International System of Units - Wikipedia

Coherent and non-coherent SI units InternationalSystemofUnits FromWikipedia,thefreeencyclopedia Jumptonavigation Jumptosearch "SI"redirectshere.Forotheruses,seeSi(disambiguation). Modernformofthemetricsystem Forbroadercoverageofthistopic,seeOutlineofthemetricsystem. TheSIlogo,producedbytheBIPM,showingthesevenSIbaseunitsandthesevendefiningconstants[1] SIbaseunits Symbol Name Quantity s second time m metre length kg kilogram mass A ampere electriccurrent K kelvin thermodynamictemperature mol mole amountofsubstance cd candela luminousintensity SIdefiningconstants Symbol Name Exactvalue ΔνCs hyperfinetransitionfrequencyofCs 9192631770 Hz c speedoflight 299792458 m/s h Planckconstant 6.62607015×10−34 J⋅s e elementarycharge 1.602176634×10−19 C k Boltzmannconstant 1.380649×10−23 J/K NA Avogadroconstant 6.02214076×1023 mol−1 Kcd luminousefficacyof540 THzradiation 683 lm/W TheInternationalSystemofUnits,knownbytheinternationalabbreviationSI[a]inalllanguages[2]: 125 [3]: iii [4]andsometimespleonasticallyastheSIsystem,[b]isthemodernform[2]: 117 [7]:41[8]ofthemetricsystem[g]andtheworld'smostwidelyusedsystemofmeasurement.[2]: 123 [10]:252[11]Establishedandmaintained[12]bytheGeneralConferenceonWeightsandMeasures[j](CGPM[k]),itistheonlysystemofmeasurementwithanofficialstatus[m]innearlyeverycountryintheworld,[n]employedinscience,technology,industry,andeverydaycommerce.TheSIcomprisesacoherent[o]systemofunitsofmeasurementstartingwithsevenbaseunits,whicharethesecond(symbols,theunitoftime),metre(m,length),kilogram(kg,mass),ampere(A,electriccurrent),kelvin(K,thermodynamictemperature),mole(mol,amountofsubstance),andcandela(cd,luminousintensity).Thesystemcanaccommodatecoherentunitsforanunlimitednumberofadditionalquantities.Thesearecalledcoherentderivedunits,whichcanalwaysberepresentedasproductsofpowersofthebaseunits.[p]Twenty-twocoherentderivedunitshavebeenprovidedwithspecialnamesandsymbols.[q]Thesevenbaseunitsandthe22coherentderivedunitswithspecialnamesandsymbolsmaybeusedincombinationtoexpressothercoherentderivedunits.[r]Sincethesizesofcoherentunitswillbeconvenientforonlysomeapplicationsandnotforothers,theSIprovidestwentyprefixeswhich,whenaddedtothenameandsymbolofacoherentunit[s]producetwentyadditional(non-coherent)SIunitsforthesamequantity;thesenon-coherentunitsarealwaysdecimal(i.e.power-of-ten)multiplesandsub-multiplesofthecoherentunit.[t][u]TheSIisintendedtobeanevolvingsystem;unitsandprefixesarecreatedandunitdefinitionsaremodifiedthroughinternationalagreementasthetechnologyofmeasurementprogressesandtheprecisionofmeasurementsimproves. Since2019,themagnitudesofallSIunitshavebeendefinedbydeclaringthatsevendefiningconstantshavecertainexactnumericalvalueswhenexpressedintermsoftheirSIunits.Thesedefiningconstantsarethespeedoflightinvacuumc,thehyperfinetransitionfrequencyofcaesiumΔνCs,thePlanckconstanth,theelementarychargee,theBoltzmannconstantk,theAvogadroconstantNA,andtheluminousefficacyKcd.ThenatureofthedefiningconstantsrangesfromfundamentalconstantsofnaturesuchasctothepurelytechnicalconstantKcd.Priorto2019,h,e,k,andNAwerenotdefinedaprioributwereratherverypreciselymeasuredquantities.In2019,theirvalueswerefixedbydefinitiontotheirbestestimatesatthetime,ensuringcontinuitywithpreviousdefinitionsofthebaseunits. ThecurrentwayofdefiningtheSIisaresultofadecades-longmovetowardsincreasinglyabstractandidealisedformulationinwhichtherealisationsoftheunitsareseparatedconceptuallyfromthedefinitions.Aconsequenceisthatasscienceandtechnologiesdevelop,newandsuperiorrealisationsmaybeintroducedwithouttheneedtoredefinetheunit.Oneproblemwithartefactsisthattheycanbelost,damaged,orchanged;anotheristhattheyintroduceuncertaintiesthatcannotbereducedbyadvancementsinscienceandtechnology.ThelastartefactusedbytheSIwastheInternationalPrototypeoftheKilogram,acylinderofplatinum-iridium. TheoriginalmotivationforthedevelopmentoftheSIwasthediversityofunitsthathadsprungupwithinthecentimetre–gram–second(CGS)systems(specificallytheinconsistencybetweenthesystemsofelectrostaticunitsandelectromagneticunits)andthelackofcoordinationbetweenthevariousdisciplinesthatusedthem.TheGeneralConferenceonWeightsandMeasures(French:Conférencegénéraledespoidsetmesures–CGPM),whichwasestablishedbytheMetreConventionof1875,broughttogethermanyinternationalorganisationstoestablishthedefinitionsandstandardsofanewsystemandtostandardisetherulesforwritingandpresentingmeasurements.Thesystemwaspublishedin1960asaresultofaninitiativethatbeganin1948,soitisbasedonthemetre–kilogram–secondsystemofunits(MKS)ratherthananyvariantoftheCGS. Contents 1Introduction 1.1Controllingbody 1.2Overviewoftheunits 1.2.1SIbaseunits 1.2.2SIderivedunits 1.2.3WhySIkeptthedistinctionbetweenbaseandderivedunits 1.2.4SImetricprefixesandthedecimalnatureoftheSI 1.2.5Coherentandnon-coherentSIunits 1.2.6Permittednon-SIunits 1.2.7Newunits 1.3Definingmagnitudesofunits 1.4Specifyingfundamentalconstantsvs.othermethodsofdefinition 1.5History 2Controllingauthority 3Unitsandprefixes 3.1Baseunits 3.2Derivedunits 3.3Prefixes 3.4Non-SIunitsacceptedforusewithSI 3.5Commonnotionsofthemetricunits 4Lexicographicconventions 4.1Unitnames 4.2Unitsymbolsandthevaluesofquantities 4.2.1Generalrules 4.2.2PrintingSIsymbols 5InternationalSystemofQuantities 6Realisationofunits 7EvolutionoftheSI 7.1ChangestotheSI 7.22019redefinitions 8History 8.1Theimprovisationofunits 8.2MetreConvention 8.3TheCGSandMKSsystems 8.4ThePracticalsystemofunits 8.5BirthoftheSI 8.6Historicaldefinitions 9MetricunitsthatarenotrecognisedbytheSI 10Seealso 11Notes 12References 13Furtherreading 14Externallinks Introduction[edit] Countriesusingthemetric(SI),imperial,andUScustomarysystemsasof2019. TheInternationalSystemofUnits,orSI,[2]: 123 isadecimal[v]andmetric[w]systemofunitsestablishedin1960andperiodicallyupdatedsincethen.TheSIhasanofficialstatusinmostcountries,[x]includingtheUnitedStates,[y]Canada,andtheUnitedKingdom,althoughthesethreecountriesareamongstahandfulofnationsthat,tovariousdegrees,alsocontinuetousetheircustomarysystems.Nevertheless,withthisnearlyuniversallevelofacceptance,theSI"hasbeenusedaroundtheworldasthepreferredsystemofunits,thebasiclanguageforscience,technology,industryandtrade."[2]: 123  TheonlyothertypesofmeasurementsystemthatstillhavewidespreaduseacrosstheworldaretheImperialandUScustomarymeasurementsystems,andtheyarelegallydefinedintermsoftheSI.[z]Thereareother,lesswidespreadsystemsofmeasurementthatareoccasionallyusedinparticularregionsoftheworld.Inaddition,therearemanyindividualnon-SIunitsthatdon'tbelongtoanycomprehensivesystemofunits,butthatareneverthelessstillregularlyusedinparticularfieldsandregions.BothofthesecategoriesofunitarealsotypicallydefinedlegallyintermsofSIunits.[aa] Controllingbody[edit] TheSIwasestablishedandismaintainedbytheGeneralConferenceonWeightsandMeasures(CGPM[k]).[12]Inpractice,theCGPMfollowstherecommendationsoftheConsultativeCommitteeforUnits(CCU),whichistheactualbodyconductingtechnicaldeliberationsconcerningnewscientificandtechnologicaldevelopmentsrelatedtothedefinitionofunitsandtheSI.TheCCUreportstotheInternationalCommitteeforWeightsandMeasures(CIPM[ab]),which,inturn,reportstotheCGPM.Seebelowformoredetails. AllthedecisionsandrecommendationsconcerningunitsarecollectedinabrochurecalledTheInternationalSystemofUnits(SI)[ac],whichispublishedbytheInternationalBureauofWeightsandMeasures(BIPM[ad])andperiodicallyupdated. Overviewoftheunits[edit] SIbaseunits[edit] TheSIselectssevenunitstoserveasbaseunits,correspondingtosevenbasephysicalquantities.[ae][af]Theyarethesecond,withthesymbols,whichistheSIunitofthephysicalquantityoftime;themetre,symbolm,theSIunitoflength;kilogram(kg,theunitofmass);ampere(A,electriccurrent);kelvin(K,thermodynamictemperature);mole(mol,amountofsubstance);andcandela(cd,luminousintensity).[2]AllunitsintheSIcanbeexpressedintermsofthebaseunits,andthebaseunitsserveasapreferredsetforexpressingoranalysingtherelationshipsbetweenunits. SIderivedunits[edit] Thesystemallowsforanunlimitednumberofadditionalunits,calledderivedunits,whichcanalwaysberepresentedasproductsofpowersofthebaseunits,possiblywithanontrivialnumericmultiplier.Whenthatmultiplierisone,theunitiscalledacoherentderivedunit.[ag]ThebaseandcoherentderivedunitsoftheSItogetherformacoherentsystemofunits(thesetofcoherentSIunits).[ah]Twenty-twocoherentderivedunitshavebeenprovidedwithspecialnamesandsymbols.