density]], [[electric flux density]], [[electric displacement]]
| style="text-align:center;" | m<sup>−2</sup>⋅s⋅A
|-
! scope="row" | farad per metre
| style="text-align:center;" | F/m
| [[permittivity]]
| style="text-align:center;" | m<sup>−3</sup>⋅kg<sup>−1</sup>⋅s<sup>4</sup>⋅A<sup>2</sup>
|-
! scope="row" | henry per metre
| style="text-align:center;" | H/m
| [[permeability (electromagnetism)|permeability]]
| style="text-align:center;" | m⋅kg⋅s<sup>−2</sup>⋅A<sup>−2</sup>
|-
! scope="row" | joule per mole
| style="text-align:center;" | J/mol
| [[joule per mole|molar energy]]
| style="text-align:center;" | m<sup>2</sup>⋅kg⋅s<sup>−2</sup>⋅mol<sup>−1</sup>
|-
! scope="row" | joule per mole-kelvin
| style="text-align:center;" | J/(mol⋅K)
| [[molar entropy]], [[molar heat capacity]]
| style="text-align:center;" | m<sup>2</sup>⋅kg⋅s<sup>−2</sup>⋅K<sup>−1</sup>⋅mol<sup>−1</sup>
|-
! scope="row" | coulomb per kilogram
| style="text-align:center;" | C/kg
| [[radiation exposure|exposure]] (x- and γ-rays)
| style="text-align:center;" | kg<sup>−1</sup>⋅s⋅A
|-
! scope="row" | gray per second
| style="text-align:center;" | Gy/s
| [[absorbed dose rate]]
| style="text-align:center;" | m<sup>2</sup>⋅s<sup>−3</sup>
|-
! scope="row" | watt per steradian
| style="text-align:center;" | W/sr
| [[radiant intensity]]
| style="text-align:center;" | m<sup>2</sup>⋅kg⋅s<sup>−3</sup>
|-
! scope="row" | watt per square metre-steradian
| style="text-align:center;" | W/(m<sup>2</sup>⋅sr)
| [[radiance]]
| style="text-align:center;" | kg⋅s<sup>−3</sup>
|-
! scope="row" | katal per cubic metre
| style="text-align:center;" | kat/m<sup>3</sup>
| [[catalytic activity concentration]]
| style="text-align:center;" | m<sup>−3</sup>⋅s<sup>−1</sup>⋅mol
|}
{{Clear}}