Editing Kilogram (section)

== Definition ==
The kilogram is defined in terms of three defining constants:<ref name="SIBrochure9thEd">{{citation |title=The International System of Units (SI) |author=International Bureau of Weights and Measures |author-link=New SI |date=20 May 2019  |edition=9th |isbn=978-92-822-2272-0 |url=https://www.bipm.org/utils/common/pdf/si-brochure/SI-Brochure-9.pdf| archive-url = https://web.archive.org/web/20211018184555/https://www.bipm.org/documents/20126/41483022/SI-Brochure-9.pdf/fcf090b2-04e6-88cc-1149-c3e029ad8232 |archive-date=18 October 2021 |url-status=live}}</ref>  
* a specific atomic transition frequency {{math|[[Caesium standard|Δ''ν''<sub>Cs</sub>]]}}, which defines the duration of the second,
* the [[speed of light]] {{mvar|c}}, which when combined with the second, defines the length of the metre,
* and the [[Planck constant]] {{mvar|h}}, which when combined with the metre and second, defines the mass of the kilogram.
The formal definition according to the [[General Conference on Weights and Measures]] (CGPM) is:
<!-- this is an exact quote. Do not change it.-->{{Blockquote|The kilogram, symbol kg, is the SI unit of mass. It is defined by taking the fixed numerical value of the [[Planck constant]] {{mvar|h}} to be {{val|6.62607015|e=-34}} when expressed in the unit J⋅s, which is equal to kg⋅m<sup>2</sup>⋅s<sup>−1</sup>, where the [[metre]] and the [[second]] are defined in terms of {{mvar|c}} and {{math|Δ''ν''<sub>Cs</sub>}}.|source= CGPM<ref name="draft-resolution-A">
{{citation
 |title=Draft Resolution A "On the revision of the International System of units (SI)" to be submitted to the CGPM at its 26th meeting (2018)
 |url=https://www.bipm.org/utils/en/pdf/CGPM/Draft-Resolution-A-EN.pdf
 |archive-url=https://web.archive.org/web/20210402142630/https://www.bipm.org/utils/en/pdf/CGPM/Draft-Resolution-A-EN.pdf
 |archive-date=April 2, 2021
 |url-status=live
}}</ref><ref>[http://www.bipm.org/en/committees/cipm/meeting/105.html Decision CIPM/105-13 (October 2016)]. The day is the 144th anniversary of the [[Metre Convention]].</ref>}}
Defined in term of those units, the kg is formulated as:<ref>[https://www.bipm.org/en/publications/si-brochure/ SI Brochure: The International System of Units (SI)]. BIPM, 9th edition, 2019.</ref>

{{block indent|1=kg = {{math|{{sfrac|({{val|299792458}}){{sup|2}}|({{val|6.62607015|e=-34}})({{val|9192631770}})}}{{sfrac|{{gaps|''h''|Δ''ν''<sub>Cs</sub>}}|''c''{{sup|2}}}}}}}}
{{block indent|1=
≈ {{math|({{val|1.4755214|e=40}}){{sfrac|{{gaps|''h''|Δ''ν''<sub>Cs</sub>}}|''c''{{sup|2}}}}}}.}}

This definition is generally consistent with previous definitions: the [[Mass versus weight|mass]] remains within 30 [[parts per million|ppm]] of the mass of one litre of water.<ref>The density of water is {{val|0.999972|u=g/cm3}} at {{val|3.984|u=°C}}. See {{cite book |last=Franks |first=Felix |title=The Physics and Physical Chemistry of Water |url=https://books.google.com/books?id=5f_xBwAAQBAJ&pg=PA376 |year=2012 |publisher=Springer |isbn=978-1-4684-8334-5}}</ref>

=== Timeline of previous definitions ===
[[File:International prototype of the kilogram aka Le Grand K.jpg|thumb|right|The [[International Prototype of the Kilogram]], whose mass was defined to be one kilogram from 1889 to 2019.]]
* 1793: The [[grave (unit)|grave]] (the precursor of the kilogram) was defined as the mass of 1 [[litre]] (dm<sup>3</sup>) of water, which was determined to be 18841 [[Grain (unit)|grains]].<ref>{{cite book |title=Annales de chimie ou Recueil de mémoires concernant la chimie et les arts qui en dépendent |date=1792|url=https://books.google.com/books?id=FufDNJHvgFEC&q=18841+grains+grave&pg=RA1-PA278 |location= Paris |publisher= Chez Joseph de Boffe |page= 277 |volume = 15–16| last1=Guyton| last2=Lavoisier| last3=Monge| last4=Berthollet| display-authors=etal|author-link1=Louis-Bernard Guyton de Morveau| author-link2=Antoine Lavoisier| author-link3=Gaspard Monge| author-link4=Claude Louis Berthollet}}</ref> 
* 1795: the gram (<sup>1</sup>/<sub>1000</sub> of a kilogram) was provisionally defined as the mass of one cubic [[centimetre]] of water at the melting point of ice.<ref>{{lang|fr|Gramme, le poids absolu d'un volume d'eau pure égal au cube de la centième partie du mètre, et à la température de la glace fondante}}</ref>
* 1799: The [[Kilogramme des Archives]] was manufactured as a prototype. It had a mass equal to the mass of 1&nbsp;dm<sup>3</sup> of water at the temperature of its maximum density, which is approximately 4&nbsp;[[Celsius|°C]].<ref name="Zupko">{{cite book |last=Zupko |first=Ronald Edward| author-link =Ronald Edward Zupko|date=1990 |title=Revolution in Measurement: Western European Weights and Measures Since the Age of Science |url=https://archive.org/details/bub_gb_uYCNFkRgXCoC |location=Philadelphia |publisher=American Philosophical Society |isbn=978-0-87169-186-6}}</ref>
* 1875–1889: The [[Metre Convention]] was signed in 1875, leading to the production of the [[International Prototype of the Kilogram]] (IPK) in 1879 and its adoption in 1889.<ref>{{cite encyclopedia|url = http://www.britannica.com/EBchecked/topic/378767/Treaty-of-the-Metre|title = Treaty of the Metre|encyclopedia = [[Encyclopædia Britannica]]|access-date = 18 July 2023|year = 2023}}</ref>
* 2019: The kilogram was [[2019 revision of the SI|defined]] in terms of the [[Planck constant]], the [[speed of light]] and [[Caesium standard|hyperfine transition frequency of <sup>133</sup>Cs]] as approved by the [[General Conference on Weights and Measures]] (CGPM) on 16 November 2018.<ref name="vox"/>