[ai]Thesevenbaseunitsandthe22derivedunitswithspecialnamesandsymbolsmaybeusedincombinationtoexpressotherderivedunits,[aj]whichareadoptedtofacilitatemeasurementofdiversequantities. WhySIkeptthedistinctionbetweenbaseandderivedunits[edit] Priortoitsredefinitionin2019,theSIwasdefinedthroughthesevenbaseunitsfromwhichthederivedunitswereconstructedasproductsofpowersofthebaseunits.Aftertheredefinition,theSIisdefinedbyfixingthenumericalvaluesofsevendefiningconstants.Thishastheeffectthatthedistinctionbetweenthebaseunitsandderivedunitsis,inprinciple,notneeded,sinceallunits,baseaswellasderived,maybeconstructeddirectlyfromthedefiningconstants.Nevertheless,thedistinctionisretainedbecause'itisusefulandhistoricallywellestablished',andalsobecausetheISO/IEC80000seriesofstandards[ak]specifiesbaseandderivedquantitiesthatnecessarilyhavethecorrespondingSIunits.[2]: 129  SImetricprefixesandthedecimalnatureoftheSI[edit] Likeallmetricsystems,theSIusesmetricprefixestosystematicallyconstruct,forthesamephysicalquantity,asetofunitsthataredecimalmultiplesofeachotheroverawiderange. Forexample,whilethecoherentunitoflengthisthemetre,[al]theSIprovidesafullrangeofsmallerandlargerunitsoflength,anyofwhichmaybemoreconvenientforanygivenapplication–forexample,drivingdistancesarenormallygiveninkilometres(symbolkm)ratherthaninmetres.Herethemetricprefix'kilo-'(symbol'k')standsforafactorof1000;thus,1 km=1000 m.[am] ThecurrentversionoftheSIprovidestwentymetricprefixesthatsignifydecimalpowersrangingfrom10−24to1024.[2]: 143–4 Mostprefixescorrespondtointegerpowersof1000;theonlyonesthatdonotarethosefor10,1/10,100,and1/100. Ingeneral,givenanycoherentunitwithaseparatenameandsymbol,[an]oneformsanewunitbysimplyaddinganappropriatemetricprefixtothenameofthecoherentunit(andacorrespondingprefixsymboltothecoherentunit'ssymbol).[ao]Sincethemetricprefixsignifiesaparticularpoweroften,thenewunitisalwaysapower-of-tenmultipleorsub-multipleofthecoherentunit.Thus,theconversionbetweendifferentSIunitsforoneandthesamephysicalquantityisalwaysthroughapoweroften.[ap]ThisiswhytheSI(andmetricsystemsmoregenerally)arecalleddecimalsystemsofmeasurementunits.[18][aq] Thegroupingformedbyaprefixsymbolattachedtoaunitsymbol(e.g.'km','cm')constitutesanewinseparableunitsymbol.Thisnewsymbolcanberaisedtoapositiveornegativepowerandcanbecombinedwithotherunitsymbolstoformcompoundunitsymbols.[2]: 143 Forexample,g/cm3isanSIunitofdensity,wherecm3istobeinterpretedas(cm)3. Coherentandnon-coherentSIunits[edit] WhenprefixesareusedwiththecoherentSIunits,theresultingunitsarenolongercoherent,becausetheprefixintroducesanumericalfactorotherthanone.[2]: 137 Theoneexceptionisthekilogram,theonlycoherentSIunitwhosenameandsymbol,forhistoricalreasons,includeaprefix.[ar] ThecompletesetofSIunitsconsistsofboththecoherentsetandthemultiplesandsub-multiplesofcoherentunitsformedbyusingtheSIprefixes.[2]: 138 Forexample,themetre,kilometre,centimetre,nanometre,etc.areallSIunitsoflength,thoughonlythemetreisacoherentSIunit.Asimilarstatementholdsforderivedunits:forexample,kg/m3,g/dm3,g/cm3,Pg/km3,etc.areallSIunitsofdensity,butofthese,onlykg/m3isacoherentSIunit. Moreover,themetreistheonlycoherentSIunitoflength.EveryphysicalquantityhasexactlyonecoherentSIunit,althoughthisunitmaybeexpressibleindifferentformsbyusingsomeofthespecialnamesandsymbols.[2]: 140 Forexample,thecoherentSIunitoflinearmomentummaybewrittenaseitherkg⋅m/sorasN⋅s,andbothformsareinuse(e.g.comparerespectivelyhere[19]:205andhere[20]:135). Ontheotherhand,severaldifferentquantitiesmaysharesamecoherentSIunit.Forexample,thejouleperkelvin(symbolJ/K)isthecoherentSIunitfortwodistinctquantities:heatcapacityandentropy;anotherexampleistheampere,whichisthecoherentSIunitforbothelectriccurrentandmagnetomotiveforce.Thisiswhyitisimportantnottousetheunitalonetospecifythequantity.[as] Furthermore,thesamecoherentSIunitmaybeabaseunitinonecontext,butacoherentderivedunitinanother.Forexample,theampereisabaseunitwhenitisaunitofelectriccurrent,butacoherentderivedunitwhenitisaunitofmagnetomotiveforce.[2]: 140 Asperhapsamorefamiliarexample,considerrainfall,definedasvolumeofrain(measuredinm3)thatfellperunitarea(measuredinm2).Sincem3/m2=m,itfollowsthatthecoherentderivedSIunitofrainfallisthemetre,eventhoughthemetreis,ofcourse,alsothebaseSIunitoflength.[at] Permittednon-SIunits[edit] Thereisaspecialgroupofunitsthatarecalled"non-SIunitsthatareacceptedforusewiththeSI".[2]: 145 SeeNon-SIunitsmentionedintheSIforafulllist.Mostofthese,inordertobeconvertedtothecorrespondingSIunit,requireconversionfactorsthatarenotpowersoften.Somecommonexamplesofsuchunitsarethecustomaryunitsoftime,namelytheminute(conversionfactorof60 s/min,since1 min=60 s),thehour(3600 s),andtheday(86400 s);thedegree(formeasuringplaneangles,1°=π/180rad);andtheelectronvolt(aunitofenergy,1 eV=1.602176634×10−19 J). Newunits[edit] TheSIisintendedtobeanevolvingsystem;units[au]andprefixesarecreatedandunitdefinitionsaremodifiedthroughinternationalagreementasthetechnologyofmeasurementprogressesandtheprecisionofmeasurementsimproves. Definingmagnitudesofunits[edit] Since2019,themagnitudesofallSIunitshavebeendefinedinanabstractway,whichisconceptuallyseparatedfromanypracticalrealisationofthem.[2]: 126 [av]Namely,theSIunitsaredefinedbydeclaringthatsevendefiningconstants[2]: 125–9 havecertainexactnumericalvalueswhenexpressedintermsoftheirSIunits.Probablythemostwidelyknownoftheseconstantsisthespeedoflightinvacuum,c,whichintheSIbydefinitionhastheexactvalueofc=299792458 m/s.TheothersixconstantsareΔνCs,thehyperfinetransitionfrequencyofcaesium;h,thePlanckconstant;e,theelementarycharge;k,theBoltzmannconstant;NA,theAvogadroconstant;andKcd,theluminousefficacyofmonochromaticradiationoffrequency540×1012 Hz.[aw]ThenatureofthedefiningconstantsrangesfromfundamentalconstantsofnaturesuchasctothepurelytechnicalconstantKcd.[2]: 128–9 Priorto2019,h,e,k,andNAwerenotdefinedaprioributwereratherverypreciselymeasuredquantities.In2019,theirvalueswerefixedbydefinitiontotheirbestestimatesatthetime,ensuringcontinuitywithpreviousdefinitionsofthebaseunits. Asfarasrealisations,whatarebelievedtobethecurrentbestpracticalrealisationsofunitsaredescribedintheso-called'misesenpratique',[ax]whicharealsopublishedbytheBIPM.[23]Theabstractnatureofthedefinitionsofunitsiswhatmakesitpossibletoimproveandchangethemisesenpratiqueasscienceandtechnologydevelopwithouthavingtochangetheactualdefinitionsthemselves.[ba] Inasense,thiswayofdefiningtheSIunitsisnomoreabstractthanthewayderivedunitsaretraditionallydefinedintermsofthebaseunits.Consideraparticularderivedunit,forexample,thejoule,theunitofenergy.Itsdefinitionintermsofthebaseunitsiskg⋅m2/s2.Evenifthepracticalrealisationsofthemetre,kilogram,andsecondareavailable,apracticalrealisationofthejoulewouldrequiresomesortofreferencetotheunderlyingphysicaldefinitionofworkorenergy—someactualphysicalprocedureforrealisingtheenergyintheamountofonejoulesuchthatitcanbecomparedtootherinstancesofenergy(suchastheenergycontentofgasolineputintoacarorofelectricitydeliveredtoahousehold). ThesituationwiththedefiningconstantsandalloftheSIunitsisanalogous.Infact,purelymathematicallyspeaking,theSIunitsaredefinedasifwedeclaredthatitisthedefiningconstant'sunitsthatarenowthebaseunits,withallotherSIunitsbeingderivedunits.Tomakethisclearer,firstnotethateachdefiningconstantcanbetakenasdeterminingthemagnitudeofthatdefiningconstant'sunitofmeasurement;[2]: 128 forexample,thedefinitionofcdefinestheunitm/sas1 m/s=c/299792458('thespeedofonemetrepersecondisequaltoone299792458thofthespeedoflight').Inthisway,thedefiningconstantsdirectlydefinethefollowingsevenunits: thehertz(Hz),aunitofthephysicalquantityoffrequency(notethatproblemscanarisewhendealingwithfrequencyorthePlanckconstantbecausetheunitsofangularmeasure(cycleorradian)areomittedinSI[24][25][5][26][27]);themetrepersecond(m/s),aunitofspeed;thejoule-second(J⋅s),aunitofaction;thecoulomb(C),aunitofelectriccharge;thejouleperkelvin(J/K),aunitofbothentropyandheatcapacity;theinversemole(mol−1),aunitofaconversionconstantbetweentheamountofsubstanceandthenumberofelementaryentities(atoms,molecules,etc.);andthelumenperwatt(lm/W),aunitofaconversionconstantbetweenthephysicalpowercarriedbyelectromagneticradiationandtheintrinsicabilityofthatsameradiationtoproducevisualperceptionofbrightnessinhumans. Further,onecanshow,usingdimensionalanalysis,thateverycoherentSIunit(whetherbaseorderived)canbewrittenasauniqueproductofpowersoftheunitsoftheSIdefiningconstants(incompleteanalogytothefactthateverycoherentderivedSIunitcanbewrittenasauniqueproductofpowersofthebaseSIunits).Forexample,thekilogramcanbewrittenaskg=(Hz)(J⋅s)/(m/s)2.