View source for International System of Units

{{redirect|SI}}
{{redirect|Kilo|unit of mass|Kilogram}}
[[File:SI base unit.svg|thumb |upright=1.2| Links between the seven [[SI base unit]] definitions. Counterclockwise from top: [[second]] ([[time]]), [[metre]] ([[length]]), [[ampere]] ([[electric current]]), [[kelvin]] ([[temperature]]), [[candela]] ([[luminous intensity]]), [[Mole (unit)|mole]] ([[amount of substance]]) and [[kilogram]] ([[mass]]). ]]
The '''International System of Units''' is the standard modern form of the [[metric system]]. The name of this system can be shortened or [[abbreviation|abbreviated]] to '''SI''', from the [[French language|French]] name '''''S'''ystème '''I'''nternational d'unités''.

The International System of Units is a [[system of measurement]] based on 7 base units: the [[metre]] (length), [[kilogram]] (mass), [[second]] (time), [[ampere]] (electric current), [[kelvin]] (temperature), [[mole (unit)|mole]] (quantity), and [[candela]] (brightness). These base units can be used in combination with each other. This creates ''SI derived units'', which can be used to describe other quantities, such as [[volume]], [[energy]], [[pressure]], and [[velocity]].

The system is used almost globally. Only [[Myanmar]], [[Liberia]], and the [[United States]] do not use SI as their official system of measurement.<ref name="ciawf">{{cite web |title=Appendix G: Weights and Measures |url=https://www.cia.gov/library/publications/the-world-factbook/appendix/appendix-g.html |work=The World Facebook |publisher=[[Central Intelligence Agency]] |date=2013 |accessdate=5 April 2013 |archive-date=6 April 2011 |archive-url=https://web.archive.org/web/20110406124728/https://www.cia.gov/library/publications/the-world-factbook/appendix/appendix-g.html |url-status=dead }}</ref> In these countries, though, SI is commonly used in science and medicine.

== History and use ==
The [[metric system]] was created in [[France]] after the [[French Revolution]] in [[1789]]. The original system only had two standard units, the kilogram and the metre. The metric system became popular amongst scientists.

In the [[1860s]], [[James Clerk Maxwell]] and [[William Thomson]] (later known as Lord Kelvin) suggested a system with three base units &ndash; length, mass, and time. Other units would be derived from those three base units. Later, this suggestion would be used to create the [[centimetre-gram-second system of units]] (CGS), which used the [[centimetre]] as the base unit for length, the [[gram]] as the base unit for mass, and the second as the base unit for time. It also added the [[dyne]] as the base unit for [[force]] and the [[erg]] as the base unit for energy.

As scientists studied [[electricity]] and [[magnetism]], they realized other base units were needed to describe these subjects. By the middle of the [[20th century]], many different versions of the metric system were being used. This was very confusing.

In [[1954]], the 9th [[CGPM|General Conference on Weights and Measures]] (CGPM) created the first version of the International System of Units. The six base units that they used were the metre, kilogram, second, ampere, Kelvin, and candela.<!-- how do you cite these things properly help --><ref name="9cgpm">{{citation |url=http://www.bipm.org/en/CGPM/db/10/6/ |author= [[International Bureau of Weights and Measures]] |title=Système pratique d'unités de mesure (Practical system of units) |year=1954}}. 9<sup>th</sup> session, Resolution 6.</ref> The seventh base unit, the mole, was added in [[1971]].<ref name="14cgpm">{{citation |url=http://www.bipm.org/en/CGPM/db/14/3/ |author= International Bureau of Weights and Measures |title=Unité SI de quantité de matière (SI unit of amount of substance) |year=1971}}. 14<sup>th</sup> session, Resolution 3.</ref>

SI is now used almost everywhere in the world, except in the [[United States]], [[Liberia]] and [[Myanmar]], where the older [[imperial unit]]s are still widely used. Other countries, most of them historically related to the [[British Empire]], are slowly replacing the old [[imperial system]] with the metric system or using both systems at the same time.

== Units of measurement ==

=== Base units ===

The SI '''base units''' are [[measurement]]s used by scientists and other people around the world. All the other units can be written by combining these seven base units in different ways. These other units are called "derived units".

