Wikipedia

Kilogram

"kg" redirects here. For other uses, seeKG.

Thekilogram(also spelledkilogramme[1]) is thebase unitofmassin theInternational System of Units(SI), having the unit symbolkg.[1]It is a widely used measure in science, engineering and commerce worldwide, and is often simply called akilocolloquially.[2]It means 'one thousandgrams'.

kilogram
A series of 5, 2, 1, 0.5 and 0.2 kilogram weights, made ofcast iron
General information
Unit systemSI
Unit ofmass
Symbolkg
Conversions
1 kgin...... is equal to...
Avoirdupois
British Gravitational≈0.0685slugs
CGS units1000grams
Atomic mass units6.02214076×1026Da

The kilogram is a SIbase unit,defined in terms of two other base units, thesecondand themetreand thePlanck constant,a SIdefining constant.[3]: 131 A properly equippedmetrologylaboratory can calibrate a mass measurement instrument such as aKibble balanceas a primary standard for the kilogram mass.[4]

The kilogram was originally defined in 1795 during theFrench Revolutionas the mass of onelitreofwater.The current definition of a kilogram agrees with this original definition to within 30parts per million.In 1799, the platinumKilogramme des Archivesreplaced it as the standard of mass. In 1889, a cylinder ofplatinum-iridium,theInternational Prototype of the Kilogram(IPK), became the standard of the unit of mass for the metric system and remained so for 130 years, before the current standard wasadopted in 2019.[5]

Definition

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The kilogram is defined in terms of three defining constants:[3]

  • a specific atomic transition frequencyΔνCs,which defines the duration of the second,
  • thespeed of lightc,which when combined with the second, defines the length of the metre,
  • and thePlanck constanth,which when combined with the metre and second, defines the mass of the kilogram.

The formal definition according to theGeneral Conference on Weights and Measures(CGPM) is:

The kilogram, symbol kg, is the SI unit of mass. It is defined by taking the fixed numerical value of thePlanck constanthto be6.62607015×10−34when expressed in the unit J⋅s, which is equal to kg⋅m2⋅s−1,where themetreand thesecondare defined in terms ofcandΔνCs.

— CGPM[6][7]

Defined in term of those units, the kg is formulated as:[8]

kg =⁠(299792458)2/(6.62607015×10−34)(9192631770)⁠⁠hΔνCs/c2⁠=⁠917097121160018/62154105072590475⁠1042⁠hΔνCs/c2⁠≈(1.475521399735270×1040)⁠hΔνCs/c2⁠.

This definition is generally consistent with previous definitions: themassremains within 30ppmof the mass of one litre of water.[9]

Timeline of previous definitions

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TheInternational Prototype of the Kilogram,whose mass was defined to be one kilogram from 1889 to 2019.

Name and terminology

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The kilogram is the onlybase SI unitwith anSI prefix(kilo) as part of its name. The wordkilogrammeorkilogramis derived from theFrenchkilogramme,[14]which itself was a learned coinage, prefixing theGreekstem ofχίλιοιkhilioi"a thousand" togramma,a Late Latin term for "a small weight", itself from Greekγράμμα.[15] The wordkilogrammewas written into French law in 1795, in theDecree of18 Germinal,[16] which revised the provisional system of units introduced by the FrenchNational Conventiontwo years earlier, where thegravethad been defined as weight (poids) of a cubic centimetre of water, equal to 1/1000 of agrave.[17]In the decree of 1795, the termgrammethus replacedgravet,andkilogrammereplacedgrave.[12]

The French spelling was adopted in Great Britain when the word was used for the first time in English in 1795,[18][14]with the spellingkilogrambeing adopted in the United States. In the United Kingdom both spellings are used, with "kilogram" having become by far the more common.[1]UK law regulating the units to be used whentrading by weight or measuredoes not prevent the use of either spelling.[19]

In the 19th century the French wordkilo,ashorteningofkilogramme,was imported into the English language where it has been used to mean both kilogram[20]and kilometre.[21]Whilekiloas an alternative is acceptable, toThe Economistfor example,[22]the Canadian government'sTermium Plussystem states that "SI (International System of Units) usage, followed in scientific and technical writing" does not allow its usage and it is described as "a common informal name" on Russ Rowlett's Dictionary of Units of Measurement.[23][24]When theUnited States Congressgave the metric system legal status in 1866, it permitted the use of the wordkiloas an alternative to the wordkilogram,[25]but in 1990 revoked the status of the wordkilo.[26]

The SI system was introduced in 1960 and in 1970 theBIPMstarted publishing theSI Brochure,which contains all relevant decisions and recommendations by theCGPMconcerning units. TheSI Brochurestates that "It is not permissible to use abbreviations for unit symbols or unit names...".[27][Note 2]

For use with east Asian character sets, the SI symbol is encoded as a single Unicode character,U+338F㎏SQUARE KGin theCJK Compatibilityblock.