[bb]Thus,thekilogramisdefinedintermsofthethreedefiningconstantsΔνCs,c,andhbecause,ontheonehand,thesethreedefiningconstantsrespectivelydefinetheunitsHz,m/s,andJ⋅s,[bc]while,ontheotherhand,thekilogramcanbewrittenintermsofthesethreeunits,namely,kg=(Hz)(J⋅s)/(m/s)2.[bd]True,thequestionofhowtoactuallyrealisethekilograminpracticewould,atthispoint,stillbeopen,butthatisnotreallydifferentfromthefactthatthequestionofhowtoactuallyrealisethejouleinpracticeisstillinprincipleopenevenonceonehasachievedthepracticalrealisationsofthemetre,kilogram,andsecond. Specifyingfundamentalconstantsvs.othermethodsofdefinition[edit] ThecurrentwayofdefiningtheSIistheresultofadecades-longmovetowardsincreasinglyabstractandidealisedformulationinwhichthe realisationsoftheunitsareseparatedconceptuallyfromthedefinitions.[2]: 126  Thegreatadvantageofdoingitthiswayisthatasscienceandtechnologiesdevelop,newandsuperiorrealisationsmaybeintroducedwithouttheneedtoredefinetheunits.[ay]Unitscannowberealisedwith'anaccuracythatisultimatelylimitedonlybythequantumstructureofnatureandourtechnicalabilitiesbutnotbythedefinitionsthemselves.[az]Anyvalidequationofphysicsrelatingthedefiningconstantstoaunitcanbeusedtorealisetheunit,thuscreatingopportunitiesforinnovation...withincreasingaccuracyastechnologyproceeds.'[2]: 122 Inpractice,theCIPMConsultativeCommitteesprovideso-called"misesenpratique"(practicaltechniques),[23]whicharethedescriptionsofwhatarecurrentlybelievedtobebestexperimentalrealisationsoftheunits.[30] Thissystemlackstheconceptualsimplicityofusingartefacts(referredtoasprototypes)asrealisationsofunitstodefinethoseunits:withprototypes,thedefinitionandtherealisationareoneandthesame.[be]However,usingartefactshastwomajordisadvantagesthat,assoonasitistechnologicallyandscientificallyfeasible,resultinabandoningthemasmeansfordefiningunits.[bi]Onemajordisadvantageisthatartefactscanbelost,damaged,[bk]orchanged.[bl]Theotheristhattheylargelycannotbenefitfromadvancementsinscienceandtechnology.ThelastartefactusedbytheSIwastheInternationalPrototypeKilogram(IPK),aparticularcylinderofplatinum-iridium;from1889to2019,thekilogramwasbydefinitionequaltothemassoftheIPK.Concernsregardingitsstabilityontheonehand,andprogressinprecisemeasurementsofthePlanckconstantandtheAvogadroconstantontheother,ledtoarevisionofthedefinitionofthebaseunits,putintoeffecton20May2019.[37]ThiswasthebiggestchangeintheSIsinceitwasfirstformallydefinedandestablishedin1960,anditresultedinthedefinitionsdescribedabove.[38] Inthepast,therewerealsovariousotherapproachestothedefinitionsofsomeoftheSIunits.Onemadeuseofaspecificphysicalstateofaspecificsubstance(thetriplepointofwater,whichwasusedinthedefinitionofthekelvin[39]: 113–4 );othersreferredtoidealisedexperimentalprescriptions[2]: 125 (asinthecaseoftheformerSIdefinitionoftheampere[39]: 113 andtheformerSIdefinition(originallyenactedin1979)ofthecandela[39]: 115 ). Inthefuture,thesetofdefiningconstantsusedbytheSImaybemodifiedasmorestableconstantsarefound,orifitturnsoutthatotherconstantscanbemorepreciselymeasured.[bm] History[edit] TheoriginalmotivationforthedevelopmentoftheSIwasthediversityofunitsthathadsprungupwithinthecentimetre–gram–second(CGS)systems(specificallytheinconsistencybetweenthesystemsofelectrostaticunitsandelectromagneticunits)andthelackofcoordinationbetweenthevariousdisciplinesthatusedthem.TheGeneralConferenceonWeightsandMeasures(French:Conférencegénéraledespoidsetmesures–CGPM),whichwasestablishedbytheMetreConventionof1875,broughttogethermanyinternationalorganisationstoestablishthedefinitionsandstandardsofanewsystemandtostandardisetherulesforwritingandpresentingmeasurements. Adoptedin1889,useoftheMKSsystemofunitssucceededthecentimetre–gram–secondsystemofunits(CGS)incommerceandengineering.ThemetreandkilogramsystemservedasthebasisforthedevelopmentoftheInternationalSystemofUnits(abbreviatedSI),whichnowservesastheinternationalstandard.Becauseofthis,thestandardsoftheCGSsystemweregraduallyreplacedwithmetricstandardsincorporatedfromtheMKSsystem.[40] In1901,GiovanniGiorgiproposedtotheAssociazioneelettrotecnicaitaliana [it](AEI)thatthissystem,extendedwithafourthunittobetakenfromtheunitsofelectromagnetism,beusedasaninternationalsystem.[41] ThissystemwasstronglypromotedbyelectricalengineerGeorgeA.Campbell.[42] TheInternationalSystemwaspublishedin1960,basedontheMKSunits,asaresultofaninitiativethatbeganin1948. Controllingauthority[edit] TheSIisregulatedandcontinuallydevelopedbythreeinternationalorganisationsthatwereestablishedin1875underthetermsoftheMetreConvention.TheyaretheGeneralConferenceonWeightsandMeasures(CGPM[k]),theInternationalCommitteeforWeightsandMeasures(CIPM[ab]),andtheInternationalBureauofWeightsandMeasures(BIPM[ad]).TheultimateauthorityrestswiththeCGPM,whichisaplenarybodythroughwhichitsMemberStates[bn]acttogetheronmattersrelatedtomeasurementscienceandmeasurementstandards;itusuallyconveneseveryfouryears.[13]TheCGPMelectstheCIPM,whichisan18-personcommitteeofeminentscientists.TheCIPMoperatesbasedontheadviceofanumberofitsConsultativeCommittees,whichbringtogethertheworld'sexpertsintheirspecifiedfieldsasadvisersonscientificandtechnicalmatters.[43][bo]OneofthesecommitteesistheConsultativeCommitteeforUnits(CCU),whichisresponsibleformattersrelatedtothedevelopmentoftheInternationalSystemofUnits(SI),preparationofsuccessiveeditionsoftheSIbrochure,andadvicetotheCIPMonmattersconcerningunitsofmeasurement.[44]ItistheCCUwhichconsidersindetailallnewscientificandtechnologicaldevelopmentsrelatedtothedefinitionofunitsandtheSI.Inpractice,whenitcomestothedefinitionoftheSI,theCGPMsimplyformallyapprovestherecommendationsoftheCIPM,which,inturn,followstheadviceoftheCCU. TheCCUhasthefollowingasmembers:[45][46]nationallaboratoriesoftheMemberStatesoftheCGPMchargedwithestablishingnationalstandards;[bp]relevantintergovernmentalorganisationsandinternationalbodies;[bq] internationalcommissionsorcommittees;[br] scientificunions;[bs]personalmembers;[bt] and,asanexofficiomemberofallConsultativeCommittees,theDirectoroftheBIPM. AllthedecisionsandrecommendationsconcerningunitsarecollectedinabrochurecalledTheInternationalSystemofUnits(SI)[2][ac],whichispublishedbytheBIPMandperiodicallyupdated. Unitsandprefixes[edit] TheInternationalSystemofUnitsconsistsofasetofbaseunits,derivedunits,andasetofdecimal-basedmultipliersthatareusedasprefixes.[39]: 103–106 Theunits,excludingprefixedunits,[bu]formacoherentsystemofunits,whichisbasedonasystemofquantitiesinsuchawaythattheequationsbetweenthenumericalvaluesexpressedincoherentunitshaveexactlythesameform,includingnumericalfactors,asthecorrespondingequationsbetweenthequantities.Forexample,1 N=1 kg×1 m/s2saysthatonenewtonistheforcerequiredtoaccelerateamassofonekilogramatonemetrepersecondsquared,asrelatedthroughtheprincipleofcoherencetotheequationrelatingthecorrespondingquantities:F=m×a. Derivedunitsapplytoderivedquantities,whichmaybydefinitionbeexpressedintermsofbasequantities,andthusarenotindependent;forexample,electricalconductanceistheinverseofelectricalresistance,withtheconsequencethatthesiemensistheinverseoftheohm,andsimilarly,theohmandsiemenscanbereplacedwitharatioofanampereandavolt,becausethosequantitiesbearadefinedrelationshiptoeachother.[bv]OtherusefulderivedquantitiescanbespecifiedintermsoftheSIbaseandderivedunitsthathavenonamedunitsintheSI,suchasacceleration,whichisdefinedinSIunitsasm/s2. Baseunits[edit] Mainarticle:SIbaseunit TheSIbaseunitsarethebuildingblocksofthesystemandalltheotherunitsarederivedfromthem. SIbaseunits[3]: 6 [49][50] Unitname Unitsymbol Dimensionsymbol Quantityname Typical symbol Definition second[n1] s T time t {\displaystylet} Thedurationof9192631770periodsoftheradiationcorrespondstothetransitionbetweenthetwohyperfinelevelsofthegroundstateofthecaesium-133atom. metre m L length l {\displaystylel} , h {\displaystyleh} , a {\displaystylea} , b {\displaystyleb} , x {\displaystylex} , y {\displaystyley} , r {\displaystyler} ,etc.[n2] Thedistancetravelledbylightinavacuumin1/299792458seconds. kilogram[n3] kg M mass m {\displaystylem} ThekilogramisdefinedbysettingthePlanckconstanthexactlyto6.62607015×10−34 J⋅s(J=kg⋅m2⋅s−2),giventhedefinitionsofthemetreandthesecond.