{| class="wikitable" style="margin:1em 0"
|+ <big>SI base units</big><ref name="NIST330">{{cite book |author-first1=Barry N. |author-last1=Taylor |author-first2=Ambler |author-last2=Thompson |title=The International System of Units (SI) (Special publication 330) |url=https://www.nist.gov/sites/default/files/documents/2016/12/07/sp330.pdf |access-date=2017-08-04 |publisher=[[National Institute of Standards and Technology]] |location=Gaithersburg, MD |date=2008 |archive-date=2017-11-20 |archive-url=https://web.archive.org/web/20171120061639/https://www.nist.gov/sites/default/files/documents/2016/12/07/sp330.pdf |url-status=dead }}</ref>{{rp|23}}<ref name="BIPM1975">
[http://old.iupac.org/publications/books/author/mills.html Quantities Units and Symbols in Physical Chemistry], IUPAC</ref><ref>{{cite book| last1 = Page| first1 = Chester Hall| last2 = Vigoureux| first2 = Paul| title = The International Bureau of Weights and Measures 1875–1975: NBS Special Publication 420| url = https://books.google.com/books?id=nOG0SxxEu64C&pg=PA240| date = 1975-05-20| publisher = [[National Bureau of Standards]]| location = [[Washington, D.C.]]| pages = 238–244| editor-first1 = Chester H.| editor-first2 = Paul| editor-last1 = Page| editor-last2 = Vigoureux }}</ref>
|-
!Unit<br />name
!Unit<br />symbol
![[Dimensional analysis|Dimension<br />symbol]]
![[Physical quantity|Quantity<br />name]]
!Definition<ref group="n">Interim definitions are given here only when there has been a ''significant'' difference in the definition.</ref>
|-
![[second]]
|style="text-align:center" |s
|style="text-align:center" |T
|[[time]]
|
* '''Prior''': <math>\frac{1}{86400}</math> of a day of 24&nbsp;hours of 60&nbsp;minutes of 60&nbsp;seconds
* '''Interim''' (1956): <math>\frac{1}{31556925.9747}</math> of the [[tropical year]] for 1900 January 0 at 12&nbsp;hours [[ephemeris time]].
* '''Current''' (1967): 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.
|-
![[metre]]
|style="text-align:center" |m
|style="text-align:center" |L
|[[length]]
|
* '''Prior''' (1793): <math>\frac{1}{10000000}</math> of the [[Meridian (geography)|meridian]] through Paris between the North Pole and the Equator.<sup>FG</sup>
* '''Interim''' (1960): {{val|1650763.73}} [[wavelength]]s in a [[vacuum]] of the [[electromagnetic radiation|radiation]] corresponding to the transition between the 2p{{sup|10}} and 5d{{sup|5}} quantum levels of the [[krypton-86]] [[atom]].
* '''Current''' (1983): The distance travelled by light in vacuum in <math>\frac{1}{299792458}</math> second.
|-
![[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" |M
|[[mass]]
|
* '''Prior''' (1793): The '''[[grave (unit)|grave]]''' was defined as being the mass (then called ''weight'') of one litre of pure water at its freezing point.<sup>FG</sup>
* '''Interim''' (1889): The mass of a small [[squat]] cylinder of ~47 cubic centimetres of platinum-iridium alloy kept in the [[International Bureau of Weights and Measures]], [[Paris]], [[France]].<ref>{{cite web|url=https://www.nist.gov/physical-measurement-laboratory/past|title=Redefining the Kilogram, The Past|first=Erik M.|last=Secula|date=7 October 2014|website=Nist.gov|accessdate=22 August 2017}}</ref>
* '''Current''' (2019): The kilogram is defined by setting the [[Planck constant]] ''h'' exactly 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=2018-11-16|work=NIST|access-date=2018-11-16|language=en}}</ref> Then the formula would be 1 kg = {{frac|h|6.62607015 × 10<sup>-34</sup>⋅m<sup>2</sup>⋅s<sup>−1</sup>}}
|-
![[ampere]]
|style="text-align:center" |A
|style="text-align:center" |I
|[[electric current]]
|
