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{{Short description|Metre-based systems of measurement}}
{{Outline|Outline of the metric system}}
[[File:FourMetricInstruments.JPG|thumb|upright=1.2|A [[Kilogram|kilogram]] mass and three metric measuring devices: a tape measure in [[Centimetre|centimetre]]s, a thermometer in [[Celsius|degrees Celsius]], and a multimeter that measures potential in [[Volt|volt]]s, current in [[Ampere|ampere]]s and resistance in [[Ohm|ohm]]s.]]

The '''metric system''' is a [[System of measurement|system of measurement]] that is a [[Decimal|decimal]] system. The current international standard for the metric system is the [[International System of Units]] (Système international d'unités or SI), in which all units can be expressed in terms of seven base units. The units that serve as the SI base units are the [[Metre|metre]], [[Kilogram|kilogram]], [[Second|second]], [[Ampere|ampere]], [[Kelvin|kelvin]], [[Mole (unit)|mole]], and [[Candela|candela]].

== Prefixes for multiples and submultiples ==
{{Main|Metric prefix}}

In the metric system, multiples and submultiples of units follow a decimal pattern.{{efn|Non-SI units for time and plane angle measurement, inherited from existing systems, are an exception to the decimal-multiplier rule.<ref>{{cite web |title=Non-SI units accepted for use with SI |url=https://metricsystem.net/non-si-units/accepted-for-use-with-si/ |website=Metric System |date=26 July 2018 |access-date=10 July 2023}}</ref>}}
{{common metric prefixes}}
A common set of decimal-based prefixes that have the effect of multiplication or division by an integer power of ten can be applied to units that are themselves too large or too small for practical use. The prefix ''kilo'', for example, is used to multiply the unit by 1000, and the prefix ''milli'' is to indicate a one-thousandth part of the unit. Thus the ''[[Kilogram|kilogram]]'' and ''[[Kilometre|kilometre]]'' are a thousand [[Gram|gram]]s and [[Metre|metre]]s respectively, and a ''milligram'' and ''[[Millimetre|millimetre]]'' are one thousandth of a gram and metre respectively. These relations can be written symbolically as:<ref name=SI_prefix>{{SIbrochure8th|pages=121,122}}</ref>
{{block indent|1=1&nbsp;mg = 0.001&nbsp;g}}
{{block indent|1=1&nbsp;km = 1000&nbsp;m}}

== Definitions of the metric system units ==

The [[Decimal|decimalised system]] based on the [[Metre|metre]], which had been introduced in {{wipe|French Revolution}}. The historical development of these systems culminated in the definition of the [[International System of Units]] (SI) in the mid-20th century, under the oversight of an international standards body. Adopting the metric system is known as ''metrication''. 

The historical evolution of metric systems has resulted in the recognition of several principles. A set of independent dimensions of nature is selected, in terms of which all natural quantities can be expressed, called base quantities. For each of these dimensions, a representative quantity is defined as a [[Base unit (measurement)|base unit]] of measure. The definition of base units has increasingly been [[Physics:Realisation (metrology)|realised]] in terms of fundamental natural phenomena, in preference to copies of physical artefacts. A unit [[SI derived unit|derived]] from the base units is used for expressing quantities of dimensions that can be derived from the base dimensions of the system—e.g., the square metre is the derived unit for area, which is derived from length. These derived units are [[Coherence (units of measurement)|coherent]], which means that they involve only products of powers of the base units, without any further factors. For any given quantity whose unit has a name and symbol, an extended set of smaller and larger units is defined that are related by factors of powers of ten. The unit of time should be the [[Second|second]]; the unit of [[Physics:Length|length]] should be either the metre or a decimal multiple of it; and the unit of mass should be the gram or a decimal multiple of it.

Metric systems have evolved since the 1790s, as science and technology have evolved, in providing a single universal measuring system. Before and in addition to the SI, metric systems include: the [[MKS system of units]] and the MKSA systems, which are the direct forerunners of the SI; the [[Centimetre–gram–second system of units|centimetre–gram–second (CGS)]] system and its subtypes, the [[Centimetre–gram–second system of units#Electrostatic units (ESU)|CGS electrostatic]] (cgs-esu) system, the [[Centimetre–gram–second system of units#Electromagnetic units (EMU)|CGS electromagnetic]] (cgs-emu) system, and their still-popular blend, the [[Physics:Gaussian units|Gaussian system]]; the [[Metre–tonne–second system of units|metre–tonne–second (MTS)]] system; and the [[Gravitational metric system|gravitational metric system]]s, which can be based on either the metre or the centimetre, and either the gram, gram-force, kilogram or kilogram-force.

The SI has been adopted as the official system of weights and measures by nearly all nations in the world.