[37] ampere A I electriccurrent I , i {\displaystyleI,\;i} Theflowofexactly1/1.602176634×10−19timestheelementarychargeepersecond. Equallingapproximately6.2415090744×1018elementarychargespersecond. kelvin K Θ thermodynamictemperature T {\displaystyleT} ThekelvinisdefinedbysettingthefixednumericalvalueoftheBoltzmannconstantkto1.380649×10−23 J⋅K−1,(J=kg⋅m2⋅s−2),giventhedefinitionofthekilogram,themetre,andthesecond. mole mol N amountofsubstance n {\displaystylen} Theamountofsubstanceofexactly6.02214076×1023elementaryentities.[n4]ThisnumberisthefixednumericalvalueoftheAvogadroconstant,NA,whenexpressedintheunitmol−1. candela cd J luminousintensity I v {\displaystyleI_{v}} Theluminousintensity,inagivendirection,ofasourcethatemitsmonochromaticradiationoffrequency5.4×1014hertzandthathasaradiantintensityinthatdirectionof1/683wattpersteradian. Notes ^WithinthecontextoftheSI,thesecondisthecoherentbaseunitoftime,andisusedinthedefinitionsofderivedunits.Thename"second"historicallyaroseasbeingthe2nd-levelsexagesimaldivision(1⁄602)ofsomequantity,thehourinthiscase,whichtheSIclassifiesasan"accepted"unitalongwithitsfirst-levelsexagesimaldivisiontheminute. ^Symbolsforlengthvarygreatlywithcontext.Problemsinvolvingintuitivethree-dimensionalquantitiesoftenuse l {\displaystylel} , w {\displaystylew} ,and h {\displaystyleh} forlength,distance,andheight,respectively.Moregenerally,physiciststendtosetupthecoordinatesystemofagivenproblemsothatoneaxisliesconvenientlyparalleltothelengthbeingmeasured.Lengthisthenoftendenotedeitherbysomeconstant(e.g. a {\displaystylea} , b {\displaystyleb} )alongsaidaxis,orbythesamesymbolastheaxisitself(e.g. x {\displaystylex} , y {\displaystyley} ,or r {\displaystyler} forhorizontal,vertical,andradialaxes,respectively). ^Despitetheprefix"kilo-",thekilogramisthecoherentbaseunitofmass,andisusedinthedefinitionsofderivedunits.Nonetheless,prefixesfortheunitofmassaredeterminedasifthegramwerethebaseunit. ^Whenthemoleisused,theelementaryentitiesmustbespecifiedandmaybeatoms,molecules,ions,electrons,otherparticles,orspecifiedgroupsofsuchparticles. Derivedunits[edit] Mainarticle:SIderivedunit ThederivedunitsintheSIareformedbypowers,products,orquotientsofthebaseunitsandarepotentiallyunlimitedinnumber.[39]: 103 [3]: 14, 16 Derivedunitsareassociatedwithderivedquantities;forexample,velocityisaquantitythatisderivedfromthebasequantitiesoftimeandlength,andthustheSIderivedunitismetrepersecond(symbolm/s).Thedimensionsofderivedunitscanbeexpressedintermsofthedimensionsofthebaseunits. Combinationsofbaseandderivedunitsmaybeusedtoexpressotherderivedunits.Forexample,theSIunitofforceisthenewton(N),theSIunitofpressureisthepascal(Pa)—andthepascalcanbedefinedasonenewtonpersquaremetre(N/m2).[51] SIderivedunitswithspecialnamesandsymbols[3]: 15  Name Symbol Quantity InSIbaseunits InotherSIunits radian[N1] rad planeangle m/m 1 steradian[N1] sr solidangle m2/m2 1 hertz Hz frequency s−1 newton N force,weight kg⋅m⋅s−2 pascal Pa pressure,stress kg⋅m−1⋅s−2 N/m2 joule J energy,work,heat kg⋅m2⋅s−2 N⋅m=Pa⋅m3 watt W power,radiantflux kg⋅m2⋅s−3 J/s coulomb C electriccharge s⋅A volt V electricalpotentialdifference(voltage),emf kg⋅m2⋅s−3⋅A−1 W/A=J/C farad F capacitance kg−1⋅m−2⋅s4⋅A2 C/V=C2/J ohm Ω resistance,impedance,reactance kg⋅m2⋅s−3⋅A−2 V/A=J⋅s/C2 siemens S electricalconductance kg−1⋅m−2⋅s3⋅A2 Ω−1 weber Wb magneticflux kg⋅m2⋅s−2⋅A−1 V⋅s tesla T magneticfluxdensity kg⋅s−2⋅A−1 Wb/m2 henry H inductance kg⋅m2⋅s−2⋅A−2 Wb/A degreeCelsius °C temperaturerelativeto273.15K K lumen lm luminousflux cd⋅sr cd⋅sr lux lx illuminance cd⋅sr⋅m−2 lm/m2 becquerel Bq activityreferredtoaradionuclide(decaysperunittime) s−1 gray Gy absorbeddose(ofionisingradiation) m2⋅s−2 J/kg sievert Sv equivalentdose(ofionisingradiation) m2⋅s−2 J/kg katal kat catalyticactivity mol⋅s−1 Notes ^abTheradianandsteradianaredefinedasdimensionlessderivedunits. Examplesofcoherentderivedunitsintermsofbaseunits[3]: 17  Name Symbol Derivedquantity Typicalsymbol squaremetre m2 area A cubicmetre m3 volume V metrepersecond m/s speed,velocity v metrepersecondsquared m/s2 acceleration a reciprocalmetre m−1 wavenumber σ,ṽ vergence(optics) V,1/f kilogrampercubicmetre kg/m3 density ρ kilogrampersquaremetre kg/m2 surfacedensity ρA cubicmetreperkilogram m3/kg specificvolume v amperepersquaremetre A/m2 currentdensity j amperepermetre A/m magneticfieldstrength H molepercubicmetre mol/m3 concentration c kilogrampercubicmetre kg/m3 massconcentration ρ,γ candelapersquaremetre cd/m2 luminance Lv Examplesofderivedunitsthatincludeunitswithspecialnames[3]: 18  Name Symbol Quantity InSIbaseunits pascal-second Pa⋅s dynamicviscosity m−1⋅kg⋅s−1 newton-metre N⋅m momentofforce m2⋅kg⋅s−2 newtonpermetre N/m surfacetension kg⋅s−2 radianpersecond rad/s angularvelocity,angularfrequency s−1 radianpersecondsquared rad/s2 angularacceleration s−2 wattpersquaremetre W/m2 heatfluxdensity,irradiance kg⋅s−3 jouleperkelvin J/K entropy,heatcapacity m2⋅kg⋅s−2⋅K−1 jouleperkilogram-kelvin J/(kg⋅K) specificheatcapacity,specificentropy m2⋅s−2⋅K−1 jouleperkilogram J/kg specificenergy m2⋅s−2 wattpermetre-kelvin W/(m⋅K) thermalconductivity m⋅kg⋅s−3⋅K−1 joulepercubicmetre J/m3 energydensity m−1⋅kg⋅s−2 voltpermetre V/m electricfieldstrength m⋅kg⋅s−3⋅A−1 coulombpercubicmetre C/m3 electricchargedensity m−3⋅s⋅A coulombpersquaremetre C/m2 surfacechargedensity,electricfluxdensity,electricdisplacement m−2⋅s⋅A faradpermetre F/m permittivity m−3⋅kg−1⋅s4⋅A2 henrypermetre H/m permeability m⋅kg⋅s−2⋅A−2 joulepermole J/mol molarenergy m2⋅kg⋅s−2⋅mol−1 joulepermole-kelvin J/(mol⋅K) molarentropy,molarheatcapacity m2⋅kg⋅s−2⋅K−1⋅mol−1 coulombperkilogram C/kg exposure(x-andγ-rays) kg−1⋅s⋅A graypersecond Gy/s absorbeddoserate m2⋅s−3 wattpersteradian W/sr radiantintensity m2⋅kg⋅s−3 wattpersquaremetre-steradian W/(m2⋅sr) radiance kg⋅s−3 katalpercubicmetre kat/m3 catalyticactivityconcentration m−3⋅s−1⋅mol Prefixes[edit] Mainarticle:Metricprefix Prefixesareaddedtounitnamestoproducemultiplesandsubmultiplesoftheoriginalunit.Alloftheseareintegerpowersoften,andaboveahundredorbelowahundredthallareintegerpowersofathousand.Forexample,kilo-denotesamultipleofathousandandmilli-denotesamultipleofathousandth,sothereareonethousandmillimetrestothemetreandonethousandmetrestothekilometre.Theprefixesarenevercombined,soforexampleamillionthofametreisamicrometre,notamillimillimetre.Multiplesofthekilogramarenamedasifthegramwerethebaseunit,soamillionthofakilogramisamilligram,notamicrokilogram.[39]: 122 [52]: 14 WhenprefixesareusedtoformmultiplesandsubmultiplesofSIbaseandderivedunits,theresultingunitsarenolongercoherent.[39]: 7  TheBIPMspecifies20prefixesfortheInternationalSystemofUnits(SI): SIprefixesvte Prefix Base10 Decimal Englishword Adoption[nb1] Etymology Name Symbol Shortscale Longscale Language Derivedword yotta Y 1024 1000000000000000000000000 septillion quadrillion 1991 Greek eight[nb2] zetta Z 1021 1000000000000000000000 sextillion trilliard 1991 Latin seven[nb2] exa E 1018 1000000000000000000 quintillion trillion 1975 Greek six peta P 1015 1000000000000000 quadrillion billiard 1975 Greek five[nb2] tera T 1012 1000000000000 trillion billion 1960 Greek four,[nb2]monster giga G 109 1000000000 billion milliard 1960 Greek giant mega M 106 1000000 million 1873 Greek great kilo k 103 1000 thousand 1795 Greek thousand hecto h 102 100 hundred 1795 Greek hundred deca da 101 10 ten 1795 Greek ten 100 1 one – deci d 10−1 0.1 tenth 1795 Latin ten centi c 10−2 0.01 hundredth 1795 Latin hundred milli m 10−3 0.001 thousandth 1795 Latin thousand micro μ 10−6 0.000001 millionth 1873 Greek small nano n 10−9 0.000000001 billionth milliardth 1960 Greek dwarf pico p 10−12 0.000000000001 trillionth billionth 1960 Spanish peak femto f 10−15 0.000000000000001 quadrillionth billiardth 1964 Danish fifteen,Fermi[nb3] atto a 10−18 0.000000000000000001 quintillionth trillionth 1964 Danish eighteen zepto z 10−21 0.000000000000000000001 sextillionth trilliardth 1991 Latin seven[nb2] yocto y 10−24 0.000000000000000000000001 septillionth quadrillionth 1991 Greek eight[nb2] ^Prefixesadoptedbefore1960alreadyexistedbeforeSI.TheintroductionoftheCGSsystemwasin1873. ^abcdefPartofthebeginningoftheprefixwasmodifiedfromtheworditwasderivedfrom,ex:"peta"(prefix)vs"penta"(derivedword). ^Thefermiwasintroducedearlierwiththesamesymbol"fm",inwhichthenthe"f"becameaprefix.TheDanishwordisusedsinceitisvaguelyspelledsimilartofermi. Non-SIunitsacceptedforusewithSI[edit] Mainarticle:Non-SIunitsacceptedforusewithSI