Redefinition based on fundamental constants

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TheSI systemafter the 2019 redefinition: the kilogram is now fixed in terms of thesecond,thespeed of lightand thePlanck constant;furthermore theampereno longer depends on the kilogram
AKibble balance,which was originally used to measure thePlanck constantin terms of the IPK, can now be used to calibrate secondary standard weights for practical use.
Main article:2019 redefinition of the SI base units

The replacement of theInternational Prototype of the Kilogram(IPK) as the primary standard was motivated by evidence accumulated over a long period of time that the mass of the IPK and its replicas had been changing; the IPK had diverged from its replicas by approximately 50 micrograms since their manufacture late in the 19th century. This led toseveral competing effortsto develop measurement technology precise enough to warrant replacing the kilogram artefact with a definition based directly on physical fundamental constants.[5]

TheInternational Committee for Weights and Measures(CIPM) approved aredefinition of the SI base unitsin November 2018 that defines the kilogram by defining thePlanck constantto be exactly6.62607015×10−34kg⋅m2⋅s−1,effectively defining the kilogram in terms of the second and the metre. The new definition took effect on May 20, 2019.[5][6][28]

Prior to the redefinition, the kilogram and several other SI units based on the kilogram were defined by a man-made metal artifact: theKilogramme des Archivesfrom 1799 to 1889, and the IPK from 1889 to 2019.[5]

In 1960, themetre,previously similarly having been defined with reference to a single platinum-iridium bar with two marks on it, was redefined in terms of an invariant physical constant (the wavelength of a particular emission of light emitted bykrypton,[29]and later thespeed of light) so that the standard can be independently reproduced in different laboratories by following a written specification.

At the 94th Meeting of the CIPM in 2005, it was recommended that the same be done with the kilogram.[30]

In October 2010, the CIPM voted to submit a resolution for consideration at theGeneral Conference on Weights and Measures(CGPM), to "take note of an intention" that the kilogram be defined in terms of thePlanck constant,h(which has dimensions of energy times time, thus mass × length2/ time) together with other physical constants.[31][32]This resolution was accepted by the 24th conference of the CGPM[33]in October 2011 and further discussed at the 25th conference in 2014.[34][35]Although the Committee recognised that significant progress had been made, they concluded that the data did not yet appear sufficiently robust to adopt the revised definition, and that work should continue to enable the adoption at the 26th meeting, scheduled for 2018.[34]Such a definition would theoretically permit any apparatus that was capable of delineating the kilogram in terms of the Planck constant to be used as long as it possessed sufficient precision, accuracy and stability. TheKibble balanceis one way to do this.[36]

As part of this project, a variety of verydifferent technologies and approacheswere considered and explored over many years. Some of these approaches were based on equipment and procedures that would enable the reproducible production of new, kilogram-mass prototypes on demand (albeit with extraordinary effort) using measurement techniques and material properties that are ultimately based on, or traceable to, physical constants. Others were based on devices that measured either the acceleration or weight of hand-tuned kilogram test masses and which expressed their magnitudes in electrical terms via special components that permit traceability to physical constants. All approaches depend on converting a weight measurement to a mass and therefore require precise measurement of the strength of gravity in laboratories (gravimetry). All approaches would have precisely fixed one or more constants of nature at a defined value.[citation needed]

SI multiples

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Main article:Orders of magnitude (mass)
"Milligram" redirects here. For the American band, seeMilligram (band).For the horse, seeMilligram (horse).
"Miligram" redirects here. For the Serbian band, seeMiligram (band).For the name, seeMilgram.

Because an SI unit may not have multiple prefixes (seeSI prefix), prefixes are added togram,rather than the base unitkilogram,which already has a prefix as part of its name.[37]For instance, one-millionth of a kilogram is 1mg (one milligram), not 1μkg (one microkilogram).