== History of the current metric system ==
[[File:BIPM courtyard.jpg|thumb|upright=1.2|Pavillon de Breteuil, Saint-Cloud, France, the home of the metric system since 1875]]
The {{wipe|French Revolution}} (1789–99) provided an opportunity for the French to reform their unwieldy and archaic system of many local weights and measures. Charles Maurice de Talleyrand championed a new system based on natural units, proposing to the French National Assembly in 1790 that such a system be developed. Talleyrand had ambitions that a new natural and standardised system would be embraced worldwide, and was keen to involve other countries in its development. [[Place:Kingdom of Great Britain|Great Britain]] ignored invitations to co-operate, so the French Academy of Sciences decided in 1791 to go it alone and they set up a commission for the purpose. The commission decided that the standard of length should be based on the size of the Earth. They defined that length to be the 'metre' and its length as one ten-millionth of the length of an Earth quadrant, the length of the meridian arc on the Earth's surface from the equator to the north pole. In 1799, after the [[Earth:Arc measurement|arc measurement]] had been surveyed, the new system was launched in France.<ref name="McGreevy" />{{rp|145–149}}

The units of the metric system, originally taken from observable features of nature, are now defined by seven [[Physics:Physical constant|physical constant]]s being given exact numerical values in terms of the units.  In the modern form of the International System of Units (SI), the seven [[Base unit (measurement)|base units]] are: ''[[Metre|metre]]'' for length, ''[[Kilogram|kilogram]]'' for mass, ''[[Second|second]]'' for time, ''[[Ampere|ampere]]'' for electric current, ''[[Kelvin|kelvin]]'' for temperature, ''[[Candela|candela]]'' for luminous intensity and ''[[Mole (unit)|mole]]'' for amount of substance. These, together with their derived units, can measure any physical quantity.  Derived units may have their own unit name, such as the [[Watt|watt]] (J/s) and [[Lux|lux]] (cd/m<sup>2</sup>), or may just be expressed as combinations of base units, such as velocity (m/s) and acceleration (m/s<sup>2</sup>).<ref name=SI2019>{{Cite web|url=https://www.bipm.org/utils/common/pdf/si-brochure/SI-Brochure-9-EN.pdf |archive-url=https://web.archive.org/web/20190530124226/https://www.bipm.org/utils/common/pdf/si-brochure/SI-Brochure-9-EN.pdf |archive-date=2019-05-30 |url-status=live|title=The International System of Units (SI), 9th Edition|date=2019|publisher=Bureau International des Poids et Mesures}}</ref>

The metric system was designed to have properties that make it easy to use and widely applicable, including units based on the natural world, decimal ratios, prefixes for multiples and sub-multiples, and a structure of base and derived units.  It is a coherent system, which means that its units do not introduce conversion factors not already present in equations relating quantities.{{Cn|date=July 2023}}

The metric system is extensible, and new derived units are defined as needed in fields such as radiology and chemistry.  For example, the [[Katal|katal]], a derived unit for catalytic activity equivalent to one [[Mole (unit)|mole]] per second (1&nbsp;mol/s), was added in 1999.<ref>{{Cite journal |last=Dybkær |first=René |date=2002-03-01 |title=The Tortuous Road to the Adoption of katal for the Expression of Catalytic Activity by the General Conference on Weights and Measures |journal=Clinical Chemistry |volume=48 |issue=3 |pages=586–590 |doi=10.1093/clinchem/48.3.586 |issn=0009-9147 |pmid=11861460|doi-access=free }}</ref>

== Principles ==
Although the metric system has changed and developed since its inception, its basic concepts have hardly changed. Designed for transnational use, it consisted of a basic set of units of measurement, now known as base units. Derived units were built up from the base units using logical rather than empirical relationships while multiples and submultiples of both base and derived units were decimal-based and identified by a standard set of prefixes.<ref name=":0" />{{Rp|pages=15-18}}

=== Realisation ===

[[File:Kilometre definition.svg|right|thumb|The [[Metre|metre]] was originally defined to be ''one ten millionth'' of the distance between the North Pole and the Equator through Paris.<ref name="Alder">{{cite book |last=Alder |first=Ken |title=The Measure of all Things—The Seven-Year-Odyssey That Transformed the World |publisher=Abacus |year=2002 |isbn=978-0-349-11507-8 |location=London}}</ref>]]

The base units used in a measurement system must be [[Physics:Realisation (metrology)|realisable]]. Each of the definitions of the base units in the SI is accompanied by a defined ''mise en pratique'' [practical realisation] that describes in detail at least one way in which the base unit can be measured.<ref>{{cite web |url = http://www.bipm.org/en/si/new_si/mise-en-pratique.html |title = What is a ''mise en pratique''? |publisher = BIPM |year=2011 |access-date = 11 March 2011}}</ref> Where possible, definitions of the base units were developed so that any laboratory equipped with proper instruments would be able to realise a standard without reliance on an artefact held by another country.  In practice, such realisation is done under the auspices of a [[Organization:International Organization of Legal Metrology#Conformance Certification|mutual acceptance arrangement]].<ref>{{cite web |url=http://www.oiml.org/maa/ |title=OIML Mutual Acceptance Arrangement (MAA) |publisher=[[Organization:International Organization of Legal Metrology|International Organization of Legal Metrology]] |access-date=23 April 2013 |url-status=dead |archive-url=https://web.archive.org/web/20130521131225/http://www.oiml.org/maa/ |archive-date=21 May 2013}}</ref>
In the SI, the standard [[Metre|metre]] is defined as exactly {{frac|1|{{val|299,792,458}}}} of the distance that light travels in a [[Second|second]].<ref>{{cite web |url=https://www.bipm.org/en/committees/cg/cgpm/17-1983/resolution-1 |title=17th General Conference on Weights and Measures (1983), Resolution 1. |access-date=17 June 2023}}</ref><ref>{{Cite web|date=20 May 2019|title=Mise en pratique for the definition of the metre in the SI|url=https://www.bipm.org/documents/20126/41489670/SI-App2-metre.pdf/0e011055-9736-d293-5e56-b8b1b267fd68?version=1.8&t=1637238031486&download=false|website=BIPM |access-date=17 June 2023}}</ref> The metre can be realised by measuring the length that a light wave travels in a given time, or equivalently by measuring the wavelength of light of a known frequency.<ref>{{cite conference |last1=Lewis |first1=A. |title=1983 realisation of the metre definition |publisher=National Physical Laboratory |conference=Varenna Summer School |url=https://static.sif.it/SIF/resources/public/files/va2019/Lewis2.pdf |access-date=10 July 2023 |page=15 |date=4 July 2019}}</ref> 