Manynon-SIunitscontinuetobeusedinthescientific,technical,andcommercialliterature.Someunitsaredeeplyembeddedinhistoryandculture,andtheirusehasnotbeenentirelyreplacedbytheirSIalternatives.TheCIPMrecognisedandacknowledgedsuchtraditionsbycompilingalistofnon-SIunitsacceptedforusewithSI:[39] WhilenotanSI-unit,thelitremaybeusedwithSIunits.Itisequivalentto(10 cm)3 = (1 dm)3 = 10−3 m3. Someunitsoftime,angle,andlegacynon-SIunitshavealonghistoryofuse.Mostsocietieshaveusedthesolardayanditsnon-decimalsubdivisionsasabasisoftimeand,unlikethefootorthepound,thesewerethesameregardlessofwheretheywerebeingmeasured.Theradian,being1/2πofarevolution,hasmathematicaladvantagesbutisrarelyusedfornavigation.Further,theunitsusedinnavigationaroundtheworldaresimilar.Thetonne,litre,andhectarewereadoptedbytheCGPMin1879andhavebeenretainedasunitsthatmaybeusedalongsideSIunits,havingbeengivenuniquesymbols.Thecataloguedunitsaregivenbelow: Non-SIunitsacceptedforusewithSIunits Quantity Name Symbol ValueinSIunits time minute min 1min=60s hour h 1h=60min=3600 s day d 1d=24h=86400 s length astronomicalunit au 1au=149597870700 m planeandphaseangle degree ° 1°=(π/180)rad minute ′ 1′=(1/60)°=(π/10800)rad second ″ 1″=(1/60)′=(π/648000)rad area hectare ha 1ha=1hm2=104m2 volume litre l,L 1l=1L=1dm3=103cm3=10−3m3 mass tonne(metricton) t 1t=1000 kg dalton Da 1Da=1.660539040(20)×10−27 kg energy electronvolt eV 1eV=1.602176634×10−19 J logarithmicratioquantities neper Np Inusingtheseunitsitisimportantthatthenatureofthequantitybespecifiedandthatanyreferencevalueusedbespecified. bel B decibel dB TheseunitsareusedincombinationwithSIunitsincommonunitssuchasthekilowatt-hour(1 kW⋅h=3.6 MJ). Commonnotionsofthemetricunits[edit] Thebasicunitsofthemetricsystem,asoriginallydefined,representedcommonquantitiesorrelationshipsinnature.Theystilldo–themodernpreciselydefinedquantitiesarerefinementsofdefinitionandmethodology,butstillwiththesamemagnitudes.Incaseswherelaboratoryprecisionmaynotberequiredoravailable,orwhereapproximationsaregoodenough,theoriginaldefinitionsmaysuffice.[bw] Asecondis1/60ofaminute,whichis1/60ofanhour,whichis1/24ofaday,soasecondis1/86400ofaday(theuseofbase60datesbacktoBabyloniantimes);asecondisthetimeittakesadenseobjecttofreelyfall4.9metresfromrest.[bx] Thelengthoftheequatoriscloseto40000000 m(moreprecisely40075014.2 m).[53]Infact,thedimensionsofourplanetwereusedbytheFrenchAcademyintheoriginaldefinitionofthemetre.[54] Themetreisclosetothelengthofapendulumthathasaperiodof2seconds;[by]mostdiningtabletopsareabout0.75metreshigh;[55]averytallhuman(basketballforward)isabout2metrestall.[56] Thekilogramisthemassofalitreofcoldwater;acubiccentimetreormillilitreofwaterhasamassofonegram;a1-eurocoinweighs7.5 g;[57]aSacagaweaUS1-dollarcoinweighs8.1 g;[58]aUK50-pencecoinweighs8.0 g.[59] Acandelaisabouttheluminousintensityofamoderatelybrightcandle,or1candlepower;a60 Wtungsten-filamentincandescentlightbulbhasaluminousintensityofabout64candelas.[bz] Amoleofasubstancehasamassthatisitsmolecularmassexpressedinunitsofgrams;themassofamoleofcarbonis12.0 g,andthemassofamoleoftablesaltis58.4 g. Sinceallgaseshavethesamevolumepermoleatagiventemperatureandpressurefarfromtheirpointsofliquefactionandsolidification(seePerfectgas),andairisabout1/5oxygen(molecularmass32)and4/5nitrogen(molecularmass28),thedensityofanynear-perfectgasrelativetoaircanbeobtainedtoagoodapproximationbydividingitsmolecularmassby29(because4/5×28+1/5×32=28.8≈29).Forexample,carbonmonoxide(molecularmass28)hasalmostthesamedensityasair. AtemperaturedifferenceofonekelvinisthesameasonedegreeCelsius:1/100ofthetemperaturedifferentialbetweenthefreezingandboilingpointsofwateratsealevel;theabsolutetemperatureinkelvinsisthetemperatureindegreesCelsiusplusabout273;humanbodytemperatureisabout37 °Cor310 K. A60 Wincandescentlightbulbratedat120 V(USmainsvoltage)consumes0.5 Aatthisvoltage.A60 Wbulbratedat240 V(Europeanmainsvoltage)consumes0.25 Aatthisvoltage.[ca] Lexicographicconventions[edit] Unitnames[edit] AccordingtotheSIBrochure,[2]: 148 unitnamesshouldbetreatedascommonnounsofthecontextlanguage.Thismeansthattheyshouldbetypesetinthesamecharactersetasothercommonnouns(e.g.LatinalphabetinEnglish,CyrillicscriptinRussian,etc.),normallyinupright(i.e.notitalic)type,followingtheusualgrammaticalandorthographicalrulesofthecontextlanguage.Forexample,inEnglishandFrench,evenwhentheunitisnamedafterapersonanditssymbolbeginswithacapitalletter,theunitnameinrunningtextshouldstartwithalowercaseletter(e.g.,newton,hertz,pascal)andiscapitalizedonlyatthebeginningofasentenceandinheadingsandpublicationtitles.Asanontrivialapplicationofthisrule,theSIBrochurenotes[2]: 148 thatthenameoftheunitwiththesymbol°Ciscorrectlyspelledas'degreeCelsius':thefirstletterofthenameoftheunit,'d',isinlowercase,whilethemodifier'Celsius'iscapitalizedbecauseitisapropername.[cb][2]: 148  TheEnglishspellingandevennamesforcertainSIunitsandmetricprefixesdependonthevarietyofEnglishused.USEnglishusesthespellingdeka-,meter,andliter,whilstInternationalEnglishusesdeca-,metre,andlitre.Additionally,thenameoftheunitwhosesymbolistandwhichisdefinedaccordingto1 t=103 kgis'metricton'USEnglishbut'tonne'inInternationalEnglish.[3]: iii  Unitsymbolsandthevaluesofquantities[edit] SymbolsofSIunitsareintendedtobeuniqueanduniversal,independentofthecontextlanguage.[39]: 130–135 TheSIBrochurehasspecificrulesforwritingthem.[39]: 130–135 TheguidelineproducedbytheNationalInstituteofStandardsandTechnology(NIST)[61]clarifieslanguage-specificdetailsforAmericanEnglishthatwereleftunclearbytheSIBrochure,butisotherwiseidenticaltotheSIBrochure.[62] Generalrules[edit] Generalrules[cc]forwritingSIunitsandquantitiesapplytotextthatiseitherhandwrittenorproducedusinganautomatedprocess: Thevalueofaquantityiswrittenasanumberfollowedbyaspace(representingamultiplicationsign)andaunitsymbol;e.g.,2.21 kg,7.3×102 m2,22 K.Thisruleexplicitlyincludesthepercentsign(%)[39]: 134 andthesymbolfordegreesCelsius(°C).[39]: 133 Exceptionsarethesymbolsforplaneangulardegrees,minutes,andseconds(°, ′,and ″,respectively),whichareplacedimmediatelyafterthenumberwithnointerveningspace. Symbolsaremathematicalentities,notabbreviations,andassuchdonothaveanappendedperiod/fullstop(.),unlesstherulesofgrammardemandoneforanotherreason,suchasdenotingtheendofasentence. Aprefixispartoftheunit,anditssymbolisprependedtoaunitsymbolwithoutaseparator(e.g.,kinkm,MinMPa,GinGHz,μinμg).Compoundprefixesarenotallowed.Aprefixedunitisatomicinexpressions(e.g.,km2isequivalentto(km)2). Unitsymbolsarewrittenusingroman(upright)type,regardlessofthetypeusedinthesurroundingtext. Symbolsforderivedunitsformedbymultiplicationarejoinedwithacentredot(⋅)oranon-breakingspace;e.g.,N⋅morN m. Symbolsforderivedunitsformedbydivisionarejoinedwithasolidus(/),orgivenasanegativeexponent.E.g.,the"metrepersecond"canbewrittenm/s,m s−1,m⋅s−1,orm/s.Asolidusfollowedwithoutparenthesesbyacentredot(orspace)orasolidusisambiguousandmustbeavoided;e.g.,kg/(m⋅s2)andkg⋅m−1⋅s−2areacceptable,butkg/m/s2isambiguousandunacceptable. Intheexpressionofaccelerationduetogravity,aspaceseparatesthevalueandtheunits,boththe'm'andthe's'arelowercasebecauseneitherthemetrenorthesecondarenamedafterpeople,andexponentiationisrepresentedwithasuperscript'2'. Thefirstletterofsymbolsforunitsderivedfromthenameofapersoniswritteninuppercase;otherwise,theyarewritteninlowercase.E.g.,theunitofpressureisnamedafterBlaisePascal,soitssymboliswritten"Pa",butthesymbolformoleiswritten"mol".Thus,"T"isthesymbolfortesla,ameasureofmagneticfieldstrength,and"t"thesymbolfortonne,ameasureofmass.Since1979,thelitremayexceptionallybewrittenusingeitheranuppercase"L"oralowercase"l",adecisionpromptedbythesimilarityofthelowercaseletter"l"tothenumeral"1",especiallywithcertaintypefacesorEnglish-stylehandwriting.TheAmericanNISTrecommendsthatwithintheUnitedStates"L"beusedratherthan"l". Symbolsdonothaveapluralform,e.g.,25 kg,butnot25 kgs. Uppercaseandlowercaseprefixesarenotinterchangeable.E.g.,thequantities1 mWand1 MWrepresenttwodifferentquantities(milliwattandmegawatt). Thesymbolforthedecimalmarkeriseitherapointorcommaontheline.Inpractice,thedecimalpointisusedinmostEnglish-speakingcountriesandmostofAsia,andthecommainmostofLatinAmericaandincontinentalEuropeancountries.[63] Spacesshouldbeusedasathousandsseparator(1000000)incontrasttocommasorperiods(1,000,000or1.000.000)toreduceconfusionresultingfromthevariationbetweentheseformsindifferentcountries. Anyline-breakinsideanumber,insideacompoundunit,orbetweennumberandunitshouldbeavoided.Wherethisisnotpossible,linebreaksshouldcoincidewiththousandsseparators. Becausethevalueof"billion"and"trillion"variesbetweenlanguages,thedimensionlessterms"ppb"(partsperbillion)and"ppt"(partspertrillion)shouldbeavoided.TheSIBrochuredoesnotsuggestalternatives. PrintingSIsymbols[edit] TherulescoveringprintingofquantitiesandunitsarepartofISO80000-1:2009.