SI multiples of gram (g)
Submultiples Multiples
Value SI symbol Name Value SI symbol Name
10−1g dg decigram 101g dag decagram
10−2g cg centigram 102g hg hectogram
10−3g mg milligram 103g kg kilogram
10−6g μg microgram 106g Mg megagram(tonne)
10−9g ng nanogram 109g Gg gigagram
10−12g pg picogram 1012g Tg teragram
10−15g fg femtogram 1015g Pg petagram
10−18g ag attogram 1018g Eg exagram
10−21g zg zeptogram 1021g Zg zettagram
10−24g yg yoctogram 1024g Yg yottagram
10−27g rg rontogram 1027g Rg ronnagram
10−30g qg quectogram 1030g Qg quettagram
Common prefixed units are in bold face.[Note 3]

Practical issues with SI weight names

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  • Serious medication errors have been made by confusing milligrams and micrograms when micrograms has been abbreviated.[38]The abbreviation "mcg" rather than the SI symbol "μg" is formally mandated for medical practitioners in the US by theJoint Commission on Accreditation of Healthcare Organizations(JCAHO).[39]In the United Kingdom, theNational Institute for Health and Care Excellenceand Scottish Palliative Care Guidelines state that "micrograms" and "nanograms" must both be written in full, and never abbreviated as "mcg" or "μg".[38][40]
  • The hectogram (100 g) (Italian:ettogrammooretto) is a very commonly used unit in the retail food trade in Italy.[41][42][43]
  • The former standard spelling and abbreviation "deka-" and "dk" produced abbreviations such as "dkm" (dekametre) and "dkg" (dekagram).[44]As of 2020,the abbreviation "dkg" (10 g) is still used in parts of central Europe in retail for some foods such as cheese and meat.[45][46][47][48][49]
  • The unit namemegagramis rarely used, and even then typically only in technical fields in contexts where especially rigorous consistency with the SI standard is desired. For most purposes, the nametonneis instead used. The tonne and its symbol, "t", were adopted by the CIPM in 1879. It is a non-SI unit accepted by the BIPM for use with the SI. According to the BIPM, "This unit is sometimes referred to as 'metric ton' in some English-speaking countries."[50]

See also

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Notes

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  1. ^The avoirdupois pound is part of bothUnited States customary system of unitsand theImperial system of units.It isdefined as exactly0.45359237kilograms.
  2. ^The French text (which is the authoritative text) states "Il n'est pas autorisé d'utiliser des abréviations pour les symboles et noms d'unités..."
  3. ^Criterion: A combined total of at least five occurrences on theBritish National Corpusand theCorpus of Contemporary American English,including both the singular and the plural for both the -gramand the -grammespelling.