The [[Kilogram|kilogram]] was originally defined as the mass of one cubic decimetre of water at 4&nbsp;°C, standardized as the mass of a man-made artefact of platinum–iridium held in a laboratory in France, which was used until a new definition was introduced in May 2019. Replicas made in 1879 at the time of the artefact's fabrication and distributed to signatories of the [[Metre Convention]] serve as ''de facto'' standards of mass in those countries. Additional replicas have been fabricated since as additional countries have joined the convention.  The replicas were subject to periodic validation by comparison to the original, called the [[International Prototype of the Kilogram|IPK]]. It became apparent that either the IPK or the replicas or both were deteriorating, and are no longer comparable: they had diverged by 50&nbsp;μg since fabrication, so figuratively, the accuracy of the kilogram was no better than 5 parts in a hundred million or a relative accuracy of {{val|5|e=-8}}. The accepted redefinition of SI base units replaced the IPK with an exact definition of the [[Physics:Planck constant|Planck constant]] as expressed in SI units, which defines the kilogram in terms of fundamental constants.<ref>{{cite web |date=16 November 2018 |title=The Latest: Landmark Change to Kilogram Approved |url=https://apnews.com/e6991383703e4ad5a9570d97b0e57822 |access-date=17 June 2023 |website=AP News |publisher=Associated Press}}</ref><ref>{{Cite web |date=7 July 2021 |title=Mise en pratique for the definition of the kilogram in the SI |url=https://www.bipm.org/documents/20126/41489673/SI-App2-kilogram.pdf/5881b6b5-668d-5d2b-f12a-0ef8ca437176?version=1.9&t=1637237674882&download=false |access-date=17 June 2023 |website=BIPM}}</ref><ref>{{cite news |last1=Resnick |first1=Brian |title=The new kilogram just debuted. It's a massive achievement. |url=https://www.vox.com/science-and-health/2019/5/17/18627757/kilogram-redefined-world-metrology-day-explained |work=Vox |date=20 May 2019 |access-date=17 June 2023}}</ref>

=== Base and derived unit structure ===
{{Main|Base unit (measurement)}}
A base quantity is one of a conventionally chosen subset of physical quantities, where no quantity in the subset can be expressed in terms of the others. A base unit is a unit adopted for expressing a base quantity. A derived unit is used for expressing any other quantity, and is a product of powers of base units. For example, in the modern metric system, length has the unit metre and time has the unit second, and speed has the derived unit metre per second.<ref name=":0" />{{Rp|page=15}} Density, or mass per unit volume, has the unit kilogram per cubic metre.<ref name=":0" />{{Rp|page=434}}

=== Decimal ratios ===
A characteristic feature of metric systems is their reliance upon multiples of 10. For example, the base unit of length is the metre, and distances much longer or much shorter than 1 metre are measured in units that are powers of 10 times a metre. This is unlike older systems of units in which the ratio between the units for longer and shorter distances varied: there are 12 inches in a foot, but the number of 5,280 feet in a mile is not a power of 12.<ref name=":0" />{{Rp|page=17}} For many everyday applications, the United States has resisted the adoption of a decimal-based system, continuing to use "a conglomeration of basically [[Imperial and US customary measurement systems|incoherent measurement systems]]".<ref>{{cite book |last=Gullberg |first=Jan |title=Mathematics from the Birth of Numbers |publisher=W. W. Norton and Company |location=New York and London |year=1997 |isbn=978-0-393-04002-9 |page=52 |chapter=2.4 Decimal Position System}}</ref>

In the early days, multipliers that were positive powers of ten were given Greek-derived prefixes such as  ''kilo-'' and ''mega-'', and those that were negative powers of ten were given Latin-derived prefixes such as ''centi-'' and ''milli-''. However, 1935 extensions to the prefix system did not follow this convention: the prefixes ''nano-'' and ''micro-'', for example have Greek roots.<ref name="McGreevy">{{cite book |title = The Basis of Measurement: Volume 2—Metrication and Current Practice |isbn = 978-0-948251-84-9 |publisher = Picton Publishing |location = Chippenham |year = 1997 |first1 = Thomas |last1 = McGreevy |editor1-first = Peter |editor1-last = Cunningham}}</ref>{{rp|222–223}} During the 19th century the prefix ''myria-'', derived from the Greek word μύριοι (''mýrioi''), was used as a multiplier for {{val|10000}}.<ref>{{cite book |url=https://archive.org/details/edinburghencyclo07brew |title=The Edinburgh Encyclopædia |first1=D. |last1=Brewster |page=[https://archive.org/details/edinburghencyclo07brew/page/494 494] |year=1830 }}</ref>