[64] Furtherrules[cc]arespecifiedinrespectofproductionoftextusingprintingpresses,wordprocessors,typewriters,andthelike. InternationalSystemofQuantities[edit] SIBrochure CoverofbrochureTheInternationalSystemofUnits TheCGPMpublishesabrochurethatdefinesandpresentstheSI.[39]ItsofficialversionisinFrench,inlinewiththeMetreConvention.[39]: 102 Itleavessomescopeforlocalvariations,particularlyregardingunitnamesandtermsindifferentlanguages.[cd][3] ThewritingandmaintenanceoftheCGPMbrochureiscarriedoutbyoneofthecommitteesoftheInternationalCommitteeforWeightsandMeasures(CIPM). Thedefinitionsoftheterms"quantity","unit","dimension"etc.thatareusedintheSIBrochurearethosegivenintheInternationalvocabularyofmetrology.[65] Mainarticle:InternationalSystemofQuantities ThequantitiesandequationsthatprovidethecontextinwhichtheSIunitsaredefinedarenowreferredtoastheInternationalSystemofQuantities(ISQ). TheISQisbasedonthequantitiesunderlyingeachofthesevenbaseunitsoftheSI.Otherquantities,suchasarea,pressure,andelectricalresistance,arederivedfromthesebasequantitiesbyclearnon-contradictoryequations.TheISQdefinesthequantitiesthataremeasuredwiththeSIunits.[66]TheISQisformalised,inpart,intheinternationalstandardISO/IEC80000,whichwascompletedin2009withthepublicationofISO80000-1,[67]andhaslargelybeenrevisedin2019–2020withtheremainderbeingunderreview. Realisationofunits[edit] Mainarticle:Realisation(metrology) SiliconspherefortheAvogadroprojectusedformeasuringtheAvogadroconstanttoarelativestandarduncertaintyof2×10−8orless,heldbyAchimLeistner[68] Metrologistscarefullydistinguishbetweenthedefinitionofaunitanditsrealisation.ThedefinitionofeachbaseunitoftheSIisdrawnupsothatitisuniqueandprovidesasoundtheoreticalbasisonwhichthemostaccurateandreproduciblemeasurementscanbemade.Therealisationofthedefinitionofaunitistheprocedurebywhichthedefinitionmaybeusedtoestablishthevalueandassociateduncertaintyofaquantityofthesamekindastheunit.Adescriptionofthemiseenpratique[ce]ofthebaseunitsisgiveninanelectronicappendixtotheSIBrochure.[69][39]: 168–169  Thepublishedmiseenpratiqueisnottheonlywayinwhichabaseunitcanbedetermined:theSIBrochurestatesthat"anymethodconsistentwiththelawsofphysicscouldbeusedtorealiseanySIunit."[39]: 111 Inthecurrent(2016)exercisetooverhaulthedefinitionsofthebaseunits,variousconsultativecommitteesoftheCIPMhaverequiredthatmorethanonemiseenpratiqueshallbedevelopedfordeterminingthevalueofeachunit.[70]Inparticular: Atleastthreeseparateexperimentsbecarriedoutyieldingvalueshavingarelativestandarduncertaintyinthedeterminationofthekilogramofnomorethan5×10−8andatleastoneofthesevaluesshouldbebetterthan2×10−8.BoththeKibblebalanceandtheAvogadroprojectshouldbeincludedintheexperimentsandanydifferencesbetweenthesebereconciled.[71][72] Whenthekelvinisbeingdetermined,therelativeuncertaintyoftheBoltzmannconstantderivedfromtwofundamentallydifferentmethodssuchasacousticgasthermometryanddielectricconstantgasthermometrybebetterthanonepartin10−6andthatthesevaluesbecorroboratedbyothermeasurements.[73] EvolutionoftheSI[edit] ChangestotheSI[edit] TheInternationalBureauofWeightsandMeasures(BIPM)hasdescribedSIas"themodernformofmetricsystem".[39]: 95 Changingtechnologyhasledtoanevolutionofthedefinitionsandstandardsthathasfollowedtwoprincipalstrands–changestoSIitself,andclarificationofhowtouseunitsofmeasurethatarenotpartofSIbutarestillneverthelessusedonaworldwidebasis. Since1960theCGPMhasmadeanumberofchangestotheSItomeettheneedsofspecificfields,notablychemistryandradiometry.Thesearemostlyadditionstothelistofnamedderivedunits,andincludethemole(symbolmol)foranamountofsubstance,thepascal(symbolPa)forpressure,thesiemens(symbolS)forelectricalconductance,thebecquerel(symbolBq)for"activityreferredtoaradionuclide",thegray(symbolGy)forionisingradiation,thesievert(symbolSv)astheunitofdoseequivalentradiation,andthekatal(symbolkat)forcatalyticactivity.[39]: 156 [74][39]: 156 [39]: 158 [39]: 159 [39]: 165  Therangeofdefinedprefixespico-(10−12)totera-(1012)wasextendedto10−24to1024.[39]: 152 [39]: 158 [39]: 164  The1960definitionofthestandardmetreintermsofwavelengthsofaspecificemissionofthekrypton-86atomwasreplacedwiththedistancethatlighttravelsinvacuuminexactly1/299792458second,sothatthespeedoflightisnowanexactlyspecifiedconstantofnature. Afewchangestonotationconventionshavealsobeenmadetoalleviatelexicographicambiguities.AnanalysisundertheaegisofCSIRO,publishedin2009bytheRoyalSociety,haspointedouttheopportunitiestofinishtherealisationofthatgoal,tothepointofuniversalzero-ambiguitymachinereadability.[75] 2019redefinitions[edit] ReversedependenciesoftheSIbaseunitsonsevenphysicalconstants,whichareassignedexactnumericalvaluesinthe2019redefinition.Unlikeinthepreviousdefinitions,thebaseunitsareallderivedexclusivelyfromconstantsofnature.Arrowsareshownintheoppositedirectioncomparedtotypicaldependencygraphs,i.e. a → b {\displaystylea\rightarrowb} inthischartmeans b {\displaystyleb} dependson a {\displaystylea} : a {\displaystylea} isusedtodefine b {\displaystyleb} . Mainarticle:2019redefinitionoftheSIbaseunits Afterthemetrewasredefinedin1960,theInternationalPrototypeoftheKilogram(IPK)wastheonlyphysicalartefactuponwhichbaseunits(directlythekilogramandindirectlytheampere,moleandcandela)dependedfortheirdefinition,makingtheseunitssubjecttoperiodiccomparisonsofnationalstandardkilogramswiththeIPK.[76]Duringthe2ndand3rdPeriodicVerificationofNationalPrototypesoftheKilogram,asignificantdivergencehadoccurredbetweenthemassoftheIPKandallofitsofficialcopiesstoredaroundtheworld:thecopieshadallnoticeablyincreasedinmasswithrespecttotheIPK.Duringextraordinaryverificationscarriedoutin2014preparatorytoredefinitionofmetricstandards,continuingdivergencewasnotconfirmed.Nonetheless,theresidualandirreducibleinstabilityofaphysicalIPKunderminedthereliabilityoftheentiremetricsystemtoprecisionmeasurementfromsmall(atomic)tolarge(astrophysical)scales. Aproposalwasmadethat:[77] Inadditiontothespeedoflight,fourconstantsofnature–thePlanckconstant,anelementarycharge,theBoltzmannconstant,andtheAvogadroconstant–bedefinedtohaveexactvalues TheInternationalPrototypeoftheKilogramberetired Thecurrentdefinitionsofthekilogram,ampere,kelvin,andmoleberevised Thewordingofbaseunitdefinitionsshouldchangeemphasisfromexplicitunittoexplicitconstantdefinitions. Thenewdefinitionswereadoptedatthe26thCGPMon16November2018,andcameintoeffecton20May2019.[78]ThechangewasadoptedbytheEuropeanUnionthroughDirective(EU)2019/1258.[79] History[edit] StonemarkingtheAustro-Hungarian/ItalianborderatPontebbadisplayingmyriametres,aunitof10 kmusedinCentralEuropeinthe19thcentury(butsincedeprecated)[80] Mainarticle:Historyofthemetricsystem Theimprovisationofunits[edit] TheunitsandunitmagnitudesofthemetricsystemwhichbecametheSIwereimprovisedpiecemealfromeverydayphysicalquantitiesstartinginthemid-18thcentury.Onlylaterweretheymouldedintoanorthogonalcoherentdecimalsystemofmeasurement. ThedegreecentigradeasaunitoftemperatureresultedfromthescaledevisedbySwedishastronomerAndersCelsiusin1742.Hisscalecounter-intuitivelydesignated100asthefreezingpointofwaterand0astheboilingpoint.Independently,in1743,theFrenchphysicistJean-PierreChristindescribedascalewith0asthefreezingpointofwaterand100theboilingpoint.Thescalebecameknownasthecenti-grade,or100gradationsoftemperature,scale. Themetricsystemwasdevelopedfrom1791onwardsbyacommitteeoftheFrenchAcademyofSciences,commissionedtocreateaunifiedandrationalsystemofmeasures.[81]Thegroup,whichincludedpreeminentFrenchmenofscience,[82]: 89 usedthesameprinciplesforrelatinglength,volume,andmassthathadbeenproposedbytheEnglishclergymanJohnWilkinsin1668[83][84]andtheconceptofusingtheEarth'smeridianasthebasisofthedefinitionoflength,originallyproposedin1670bytheFrenchabbotMouton.[85][86] CarlFriedrichGauss InMarch1791,theAssemblyadoptedthecommittee'sproposedprinciplesforthenewdecimalsystemofmeasureincludingthemetredefinedtobe1/10,000,000ofthelengthofthequadrantofEarth'smeridianpassingthroughParis,andauthorisedasurveytopreciselyestablishthelengthofthemeridian.InJuly1792,thecommitteeproposedthenamesmetre,are,litreandgravefortheunitsoflength,area,capacity,andmass,respectively.Thecommitteealsoproposedthatmultiplesandsubmultiplesoftheseunitsweretobedenotedbydecimal-basedprefixessuchascentiforahundredthandkiloforathousand.