References

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  1. ^abc "Kilogram".Oxford Dictionaries.Archived fromthe originalon January 31, 2013.RetrievedNovember 3,2011.
  2. ^Merriam-Mebster definition of Kilo
  3. ^abInternational Bureau of Weights and Measures(May 20, 2019),The International System of Units (SI)(PDF)(9th ed.),ISBN978-92-822-2272-0,archivedfrom the original on October 18, 2021
  4. ^"Mise en pratique for the definition of the kilogram in the SI".BIPM.org.July 7, 2021.RetrievedFebruary 18,2022.
  5. ^abcdeResnick, Brian (May 20, 2019)."The new kilogram just debuted. It's a massive achievement".vox.com.RetrievedMay 23,2019.
  6. ^abDraft Resolution A "On the revision of the International System of units (SI)" to be submitted to the CGPM at its 26th meeting (2018)(PDF),archived(PDF)from the original on April 2, 2021
  7. ^Decision CIPM/105-13 (October 2016).The day is the 144th anniversary of theMetre Convention.
  8. ^SI Brochure: The International System of Units (SI).BIPM, 9th edition, 2019.
  9. ^The density of water is0.999972g/cm3at3.984 °C.SeeFranks, Felix (2012).The Physics and Physical Chemistry of Water.Springer.ISBN978-1-4684-8334-5.
  10. ^Guyton;Lavoisier;Monge;Berthollet;et al. (1792).Annales de chimie ou Recueil de mémoires concernant la chimie et les arts qui en dépendent.Vol. 15–16. Paris: Chez Joseph de Boffe. p. 277.
  11. ^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
  12. ^abZupko, Ronald Edward(1990).Revolution in Measurement: Western European Weights and Measures Since the Age of Science.Philadelphia: American Philosophical Society.ISBN978-0-87169-186-6.
  13. ^"Treaty of the Metre".Encyclopædia Britannica.2023.RetrievedJuly 18,2023.
  14. ^ab"Kilogram".Oxford English Dictionary.Oxford University Press.RetrievedNovember 3,2011.[permanent dead link]
  15. ^ Fowlers, HW; Fowler, FG (1964).The Concise Oxford Dictionary.Oxford: The Clarendon Press.Greekγράμμα(as it wereγράφ-μα,Doricγράθμα) means "something written, a letter", but it came to be used as a unit of weight, apparently equal to⁠1/24⁠of anounce(⁠1/288⁠of alibra,which would correspond to about 1.14 grams in modern units), at some time during Late Antiquity. Frenchgrammewas adopted from Latingramma,itself quite obscure, but found in theCarmen de ponderibus et mensuris(8.25) attributed byRemmius Palaemon(fl. 1st century), where it is the weight of twooboli(Charlton T. Lewis, Charles Short,A Latin Dictionarys.v. "gramma",1879). Henry George Liddell. Robert Scott.A Greek-English Lexicon(revised and augmented edition, Oxford, 1940)s.v. γράμμα,citing the 10th-century workGeoponicaand a 4th-century papyrus edited in L. Mitteis,Griechische Urkunden der Papyrussammlung zu Leipzig,vol. i (1906), 62 ii 27.
  16. ^ "Décret relatif aux poids et aux mesures du 18 germinal an 3 (7 avril 1795)"[Decree of 18 Germinal, year III (April 7, 1795) regarding weights and measures].Grandes lois de la République(in French). Digithèque de matériaux juridiques et politiques, Université de Perpignan.RetrievedNovember 3,2011.
  17. ^Convention nationale, décret du 1eraoût 1793, ed. Duvergier,Collection complète des lois, décrets, ordonnances, règlemens avis du Conseil d'état, publiée sur les éditions officielles du Louvre,vol. 6 (2nd ed. 1834),p. 70. Themetre(mètre) on which this definition depends was itself defined as the ten-millionth part of a quarter of Earth'smeridian,given intraditional unitsas 3pieds,11.44lignes(alignebeing the 12th part of apouce(inch), or the 144th part of apied.
  18. ^Peltier, Jean-Gabriel (1795)."Paris, during the year 1795".Monthly Review.17:556.RetrievedAugust 2,2018.Contemporaneous English translation of the French decree of 1795
  19. ^ "Spelling of" gram ", etc".Weights and Measures Act 1985.Her Majesty's Stationery Office.October 30, 1985.RetrievedNovember 6,2011.
  20. ^ "kilo (n1)".Oxford English Dictionary(2nd ed.). Oxford: Oxford University Press. 1989.RetrievedNovember 8,2011.
  21. ^"kilo (n2)".Oxford English Dictionary(2nd ed.). Oxford: Oxford University Press. 1989.RetrievedNovember 8,2011.
  22. ^"Style Guide"(PDF).The Economist.January 7, 2002. Archived fromthe original(PDF)on July 1, 2017.RetrievedNovember 8,2011.
  23. ^ "kilogram, kg, kilo".Termium Plus.Government of Canada. October 8, 2009.RetrievedMay 29,2019.
  24. ^ "kilo".How Many?.Archived fromthe originalon November 16, 2011.RetrievedNovember 6,2011.
  25. ^ 29th Congress of the United States, Session 1 (May 13, 1866)."H.R. 596, An Act to authorize the use of the metric system of weights and measures".Archived fromthe originalon July 5, 2015.{{cite web}}:CS1 maint: numeric names: authors list (link)
  26. ^ "Metric System of Measurement:Interpretation of the International System of Units for the United States; Notice"(PDF).Federal Register.63(144): 40340. July 28, 1998. Archived fromthe original(PDF)on October 15, 2011.RetrievedNovember 10,2011.Obsolete UnitsAs stated in the 1990 Federal Register notice,...