When applying prefixes to derived units of area and volume that are expressed in terms of units of length squared or cubed, the square and cube operators are applied to the unit of length including the prefix, as illustrated below.<ref name=SI_prefix />
{| style="margin-left:3em !important; white-space:nowrap"
|-
|1&nbsp;mm<sup>2</sup> (square millimetre)         ||= (1&nbsp;mm)<sup>2</sup>&nbsp;||= (0.001&nbsp;m)<sup>2</sup>&nbsp;||= {{val|0.000001|u=m2}}
|-
|1&nbsp;km<sup>2</sup> ([[Square kilometre|square kilometre]])&nbsp;||= (1&nbsp;km)<sup>2</sup>      ||= (1000&nbsp;m)<sup>2</sup>       ||= {{val|1000000|u=m2}}
|-
|1&nbsp;mm<sup>3</sup> (cubic millimetre)          ||= (1&nbsp;mm)<sup>3</sup>      ||= (0.001&nbsp;m)<sup>3</sup>      ||= {{val|0.000000001|u=m3}}
|-
|1&nbsp;km<sup>3</sup> (cubic kilometre)           ||= (1&nbsp;km)<sup>3</sup>      ||= (1000&nbsp;m)<sup>3</sup>       ||= {{val|1000000000|u=m3}}
|}

Prefixes are not usually used to indicate multiples of a second greater than 1; the non-SI units of [[Minute|minute]], [[Hour|hour]] and [[Day|day]] are used instead. On the other hand, prefixes are used for multiples of the non-SI unit of volume, the [[Litre|litre]] (l, L) such as millilitres (ml).<ref name=SI_prefix />

=== Coherence ===
{{Main|Coherence (units of measurement)}}
[[File:James Clerk Maxwell.jpg|thumb|upright|[[Biography:James Clerk Maxwell|James Clerk Maxwell]] played a major role in developing the concept of a coherent CGS system and in extending the metric system to include electrical units.]]
Each variant of the metric system has a degree of coherence—the derived units are directly related to the base units without the need for intermediate conversion factors.<ref>{{citation
| author = Working Group 2 of the Joint Committee for Guides in Metrology (JCGM/WG 2).
| publisher = [[Organization:International Bureau of Weights and Measures|International Bureau of Weights and Measures]] (BIPM) on behalf of the Joint Committee for Guides in Metrology
| year = 2008
| url = http://www.bipm.org/utils/common/documents/jcgm/JCGM_200_2008.pdf
| title = International vocabulary of metrology – Basic and general concepts and associated terms (VIM)
| edition = 3rd
| at = 1.12
|access-date = 12 April 2012}}</ref> For example, in a coherent system the units of [[Physics:Force|force]], [[Physics:Energy|energy]], and [[Physics:Power|power]] are chosen so that the equations
{| style="margin-left:3em !important"
|-
| ''force''  || = || ''mass''  || × || ''acceleration''
|-
| ''energy'' || = || ''force'' || × || ''distance''
|-
| ''energy'' || = || ''power'' || × || ''time''
|}
hold without the introduction of unit conversion factors. Once a set of coherent units has been defined, other relationships in physics that use this set of units will automatically be true. Therefore, [[Biography:Albert Einstein|Einstein]]'s [[Mass–energy equivalence|mass–energy equation]], {{nowrap|1=''E'' = ''mc''{{i sup|2}}}}, does not require extraneous constants when expressed in coherent units.<ref>{{cite web
 |url=http://www.unc.edu/~mgood/research/RestEnergy.pdf
 |title=Some Derivations of ''E'' = ''mc''<sup>2</sup>
 |first1=Michael
 |last1=Good
 |access-date=18 March 2011
 |url-status=dead
 |archive-url=https://web.archive.org/web/20111107023429/https://www.unc.edu/~mgood/research/RestEnergy.pdf
 |archive-date=7 November 2011
}}</ref>

The [[Centimetre–gram–second system of units|CGS system]] had two units of energy, the [[Physics:Erg|erg]] that was related to [[Physics:Mechanics|mechanics]] and the [[Calorie|calorie]] that was related to [[Physics:Thermal energy|thermal energy]]; so only one of them (the erg) could bear a coherent relationship to the base units. Coherence was a design aim of SI, which resulted in only one unit of energy being defined – the [[Joule|joule]].<ref name=SI_units>{{SIbrochure8th|pages = 111–120}}</ref>

=== Rationalisation ===
Maxwell's equations of electromagnetism contained a factor of <math>1/(4\pi)</math> relating to [[Steradian|steradian]]s, representative of the fact that electric charges and magnetic fields may be considered to emanate from a point and propagate equally in all directions, i.e. spherically. This factor made equations more awkward than necessary, and so Oliver Heaviside suggested adjusting the system of units to remove it.<ref name=":1" />