[87]: 82  ThomsonMaxwellWilliamThomson(LordKelvin)andJamesClerkMaxwellplayedaprominentroleinthedevelopmentoftheprincipleofcoherenceandinthenamingofmanyunitsofmeasure.[88][89][90][91][92] Later,duringtheprocessofadoptionofthemetricsystem,theLatingrammeandkilogramme,replacedtheformerprovincialtermsgravet(1/1000grave)andgrave.InJune1799,basedontheresultsofthemeridiansurvey,thestandardmètredesArchivesandkilogrammedesArchivesweredepositedintheFrenchNationalArchives.Subsequently,thatyear,themetricsystemwasadoptedbylawinFrance.[93] [94]TheFrenchsystemwasshort-livedduetoitsunpopularity.Napoleonridiculedit,andin1812,introducedareplacementsystem,themesuresusuellesor"customarymeasures"whichrestoredmanyoftheoldunits,butredefinedintermsofthemetricsystem. Duringthefirsthalfofthe19thcenturytherewaslittleconsistencyinthechoiceofpreferredmultiplesofthebaseunits:typicallythemyriametre(10000 metres)wasinwidespreaduseinbothFranceandpartsofGermany,whilethekilogram(1000grams)ratherthanthemyriagramwasusedformass.[80] In1832,theGermanmathematicianCarlFriedrichGauss,assistedbyWilhelmWeber,implicitlydefinedthesecondasabaseunitwhenhequotedtheEarth'smagneticfieldintermsofmillimetres,grams,andseconds.[88]Priortothis,thestrengthoftheEarth'smagneticfieldhadonlybeendescribedinrelativeterms.ThetechniqueusedbyGausswastoequatethetorqueinducedonasuspendedmagnetofknownmassbytheEarth'smagneticfieldwiththetorqueinducedonanequivalentsystemundergravity.Theresultantcalculationsenabledhimtoassigndimensionsbasedonmass,lengthandtimetothemagneticfield.[cf][95] Acandlepowerasaunitofilluminancewasoriginallydefinedbyan1860Englishlawasthelightproducedbyapurespermaceticandleweighing1⁄6pound(76grams)andburningataspecifiedrate.Spermaceti,awaxysubstancefoundintheheadsofspermwhales,wasonceusedtomakehigh-qualitycandles.AtthistimetheFrenchstandardoflightwasbasedupontheilluminationfromaCarceloillamp.Theunitwasdefinedasthatilluminationemanatingfromalampburningpurerapeseedoilatadefinedrate.ItwasacceptedthattenstandardcandleswereaboutequaltooneCarcellamp. MetreConvention[edit] Mainarticle:MetreConvention AFrench-inspiredinitiativeforinternationalcooperationinmetrologyledtothesigningin1875oftheMetreConvention,alsocalledTreatyoftheMetre,by17nations.[cg][82]: 353–354 Initiallytheconventiononlycoveredstandardsforthemetreandthekilogram.In1921,theMetreConventionwasextendedtoincludeallphysicalunits,includingtheampereandotherstherebyenablingtheCGPMtoaddressinconsistenciesinthewaythatthemetricsystemhadbeenused.[89][39]: 96  Asetof30prototypesofthemetreand40prototypesofthekilogram,[ch]ineachcasemadeofa90%platinum-10%iridiumalloy,weremanufacturedbyBritishmetallurgyspecialtyfirm[who?]andacceptedbytheCGPMin1889.OneofeachwasselectedatrandomtobecometheInternationalprototypemetreandInternationalprototypekilogramthatreplacedthemètredesArchivesandkilogrammedesArchivesrespectively.Eachmemberstatewasentitledtooneofeachoftheremainingprototypestoserveasthenationalprototypeforthatcountry.[96] Thetreatyalsoestablishedanumberofinternationalorganisationstooverseethekeepingofinternationalstandardsofmeasurement.[97][ci] TheCGSandMKSsystems[edit] Seealso:CGSsystemofunitsandMKSsystemofunits CloseupoftheNationalPrototypeMetre,serialnumber27,allocatedtotheUnitedStates Inthe1860s,JamesClerkMaxwell,WilliamThomson(laterLordKelvin)andothersworkingundertheauspicesoftheBritishAssociationfortheAdvancementofScience,builtonGauss'sworkandformalisedtheconceptofacoherentsystemofunitswithbaseunitsandderivedunitschristenedthecentimetre–gram–secondsystemofunitsin1874.TheprincipleofcoherencewassuccessfullyusedtodefineanumberofunitsofmeasurebasedontheCGS,includingtheergforenergy,thedyneforforce,thebaryeforpressure,thepoisefordynamicviscosityandthestokesforkinematicviscosity.[91] In1879,theCIPMpublishedrecommendationsforwritingthesymbolsforlength,area,volumeandmass,butitwasoutsideitsdomaintopublishrecommendationsforotherquantities.Beginninginabout1900,physicistswhohadbeenusingthesymbol"μ"(mu)for"micrometre"or"micron","λ"(lambda)for"microlitre",and"γ"(gamma)for"microgram"startedtousethesymbols"μm","μL"and"μg".[98] Atthecloseofthe19thcenturythreedifferentsystemsofunitsofmeasureexistedforelectricalmeasurements:aCGS-basedsystemforelectrostaticunits,alsoknownastheGaussianorESUsystem,aCGS-basedsystemforelectromechanicalunits(EMU)andanInternationalsystembasedonunitsdefinedbytheMetreConvention.[99]forelectricaldistributionsystems. Attemptstoresolvetheelectricalunitsintermsoflength,mass,andtimeusingdimensionalanalysiswasbesetwithdifficulties—thedimensionsdependedonwhetheroneusedtheESUorEMUsystems.[92]Thisanomalywasresolvedin1901whenGiovanniGiorgipublishedapaperinwhichheadvocatedusingafourthbaseunitalongsidetheexistingthreebaseunits.Thefourthunitcouldbechosentobeelectriccurrent,voltage,orelectricalresistance.[100]Electriccurrentwithnamedunit'ampere'waschosenasthebaseunit,andtheotherelectricalquantitiesderivedfromitaccordingtothelawsofphysics.ThisbecamethefoundationoftheMKSsystemofunits. Inthelate19thandearly20thcenturies,anumberofnon-coherentunitsofmeasurebasedonthegram/kilogram,centimetre/metre,andsecond,suchasthePferdestärke(metrichorsepower)forpower,[101][cj]thedarcyforpermeability[102]and"millimetresofmercury"forbarometricandbloodpressureweredevelopedorpropagated,someofwhichincorporatedstandardgravityintheirdefinitions. AttheendoftheSecondWorldWar,anumberofdifferentsystemsofmeasurementwereinusethroughouttheworld.Someofthesesystemsweremetricsystemvariations;otherswerebasedoncustomarysystemsofmeasure,liketheU.ScustomarysystemandImperialsystemoftheUKandBritishEmpire. ThePracticalsystemofunits[edit] In1948,the9thCGPMcommissionedastudytoassessthemeasurementneedsofthescientific,technical,andeducationalcommunitiesand"tomakerecommendationsforasinglepracticalsystemofunitsofmeasurement,suitableforadoptionbyallcountriesadheringtotheMetreConvention".[103]ThisworkingdocumentwasPracticalsystemofunitsofmeasurement.Basedonthisstudy,the10thCGPMin1954definedaninternationalsystemderivedfromsixbaseunitsincludingunitsoftemperatureandopticalradiationinadditiontothosefortheMKSsystemmass,length,andtimeunitsandGiorgi'scurrentunit.Sixbaseunitswererecommended:themetre,kilogram,second,ampere,degreeKelvin,andcandela. The9thCGPMalsoapprovedthefirstformalrecommendationforthewritingofsymbolsinthemetricsystemwhenthebasisoftherulesastheyarenowknownwaslaiddown.[104]Theserulesweresubsequentlyextendedandnowcoverunitsymbolsandnames,prefixsymbolsandnames,howquantitysymbolsshouldbewrittenandused,andhowthevaluesofquantitiesshouldbeexpressed.[39]: 104, 130  BirthoftheSI[edit] In1960,the11thCGPMsynthesisedtheresultsofthe12-yearstudyintoasetof16resolutions.ThesystemwasnamedtheInternationalSystemofUnits,abbreviatedSIfromtheFrenchname,LeSystèmeInternationald'Unités.[39]: 110 [105] Historicaldefinitions[edit] WhenMaxwellfirstintroducedtheconceptofacoherentsystem,heidentifiedthreequantitiesthatcouldbeusedasbaseunits:mass,length,andtime.Giorgilateridentifiedtheneedforanelectricalbaseunit,forwhichtheunitofelectriccurrentwaschosenforSI.Anotherthreebaseunits(fortemperature,amountofsubstance,andluminousintensity)wereaddedlater. Theearlymetricsystemsdefinedaunitofweightasabaseunit,whiletheSIdefinesananalogousunitofmass.Ineverydayuse,thesearemostlyinterchangeable,butinscientificcontextsthedifferencematters.Mass,strictlytheinertialmass,representsaquantityofmatter.ItrelatestheaccelerationofabodytotheappliedforceviaNewton'slaw,F=m×a:forceequalsmasstimesacceleration.Aforceof1 N(newton)appliedtoamassof1 kgwillaccelerateitat1 m/s2.Thisistruewhethertheobjectisfloatinginspaceorinagravityfielde.g.attheEarth'ssurface.Weightistheforceexertedonabodybyagravitationalfield,andhenceitsweightdependsonthestrengthofthegravitationalfield.Weightofa1 kgmassattheEarth'ssurfaceism×g;masstimestheaccelerationduetogravity,whichis9.81 newtonsattheEarth'ssurfaceandisabout3.5 newtonsatthesurfaceofMars.SincetheaccelerationduetogravityislocalandvariesbylocationandaltitudeontheEarth,weightisunsuitableforprecisionmeasurementsofapropertyofabody,andthismakesaunitofweightunsuitableasabaseunit. SIbaseunits[3]: 6 [49][106] Unitname Definition[n1] second Prior:(1675)1/86400ofadayof24hoursof60minutesof60seconds.TLB Interim(1956):1/31556925.9747ofthetropicalyearfor1900January0at12hoursephemeristime. Current(1967):Thedurationof9192631770periodsoftheradiationcorrespondingtothetransitionbetweenthetwohyperfinelevelsofthegroundstateofthecaesium-133atom. metre Prior(1793):1/10000000ofthemeridianthroughParisbetweentheNorthPoleandtheEquator.FG Interim(1889):ThePrototypeofthemetrechosenbytheCIPM,atthetemperatureofmeltingice,representsthemetricunitoflength. Interim(1960):1650763.73wavelengthsinvacuumoftheradiationcorrespondingtothetransitionbetweenthe2p10and5d5quantumlevelsofthekrypton-86atom. Current(1983):Thedistancetravelledbylightinvacuumin1/299792458second. kilogram Prior(1793):Thegravewasdefinedasbeingthemass(thencalledweight)ofonelitreofpurewateratitsfreezingpoint.FG Interim(1889):Themassofasmallsquatcylinderof≈47cubiccentimetresofplatinum-iridiumalloykeptintheInternationalBurueauofWeightsandMeasures(BIPM),PavillondeBreteuil,France.