* '''Prior''' (1881): A tenth of the electromagnetic CGS unit of current. The [CGS] electromagnetic unit of current is that current, flowing in an arc 1&nbsp;cm long of a circle 1&nbsp;cm in radius, that creates a field of one [[oersted]] at the centre.<ref>{{cite book| title = Magnetism and Electricity| url = https://books.google.com/books?id=m7c6AAAAIAAJ&pg=PA322| date = 1961| publisher = Cambridge University Press| page = 322| author-first = A. E. E.| author-last = McKenzie }}</ref> <sup>IEC</sup>
* '''Interim''' (1946): The constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1&nbsp;m apart in vacuum, would produce between these conductors a [[force]] equal to {{val|2|e=-7}} [[Newton (unit)|newton]]s per metre of length.
* '''Current''' (2019): The flow of {{frac|{{val|1.602176634|e=-19}}}} times the [[elementary charge]] ''e'' per second.
|-
![[kelvin]]
|style="text-align:center" |K
|style="text-align:center" |Θ
|[[thermodynamic temperature|thermodynamic<br>temperature]]
|
* '''Prior''' (1743): The '''centigrade scale''' is obtained by assigning 0&nbsp;°C to the [[Melting point|freezing]] point of water and 100&nbsp;°C to the [[boiling point]] of water.
* '''Interim''' (1954): The [[triple point of water]] (0.01&nbsp;°C) defined to be exactly 273.16&nbsp;K.<ref group="n">In 1954 the unit of thermodynamic temperature was known as the "degree Kelvin" (symbol °K; "Kelvin" spelt with an upper-case "K"). It was renamed the "kelvin" (symbol "K"; "kelvin" spelt with a lower-case "k") in 1967.</ref>
* '''Previous''' (1967): <math>\frac{1}{273.16}</math> of the [[thermodynamic temperature]] of the triple point of water.
* '''Current''' (2019): The kelvin is defined by setting the fixed numerical value of the [[Boltzmann constant]] ''k'' to {{val|1.380649|e=-23|u=J⋅K<sup>−1</sup>}}, (J = kg⋅m<sup>2</sup>⋅s<sup>−2</sup>), given the definition of the kilogram, the metre and the second.
|-
![[Mole (unit)|mole]]
|style="text-align:center" |mol
|style="text-align:center" |N
|[[amount of substance|amount of<br>substance]]
|
* '''Prior''' (1900): A stoichiometric quantity which is the equivalent mass in grams of [[Avogadro's number]] of molecules of a substance.<sup>ICAW</sup>
* '''Interim''' (1967): The amount of substance of a system which contains as many 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> as there are atoms in 0.012 kilogram of [[carbon-12]].
* '''Current''' (2019): The amount of substance of exactly {{val|6.02214076|e=23}} elementary entities. This number is the fixed numerical value of the [[Avogadro constant]], ''N''<sub>A</sub>, when expressed in the unit mol<sup>−1</sup> and is called the Avogadro number.
|-
![[candela]]
|style="text-align:center" |cd
|style="text-align:center" |J
|[[luminous intensity|luminous<br>intensity]]
|
*'''Prior''' (1946): The value of the new candle (early name for the candela) is such that the brightness of the full radiator at the temperature of solidification of [[platinum]] is 60 new candles per square centimetre.
* '''Current''' (1979): The luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency {{val|5.4|e=14}} hertz and that has a radiant intensity in that direction of <math>{683}</math> watt per [[steradian]].
:Note: both old and new definitions are approximately the luminous intensity of a [[whale blubber]] candle burning modestly bright, in the late 19th century called a "candlepower" or a "candle".
|-
|colspan=5|
;Notes
{{reflist|group=n}}
The '''Prior''' definitions of the various base units in the above table were made by the following authorities:
:* '''FG''' = French Government
:* '''IEC''' = [[International Electrotechnical Commission]]
:* '''ICAW''' = [[International Committee on Atomic Weights]]
All other definitions result from resolutions by either CGPM or the CIPM and are catalogued in the ''SI Brochure''.
|}