===Common notions===
The basic units of the metric system, as originally defined, represented common quantities or relationships in nature. They still do – the modern precisely defined quantities are refinements of definition and methodology, but still with the same magnitudes. In cases where laboratory precision may not be required or available, or where approximations are good enough, the original definitions may suffice.{{efn|While the second is readily determined from the Earth's rotation period, the metre, originally defined in terms of the Earth's size and shape, is less amenable; however, the fact that the Earth's circumference is very close to {{val|40000|u=km}} may be a useful mnemonic.}}

*A second is {{sfrac|1|60}} of a minute, which is {{sfrac|1|60}} of an hour, which is {{sfrac|1|24}} of a day, so a second is {{sfrac|1|{{val|86400}}}} of a day (the use of base 60 dates back to Babylonian times); a second is the time it takes a dense object to freely fall 4.9 metres from rest.{{efn|This is evident from the formula {{math|''s'' {{=}} ''v''{{sub|0}} ''t'' + {{sfrac|1|2}} ''a'' ''t''{{sup|2}}}} with {{math|''v''{{sub|0}} {{=}} 0}} and {{math|''a'' {{=}} {{val|9.81|u=m/s2}}}}.}}
*The length of the [[Astronomy:Equator|equator]] is close to {{val|40000000|u=metres}} (more precisely {{val|40075014.2|u=metres}}).<ref>{{cite web|url=https://www.space.com/17638-how-big-is-earth.html|title=How Big Is Earth?|last1=Science|first1=Tim Sharp 2017-09-15T15:47:00Z|last2=Astronomy|website=Space.com|access-date=22 October 2019}}</ref> In fact, the dimensions of our planet were used by the French Academy in the original definition of the metre.<ref>{{cite web|url=https://www.britannica.com/science/metre-measurement|title=Metre {{!}} measurement|website=Encyclopedia Britannica|access-date=22 October 2019}}</ref>
*The metre is close to the length of [[Seconds pendulum|a pendulum that has a period of 2 seconds]];{{efn|This is evident from the formula {{math|1=''T'' = 2{{pi}} {{radic|''L'' / ''g''}}}}.}} most dining tabletops are about 0.75 metres high;<ref>{{cite web|url=https://www.bassettfurniture.com/blog/standard-table-sizes.aspx|title=Standard Table Sizes|website=Bassett Furniture|access-date=22 October 2019}}</ref> a very tall human (basketball forward) is about 2 metres tall.<ref>{{cite web|url=https://www.thehoopsgeek.com/average-nba-height/|title=The Average Height of NBA Players – From Point Guards to Centers|date=9 December 2018|website=The Hoops Geek|access-date=22 October 2019}}</ref>
*The kilogram is the mass of a litre of cold water; a cubic centimetre or millilitre of water has a mass of one gram; a 1-euro coin weighs 7.5&nbsp;g;<ref>{{cite web|url=http://www.rubinghscience.org/surv/euroweights1.html|title=RUBINGHSCIENCE.ORG / Using Euro coins as weights|website=www.rubinghscience.org|access-date=22 October 2019}}</ref> a Sacagawea US 1-dollar coin weighs 8.1&nbsp;g;<ref>{{cite web|url=https://www.usmint.gov/learn/coin-and-medal-programs/coin-specifications|title=Coin Specifications {{!}} U.S. Mint|website=www.usmint.gov|date=20 September 2016 |access-date=22 October 2019}}</ref> a UK 50-pence coin weighs 8.0&nbsp;g.<ref>{{cite web|url=https://www.royalmint.com/discover/uk-coins/coin-design-and-specifications/fifty-pence-coin/|title=Fifty Pence Coin|website=www.royalmint.com|access-date=22 October 2019}}</ref>
*A candela is about the luminous intensity of a moderately bright candle, or 1 candle power; a 60&nbsp;W tungsten-filament incandescent light bulb has a luminous intensity of about 64 candelas.{{efn|1=A 60 watt light bulb has about 800 lumens<ref>{{cite web|title=Lumens and the Lighting Facts Label|url=https://www.energy.gov/energysaver/save-electricity-and-fuel/lighting-choices-save-you-money/lumens-and-lighting-facts|access-date=11 June 2020|website=Energy.gov|language=en}}</ref> which is radiated equally in all directions (i.e. 4{{pi}} steradians), thus is equal to {{math|''I''<sub>v</sub> {{=}} {{sfrac|800 lm|4{{pi}} sr}} ≈ 64 cd}}.}}
*A mole of a substance has a mass that is its [[Physics:Molecular mass|molecular mass]] expressed in units of grams; the mass of a mole of carbon is 12.0&nbsp;g, and the mass of a mole of table salt is 58.4&nbsp;g.
*Since all gases have the same volume per mole at a given temperature and pressure far from their points of liquefaction and solidification (see [[Physics:Perfect gas|Perfect gas]]), and air is about {{sfrac|1|5}} oxygen (molecular mass 32) and {{sfrac|4|5}} nitrogen (molecular mass 28), the density of any near-perfect gas relative to air can be obtained to a good approximation by dividing its molecular mass by 29 (because {{nowrap|{{sfrac|4|5}} × 28 + {{sfrac|1|5}} × 32 {{=}} 28.8 ≈ 29}}). For example, [[Chemistry:Carbon monoxide|carbon monoxide]] (molecular mass 28) has almost the same density as air.
*A temperature difference of one kelvin is the same as one degree Celsius: {{sfrac|1|100}} of the temperature differential between the freezing and boiling points of water at sea level; the absolute temperature in kelvins is the temperature in degrees Celsius plus about 273; [[Physics:Human body temperature|human body temperature]] is about 37&nbsp;°C or 310&nbsp;K.
*A 60&nbsp;W incandescent light bulb rated at 120&nbsp;V (US mains voltage) consumes 0.5&nbsp;A at this voltage. A 60&nbsp;W bulb rated at 230&nbsp;V (European mains voltage) consumes 0.26&nbsp;A at this voltage.{{efn|This is evident from the formula {{math|''P'' {{=}} ''I'' ''V''}}.}}