  27. ^International Bureau of Weights and Measures(2006),The International System of Units (SI)(PDF)(8th ed.), p. 130,ISBN92-822-2213-6,archived(PDF)from the original on June 4, 2021,retrievedDecember 16,2021
  28. ^ Pallab Ghosh (November 16, 2018)."Kilogram gets a new definition".BBC News.RetrievedNovember 16,2018.
  29. ^International Bureau of Weights and Measures(2006),The International System of Units (SI)(PDF)(8th ed.), p. 112,ISBN92-822-2213-6,archived(PDF)from the original on June 4, 2021,retrievedDecember 16,2021
  30. ^ Recommendation 1: Preparative steps towards new definitions of the kilogram, the ampere, the kelvin and the mole in terms of fundamental constants(PDF).94th meeting of the International Committee for Weights and Measures. October 2005. p. 233.Archived(PDF)from the original on June 30, 2007.RetrievedFebruary 7,2018.
  31. ^"NIST Backs Proposal for a Revamped System of Measurement Units".NIST.Nist.gov. October 26, 2010.RetrievedApril 3,2011.
  32. ^ Ian Mills (September 29, 2010)."Draft Chapter 2 for SI Brochure, following redefinitions of the base units"(PDF).CCU.RetrievedJanuary 1,2011.
  33. ^ Resolution 1 – On the possible future revision of the International System of Units, the SI(PDF).24th meeting of the General Conference on Weights and Measures. Sèvres, France. October 17–21, 2011.RetrievedOctober 25,2011.
  34. ^ab"BIPM – Resolution 1 of the 25th CGPM".www.bipm.org.RetrievedMarch 27,2017.
  35. ^ "General Conference on Weights and Measures approves possible changes to the International System of Units, including redefinition of the kilogram"(PDF)(Press release). Sèvres, France:General Conference on Weights and Measures.October 23, 2011.RetrievedOctober 25,2011.
  36. ^Robinson, Ian A.; Schlamminger, Stephan (2016)."The watt or Kibble balance: A technique for implementing the new SI definition of the unit of mass".Metrologia.53(5): A46–A74.Bibcode:2016Metro..53A..46R.doi:10.1088/0026-1394/53/5/A46.PMC8752041.PMID35023879.
  37. ^BIPM: SI Brochure: Section 3.2,The kilogramArchivedMarch 29, 2016, at theWayback Machine
  38. ^ab"Prescribing Information for Liquid Medicines".Scottish Palliative Care Guidelines.Archived fromthe originalon July 10, 2018.RetrievedJune 15,2015.
  39. ^"New Joint Commission" Do Not Use "List: Abbreviations, Acronyms, and Symbols".American Academy of Physical Medicine and Rehabilitation. Archived fromthe originalon September 15, 2015.RetrievedFebruary 19,2024.
  40. ^"Prescription writing".National Institute for Health and Care Excellence.RetrievedFebruary 19,2024.
  41. ^Tom Stobart,The Cook's Encyclopedia,1981, p. 525
  42. ^J.J. Kinder, V.M. Savini,Using Italian: A Guide to Contemporary Usage,2004,ISBN0521485568,p. 231
  43. ^Giacomo Devoto, Gian Carlo Oli,Nuovo vocabolario illustrato della lingua italiana,1987,s.v.'ètto': "frequentissima nell'uso comune:un e. di caffè, un e. di mortadella; formaggio a 2000 lire l'etto"
  44. ^U.S. National Bureau of Standards,The International Metric System of Weights and Measures,"Official Abbreviations of International Metric Units", 1932,p. 13
  45. ^"Jestřebická hovězí šunka 10 dkg | Rancherské speciality".eshop.rancherskespeciality.cz(in Czech). Archived fromthe originalon June 16, 2020.RetrievedJune 16,2020.
  46. ^"Sedliacka šunka 1 dkg | Gazdovský dvor – Farma Busov Gaboltov".Sedliacka šunka 1 dkg(in Slovak). Archived fromthe originalon June 16, 2020.RetrievedJune 16,2020.
  47. ^"sýr bazalkový – Farmářské Trhy".www.e-farmarsketrhy.cz(in Czech). Archived fromthe originalon June 16, 2020.RetrievedJune 16,2020.
  48. ^"English Menu – Cafe Mediterran".Archived fromthe originalon June 16, 2020.RetrievedJune 16,2020.Beef steak 20 dkg; Beef steak 40 dkg;Thick crust 35 dkg
  49. ^"Termékek – Csíz Sajtműhely"(in Hungarian). Archived fromthe originalon June 16, 2020.RetrievedJune 16,2020.
  50. ^Non-SI units that are accepted for use with the SI,SI Brochure: Section 4 (Table 8),BIPM
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Wikimedia Commons has media related toKilogram.
NIST:K20, the US National Prototype Kilogramresting on an egg crate fluorescent light panel
BIPM:Steam cleaning a 1 kg prototype before a mass comparison
BIPM:The IPK and its six sister copies in their vault
The Age:Silicon sphere for the Avogadro Project
NPL:The NPL's Watt Balance project
NIST: This particularRueprecht Balance,an Austrian-made precision balance, was used by the NIST from 1945 until 1960
BIPM:The FB‑2 flexure-strip balance,the BIPM's modern precision balance featuring a standard deviation of one ten-billionth of a kilogram (0.1μg)
BIPM:Mettler HK1000 balance,featuring 1μg resolution and a 4kg maximum mass. Also used by NIST and Sandia National Laboratories' Primary Standards Laboratory
Micro-g LaCoste:FG‑5 absolute gravimeter,(diagram), used in national laboratories to measure gravity to 2μGalaccuracy

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