=== [[SI derived unit|Derived units]] ===
Derived units are created by combining the base units. The base units can be divided, multiplied, or raised to [[exponent|powers]]. Some derived units have special names. Usually these were created to make calculations simpler.

{| class="wikitable" style="margin:1em 0; text-align:center;"
|+ style="font-size:larger;font-weight:bold;"|Named units derived from SI base units
|-
! Name
! [[Symbol]]
! [[Physical quantity|Quantity]]
! Definition <br>other units
! Definition<br>[[SI base unit]]s
|-
| '''[[radian]]'''
| '''rad'''
| style="text-align:left" | plane [[angle]]
|
| −
|-
| '''[[steradian]]'''
| '''sr'''
| style="text-align:left" | solid angle
|
| −
|-
| '''[[hertz]]'''
| '''Hz'''
| style="text-align:left" | [[frequency]]
|
| s<sup>−1</sup>
|-
| '''[[newton (unit)|newton]]'''
| '''N'''
| style="text-align:left" | [[Force (physics)|force]], [[weight]]
|
| m⋅kg⋅s<sup>−2</sup>
|-
| '''[[pascal (unit)|pascal]]'''
| '''Pa'''
| style="text-align:left" | [[pressure]], [[Stress (physics)|stress]]
| N/m<sup>2</sup>
| m<sup>−1</sup>⋅kg⋅s<sup>−2</sup>
|-
| '''[[joule]]'''
| '''J'''
| style="text-align:left" | [[energy]], [[Mechanical work|work]], [[heat]]
| N⋅m
| m<sup>2</sup>⋅kg⋅s<sup>−2</sup>
|-
| '''[[watt]]'''
| '''W'''
| style="text-align:left" | [[Power (physics)|power]], [[radiant flux]]
| J/s
| m<sup>2</sup>⋅kg⋅s<sup>−3</sup>
|-
| '''[[coulomb]]'''
| '''C'''
| style="text-align:left" | [[electric charge]]
|
| s⋅A
|-
| '''[[volt]]'''
| '''V'''
| style="text-align:left" | [[voltage]], electrical [[potential difference]], [[electromotive force]]
| W/A <br> J/C
| m<sup>2</sup>⋅kg⋅s<sup>−3</sup>⋅A<sup>−1</sup>
|-
| '''[[farad]]'''
| '''F'''
| style="text-align:left" | [[electrical capacitance]]
| C/V
| m<sup>−2</sup>⋅kg<sup>−1</sup>⋅s<sup>4</sup>⋅A<sup>2</sup>
|-
| '''[[ohm (unit)|ohm]]'''
| '''Ω'''
| style="text-align:left" | [[electrical resistance]], [[electrical impedance|impedance]], [[reactance]]
| V/A
| m<sup>2</sup>⋅kg⋅s<sup>−3</sup>⋅A<sup>−2</sup>
|-
| '''[[Siemens (unit)|siemens]]'''
| '''S'''
| style="text-align:left" | [[electrical conductance]]
| 1/Ω
| m<sup>−2</sup>⋅kg<sup>−1</sup>⋅s<sup>3</sup>⋅A<sup>2</sup>
|-
| '''[[Weber (Wb)|weber]]'''
| '''Wb'''
| style="text-align:left" | [[magnetic flux]]
| J/A
| m<sup>2</sup>⋅kg⋅s<sup>−2</sup>⋅A<sup>−1</sup>
|-
| '''[[tesla (unit)|tesla]]'''
| '''T'''
| style="text-align:left" | [[magnetic field]] strength
| Wb/m<sup>2</sup> <br> V⋅s/m<sup>2</sup> <br> N/(A⋅m)
| kg⋅s<sup>−2</sup>⋅A<sup>−1</sup>
|-
| '''[[henry (inductance)|henry]]'''
| '''H'''
| style="text-align:left" | [[inductance]]
| Wb/A <br> V⋅s/A
| m<sup>2</sup>⋅kg⋅s<sup>−2</sup>⋅A<sup>−2</sup>
|-
| '''[[degree Celsius]]'''
| '''°C'''
| style="text-align:left" | [[temperature]] relative to 273.15&nbsp;K
| T<sub>K</sub>&nbsp;−&nbsp;273.15
| K
|-
| '''[[lumen (unit)|lumen]]'''
| '''lm'''
| style="text-align:left" | [[luminous flux]]
| cd⋅sr
| cd
|-
| '''[[lux]]'''
| '''lx'''
| style="text-align:left" | [[illuminance]]
| lm/m<sup>2</sup>
| m<sup>−2</sup>⋅cd
|-
| '''[[becquerel]]'''
| '''Bq'''
| style="text-align:left" | [[radioactivity]] (decays per unit time)
|
| s<sup>−1</sup>
|-
| '''[[gray (unit)|gray]]'''
| '''Gy'''
| style="text-align:left" | [[absorbed dose]] (of [[ionizing radiation]])
| J/kg
| m<sup>2</sup>⋅s<sup>−2</sup>
|-
| '''[[sievert]]'''
| '''Sv'''
| style="text-align:left" | [[equivalent dose]] (of [[ionizing radiation]])
| J/kg
| m<sup>2</sup>⋅s<sup>−2</sup>
|-
| '''[[katal]]'''
| '''kat'''
| style="text-align:left" | [[catalytic activity]]
|
| s<sup>−1</sup>⋅mol
|}

=== Prefixes ===
<!-- [[SI prefix]] redirects here -->
Very large or very small measurements can be written using [[prefix]]es. Prefixes are added to the beginning of the unit to make a new unit. For example, the prefix ''kilo-'' means "1000" times the original unit and the prefix ''milli-'' means "0.001" times the original unit. So one ''[[kilometre]]'' is 1000&nbsp;metres and one ''[[milligram]]'' is a 1000th of a [[gram]].

{{SI prefixes (infobox)}}

== References ==
{{reflist}}
{{reflist|group="nb"}}
{{reflist|group=Note}}
{{SI units}}
[[Category:SI units| ]]
[[Category:Systems]]