== <span class="anchor" id="other metric systems"></span> Common metric systems ==
A number of different metric system have been developed, all using the ''Mètre des Archives'' and ''Kilogramme des Archives'' (or their descendants) as their base units, but differing in the definitions of the various derived units.

{| class="wikitable floatright" style="font-size: 95%; width:230px;"
|+Variants of the metric system<!-- without gravitational ones, mechanical units-->
! Quantity
! {{abbrlink|SI|International System of Units}}/{{abbrlink|MKS|Metre–kilogram–second system of units}}
! {{abbrlink|CGS|Centimetre–gram–second system of units}}
! {{abbrlink|MTS|Metre–tonne–second system of units}}
|-
|distance, length, height, etc. {{br}}(''d'', ''l'', ''h'', ...)
| [[Metre|metre]] {{br}}(m)
| [[Centimetre|centimetre]] {{br}}(cm)
| metre {{br}}(m)
|-
|mass {{br}}(''m'')
| [[Kilogram|kilogram]] {{br}}(kg)
| [[Gram|gram]] {{br}}(g)
| [[Tonne|tonne]] {{br}}(t)
|-
|time {{br}}(''t'')
| [[Second|second]] {{br}}(s)
| second {{br}}(s)
| second {{br}}(s)
|-
|speed, velocity {{br}}(''v'', '''v''')
| m/s
| cm/s
| m/s
|-
|acceleration {{br}}(''a'')
| m/s<sup>2</sup>
| [[Physics:Gal (unit)|gal {{br}}(Gal)]]
| m/s<sup>2</sup>
|-
|force {{br}}(''F'')
| [[Newton (unit)|newton (N)]]
| [[Physics:Dyne|dyne]] {{br}}(dyn)
| sthene {{br}}(sn)
|-
|pressure {{br}}(''P'' or ''p'')
| [[Pascal (unit)|pascal (Pa)]]
| [[Physics:Barye|barye]] {{br}}(Ba)
| [[Pièze|pièze]] {{br}}(pz)
|-
|energy {{br}}(''E'', ''Q'', ''W'')
| [[Joule|joule]] {{br}}(J)
| [[Physics:Erg|erg]] {{br}}(erg)
| kilojoule {{br}}(kJ)
|-
|power {{br}}(''P'')
| [[Watt|watt]] {{br}}(W)
| erg/s {{br}}(erg/s)
| kilowatt {{br}}(kW)
|-
|viscosity {{br}}(''μ'')
| Pa⋅s
| [[Physics:Poise (unit)|poise]] {{br}}(P)
| pz⋅s
|}

=== 19th century ===
In 1832, Gauss used the astronomical second as a base unit in defining the gravitation of the Earth, and together with the milligram and millimetre, this became [[Physics:Gaussian units|the first system of mechanical units]]. He showed that the strength of a magnet could also be quantified in terms of these units, by measuring the oscillations of a magnetized needle and finding the quantity of "magnetic fluid" that produces an acceleration of one unit when applied to a unit mass.<ref>{{Cite journal |last=O'Hara |first=James Gabriel |date=1983 |title=Gauss and the Royal Society: The Reception of His Ideas on Magnetism in Britain (1832-1842) |url=https://www.jstor.org/stable/531344 |journal=Notes and Records of the Royal Society of London |volume=38 |issue=1 |pages=17–78 |doi=10.1098/rsnr.1983.0002 |jstor=531344 |s2cid=145724822 |issn=0035-9149}}</ref><ref>{{Cite journal |last=Van Baak |first=D. A. |date=October 2013 |title=Re-creating Gauss's method for non-electrical absolute measurements of magnetic fields and moments |url=https://pubs.aip.org/aapt/ajp/article/81/10/738-744/1057517 |journal=American Journal of Physics |language=en |volume=81 |issue=10 |pages=738–744 |doi=10.1119/1.4816806 |bibcode=2013AmJPh..81..738V |issn=0002-9505}}</ref> The [[Centimetre–gram–second system of units|centimetre–gram–second system of units]] (CGS) was the first coherent metric system, having been developed in the 1860s and promoted by Maxwell and Thomson. In 1874, this system was formally promoted by the British Association for the Advancement of Science (BAAS).<ref name=SI_1_8>{{SIBrochure8th|page=109}}</ref> The system's characteristics are that density is expressed in {{nowrap|g/cm<sup>3</sup>}}, force expressed in [[Physics:Dyne|dyne]]s and mechanical energy in [[Physics:Erg|erg]]s. Thermal energy was defined in [[Calorie|calorie]]s, one calorie being the energy required to raise the temperature of one gram of water from 15.5&nbsp;°C to 16.5&nbsp;°C. The meeting also recognised two sets of units for electrical and magnetic properties – the electrostatic set of units and the electromagnetic set of units.<ref>{{cite book |title = Reports on the Committee on Standards of Electrical Resistance – Appointed by the British Association for the Advancement of Science |chapter-url = https://archive.org/stream/reportscommitte00maxwgoog |chapter = First Report – Cambridge 3 October 1862 |pages = 1–3 |first1 = William |last1 =Thomson |first2 =James Prescott |last2 =Joule |first3 = James Clerk |last3 =Maxwell |first4 =Flemming |last4 =Jenkin |editor1-first = Flemming |editor1-last =Jenkin |location = London |year =1873 |access-date = 12 May 2011}}</ref>

The CGS units of electricity were cumbersome to work with. This was remedied at the 1893 International Electrical Congress held in Chicago by defining the "international" ampere and ohm using definitions based on the [[Metre|metre]], [[Kilogram|kilogram]] and [[Second|second]], in the [[International System of Electrical and Magnetic Units]].<ref>{{cite web |url = http://physics.nist.gov/cuu/Units/ampere.html |title = Historical context of the SI—Unit of electric current (ampere) |publisher = The NIST Reference on Constants, Units and Uncertainty |access-date = 10 April 2011}}</ref> During the same period in which the CGS system was being extended to include electromagnetism, other systems were developed, distinguished by their choice of coherent base unit, including the Practical System of Electric Units, or QES (quad–eleventhgram–second) system, was being used. Here, the base units are the quad, equal to {{val|e=7|u=m}} (approximately a quadrant of the Earth's circumference), the eleventhgram, equal to {{val|e=-11|u=g}}, and the second.  These were chosen so that the corresponding electrical units of potential difference, current and resistance had a convenient magnitude.{{refn|{{citation |author=James Clerk Maxwell |year=1954 |orig-year=1891 |title=A Treatise on Electricity & Magnetism |volume=2 |edition=3rd | publisher=[[Social:Dover Publications|Dover Publications]]}}}}{{rp|268}}{{refn|name="Carron Babel"|{{cite arXiv |last=Carron |first=Neal |eprint=1506.01951 |title= Babel of Units. The Evolution of Units Systems in Classical Electromagnetism |class= physics.hist-ph |date=2015 }}}}{{rp|17}}

=== 20th century ===
In 1901, Giovanni Giorgi showed that by adding an electrical unit as a fourth base unit, the various anomalies in electromagnetic systems could be resolved. The metre–kilogram–second–[[Coulomb|coulomb]] (MKSC) and metre–kilogram–second–[[Ampere|ampere]] (MKSA) systems are examples of such systems.<ref name=IECGiorgi>{{cite web|url = http://www.iec.ch/about/history/beginning/giovanni_giorgi.htm|title = In the beginning... Giovanni Giorgi|year = 2011
|publisher = [[Organization:International Electrotechnical Commission|International Electrotechnical Commission]]|access-date = 5 April 2011|archive-date = 15 May 2011|archive-url = https://web.archive.org/web/20110515134553/http://www.iec.ch/about/history/beginning/giovanni_giorgi.htm|url-status = dead}}</ref><ref name=":1">{{Cite journal |last=Jayson |first=Joel S. |date=January 2014 |title=The Daniell cell, Ohm's law, and the emergence of the International System of Units |url=https://pubs.aip.org/aapt/ajp/article/82/1/60-65/1058039 |journal=American Journal of Physics |language=en |volume=82 |issue=1 |pages=60–65 |arxiv=1512.07306 |doi=10.1119/1.4826445 |bibcode=2014AmJPh..82...60J |s2cid=119278961 |issn=0002-9505}}</ref> 

The [[Metre–tonne–second system of units|metre–tonne–second system of units]] (MTS) was based on the metre, [[Tonne|tonne]] and second – the unit of force was the [[Sthène|sthène]] and the unit of pressure was the [[Pièze|pièze]]. It was invented in France for industrial use and from 1933 to 1955 was used both in France and in the [[Place:Soviet Union|Soviet Union]].<ref name=ieeeghn>{{cite web |url=http://www.ieeeghn.org/wiki/index.php/System_of_Measurement_Units |title = System of Measurement Units |work = IEEE Global History Network |publisher= [[Organization:Institute of Electrical and Electronics Engineers|Institute of Electrical and Electronics Engineers]] (IEEE) |access-date = 21 March 2011}}</ref><ref>{{cite web |url = http://www.hydrelect.info/articles.php?lng=fr&pg=3 |title = Notions de physique – Systèmes d'unités |language = fr |trans-title=Symbols used in physics – units of measure |access-date = 21 March 2011 |publisher = Hydrelect.info}}</ref> [[Gravitational metric system]]s use the [[Kilogram-force|kilogram-force]] (kilopond) as a base unit of force, with mass measured in a unit known as the [[Gravitational metric system|hyl]], ''Technische Masseneinheit'' (TME), mug or [[Slug (unit)|metric slug]].<ref>{{cite web
|url = http://www.numericana.com/answer/units.htm#slug
|title = Final Answers
|first1 = Gérard P
|last1 = Michon
|publisher = Numericana.com
|date = 9 September 2000
|access-date = 11 October 2012}}</ref> Although the CGPM passed a resolution in 1901 defining the standard value of [[Physics:Standard gravity|acceleration due to gravity]] to be 980.665&nbsp;cm/s<sup>2</sup>, gravitational units are not part of the [[International System of Units]] (SI).<ref>{{cite web
|url = http://www.bipm.org/en/CGPM/db/3/2/
|title = Resolution of the 3rd meeting of the CGPM (1901)
|publisher = General Conference on Weights and Measures
|access-date = 11 October 2012}}</ref>

=== International System of Units ===
The International System of Units is the modern metric system. It is based on the metre–kilogram–second–ampere (MKSA) system of units from early in the 20th century.<ref name=SI_units /> It also includes numerous coherent derived units for common quantities like power (watt) and irradience (lumen). Electrical units were taken from the International system then in use.  Other units like those for energy (joule) were modelled on those from the older CGS system, but scaled to be coherent with MKSA units. Two additional base units – the ''kelvin'', which is equivalent to degree Celsius for change in thermodynamic temperature but set so that 0&nbsp;K is [[Physics:Absolute zero|absolute zero]], and the ''candela'', which is roughly equivalent to the [[International candle|international candle]] unit of illumination – were introduced. Later, another base unit, the ''mole'', a unit of [[Physics:Amount of substance|amount of substance]] equivalent to the [[Chemistry:Avogadro number|Avogadro number]] number of specified molecules, was added along with several other derived units.<ref name="Gold Book mole">{{Cite book |url=https://goldbook.iupac.org/terms/view/M03980 |title=IUPAC – mole (M03980) |author=IUPAC Gold Book |publisher=[[Organization:International Union of Pure and Applied Chemistry|International Union of Pure and Applied Chemistry]]|doi=10.1351/goldbook.M03980 |s2cid=241546445 }}</ref>

The system was promulgated by the General Conference on Weights and Measures (French: ''Conférence générale des poids et mesures'' – CGPM) in 1960.  At that time, the metre was redefined in terms of the wavelength of a spectral line of the [[Physics:Krypton-86|krypton-86]] atom (krypton-86 being a stable isotope of an inert gas that occurs in undetectable or trace amounts naturally), and the standard metre artefact from 1889 was retired.<ref name=":0">{{cite book|last1=Urone |first1=Peter Paul |last2=Hinrichs |first2=Roger |last3=Dirks |first3=Kim |last4=Sharma |first4=Manjula |title=College Physics |publisher=OpenStax |isbn=978-1-947172-01-2 |year=2020 |url=https://openstax.org/details/books/college-physics}}</ref>{{rp|16}}

Today, the International system of units consists of 7 base units and innumerable coherent derived units including 22 with special names. The last new derived unit, the ''katal'' for catalytic activity, was added in 1999. All the base units except the second are now defined in terms of exact and invariant constants of physics or mathematics, barring those parts of their definitions which are dependent on the second itself. As a consequence, the speed of light has now become an exactly defined constant, and defines the metre as {{frac|299,792,458}} of the distance light travels in a second. The kilogram was defined by a [[International Prototype of the Kilogram|cylinder of platinum-iridium alloy]] until a [[2019 redefinition of the SI base units#Kilogram|new definition]] in terms of  [[Physics:Physical constant|natural physical constants]] was adopted in 2019. As of 2022, the range of decimal prefixes has been extended to those for 10<sup>30</sup> (''quetta–'') and 10<sup>−30</sup> (''quecto–'').<ref>{{cite web |url=https://www.theregister.com/2022/11/22/new_si_prefixes_clear_the/|title=New SI prefixes clear the way for quettabytes of storage|date=22 November 2022|publisher=The Register|access-date=23 Nov 2022|df=dmy-all}}</ref>

== See also ==
* [[Outline of metrology and measurement]]
{{Columnslist|colwidth=25em|
* [[Binary prefix]], used in computer science
* [[Physics:Electrostatic units|Electrostatic units]]
* [[History of measurement]]
* ISO/IEC 80000, international standard of quantities and their units, superseding [[Physics:ISO 31|ISO 31]]
* [[List of metric units]]
* [[Metrology]]
* [[Preferred metric sizes]]
* [[Unified Code for Units of Measure]]
}}

== Notes ==
{{notelist}}

== References ==
{{Reflist}}

== External links ==

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[[Category:Metric system| ]]
[[Category:International System of Units]]

{{Sourceattribution|Metric system}}