[ck]Also,inpractice,anyofnumerousofficialreplicasofit.[cl][107] Current(2019):ThekilogramisdefinedbysettingthePlanckconstanthexactlyto6.62607015×10−34 J⋅s(J=kg⋅m2⋅s−2),giventhedefinitionsofthemetreandthesecond.[37]Thentheformulawouldbekg=h/6.62607015×10−34⋅m2⋅s−1 ampere Prior(1881):AtenthoftheelectromagneticCGSunitofcurrent.The[CGS]electromagneticunitofcurrentisthatcurrent,flowinginanarc1 cmlongofacircle1 cminradius,thatcreatesafieldofoneoerstedatthecentre.[108]IEC Interim(1946):Theconstantcurrentwhich,ifmaintainedintwostraightparallelconductorsofinfinitelength,ofnegligiblecircularcross-section,andplaced1 mapartinvacuum,wouldproducebetweentheseconductorsaforceequalto2×10−7newtonspermetreoflength. Current(2019):Theflowof1/1.602176634×10−19timestheelementarychargeepersecond. kelvin Prior(1743):Thecentigradescaleisobtainedbyassigning0 °Ctothefreezingpointofwaterand100 °Ctotheboilingpointofwater. Interim(1954):Thetriplepointofwater(0.01 °C)definedtobeexactly273.16 K.[n2] Previous(1967):1/273.16ofthethermodynamictemperatureofthetriplepointofwater. Current(2019):ThekelvinisdefinedbysettingthefixednumericalvalueoftheBoltzmannconstantkto1.380649×10−23 J⋅K−1,(J=kg⋅m2⋅s−2),giventhedefinitionofthekilogram,themetre,andthesecond. mole Prior(1900):AstoichiometricquantitywhichistheequivalentmassingramsofAvogadro'snumberofmoleculesofasubstance.ICAW Interim(1967):Theamountofsubstanceofasystemwhichcontainsasmanyelementaryentitiesasthereareatomsin0.012kilogramofcarbon-12. Current(2019):Theamountofsubstanceofexactly6.02214076×1023elementaryentities.ThisnumberisthefixednumericalvalueoftheAvogadroconstant,NA,whenexpressedintheunitmol−1andiscalledtheAvogadronumber. candela Prior(1946):Thevalueofthenewcandle(earlynameforthecandela)issuchthatthebrightnessofthefullradiatoratthetemperatureofsolidificationofplatinumis60newcandlespersquarecentimetre. Current(1979):Theluminousintensity,inagivendirection,ofasourcethatemitsmonochromaticradiationoffrequency5.4×1014hertzandthathasaradiantintensityinthatdirectionof1/683wattpersteradian. Note:botholdandnewdefinitionsareapproximatelytheluminousintensityofaspermaceticandleburningmodestlybright,inthelate19thcenturycalleda"candlepower"ora"candle". Notes ^Interimdefinitionsaregivenhereonlywhentherehasbeenasignificantdifferenceinthedefinition. ^In1954theunitofthermodynamictemperaturewasknownasthe"degreeKelvin"(symbol°K;"Kelvin"speltwithanupper-case"K").Itwasrenamedthe"kelvin"(symbol"K";"kelvin"speltwithalowercase"k")in1967. ThePriordefinitionsofthevariousbaseunitsintheabovetableweremadebythefollowingauthorsandauthorities: TLB=TitoLivioBurattini,Misurauniversale,Vilnius,1675 FG=FrenchGovernment IEC=InternationalElectrotechnicalCommission ICAW=InternationalCommitteeonAtomicWeights AllotherdefinitionsresultfromresolutionsbyeitherCGPMortheCIPMandarecataloguedintheSIBrochure. MetricunitsthatarenotrecognisedbytheSI[edit] Mainarticle:Metricunits AlthoughthetermmetricsystemisoftenusedasaninformalalternativenamefortheInternationalSystemofUnits,[109]othermetricsystemsexist,someofwhichwereinwidespreaduseinthepastorareevenstillusedinparticularareas.Therearealsoindividualmetricunitssuchasthesverdrupandthedarcythatexistoutsideofanysystemofunits.MostoftheunitsoftheothermetricsystemsarenotrecognisedbytheSI.[cm][cp] Herearesomeexamples.Thecentimetre–gram–second(CGS)systemwasthedominantmetricsysteminthephysicalsciencesandelectricalengineeringfromthe1860suntilatleastthe1960s,andisstillinuseinsomefields.ItincludessuchSI-unrecognisedunitsasthegal,dyne,erg,barye,etc.initsmechanicalsector,aswellasthepoiseandstokesinfluiddynamics.Whenitcomestotheunitsforquantitiesinelectricityandmagnetism,thereareseveralversionsoftheCGSsystem.Twooftheseareobsolete:theCGSelectrostatic('CGS-ESU',withtheSI-unrecognisedunitsofstatcoulomb,statvolt,statampere,etc.)andtheCGSelectromagneticsystem('CGS-EMU',withabampere,abcoulomb,oersted,maxwell,abhenry,gilbert,etc.).[cq][cs]A'blend'ofthesetwosystemsisstillpopularandisknownastheGaussiansystem(whichincludesthegaussasaspecialnamefortheCGS-EMUunitmaxwellpersquarecentimetre).[ct] Inengineering(otherthanelectricalengineering),therewasformerlyalongtraditionofusingthegravitationalmetricsystem,whoseSI-unrecognisedunitsincludethekilogram-force(kilopond),technicalatmosphere,metrichorsepower,etc.Themetre–tonne–second(mts)system,usedintheSovietUnionfrom1933to1955,hadsuchSI-unrecognisedunitsasthesthène,pièze,etc.OthergroupsofSI-unrecognisedmetricunitsarethevariouslegacyandCGSunitsrelatedtoionisingradiation(rutherford,curie,roentgen,rad,rem,etc.),radiometry(langley,jansky),photometry(phot,nox,stilb,nit,metre-candle,[115]:17lambert,apostilb,skot,brill,troland,talbot,candlepower,candle),thermodynamics(calorie),andspectroscopy(reciprocalcentimetre). Theangstromisstillusedinvariousfields.SomeotherSI-unrecognisedmetricunitsthatdon'tfitintoanyofthealreadymentionedcategoriesincludetheare,bar,barn,fermi,gradian(gon,grad,orgrade),metriccarat,micron,millimetreofmercury,torr,millimetre(orcentimetre,ormetre)ofwater,millimicron,mho,stere,xunit,γ(unitofmass),γ(unitofmagneticfluxdensity),andλ(unitofvolume).[116]: 20–21 Insomecases,theSI-unrecognisedmetricunitshaveequivalentSIunitsformedbycombiningametricprefixwithacoherentSIunit.Forexample,1 γ(unitofmagneticfluxdensity)=1 nT,1 Gal=1 cm⋅s−2,1 barye=1 decipascal,etc.(arelatedgrouparethecorrespondences[cq]suchas1 abampere≘1 decaampere,1 abhenry≘1 nanohenry,etc.[cu]).Sometimes,itisnotevenamatterofametricprefix:theSI-nonrecognisedunitmaybeexactlythesameasanSIcoherentunit,exceptforthefactthattheSIdoesnotrecognisethespecialnameandsymbol.Forexample,thenitisjustanSI-unrecognisednamefortheSIunitcandelapersquaremetreandthetalbotisanSI-unrecognisednamefortheSIunitlumensecond.Frequently,anon-SImetricunitisrelatedtoanSIunitthroughapower-of-tenfactor,butnotonethathasametricprefix,e.g.,1 dyn=10−5 newton,1 Å=10−10 m,etc.(andcorrespondences[cq]like1 gauss≘10−4 tesla).Finally,therearemetricunitswhoseconversionfactorstoSIunitsarenotpowersoften,e.g.,1 calorie=4.184 joulesand1 kilogram-force=9.806650 newtons.SomeSI-unrecognisedmetricunitsarestillfrequentlyused,e.g.,thecalorie(innutrition),therem(intheU.S.),thejansky(inradioastronomy),thegauss(inindustry)andtheCGS-Gaussianunits[ct]moregenerally(insomesubfieldsofphysics),themetrichorsepower(forenginepower,inEurope),thekilogram-force(forrocketenginethrust,inChinaandsometimesinEurope),etc.Othersarenowrarelyused,suchasthesthèneandtherutherford. Seealso[edit] Non-SIunitsmentionedintheSI Conversionofunits –Comparisonofvariousscales Outlineofthemetricsystem –Overviewofandtopicalguidetothemetricsystem Listofinternationalcommonstandards –Wikipedialistarticle Organisations InternationalBureauofWeightsandMeasures –Intergovernmentalmeasurementscienceandmeasurementstandardssettingorganisation InstituteforReferenceMaterialsandMeasurements(EU) NationalInstituteofStandardsandTechnology –MeasurementstandardslaboratoryintheUnitedStates(US) Standardsandconventions Conventionalelectricalunit CoordinatedUniversalTime (UTC) –Primarytimestandard UnifiedCodeforUnitsofMeasure Notes[edit] ^'SI'isaninitialismofSystèmeinternational,whichisanabbreviatedformofitsfullFrenchnameSystèmeinternationald’unités,[2]: 165 whichliterallymeans'InternationalSystemofUnits'.ByResolution12ofthe11thCGPM(1960),theinternationalabbreviationofthenameofthesystemis:SI.[2]: 165  ^Whenwesay'SIsystem',wearebasicallysayingtheword'system'twice:'InternationalSystemsystem'(notethat'SI'standsfortheFrenchnameSystèmeinternational,whichliterallymeans'InternationalSystem').Thisisatypeoflinguisticredundancycalledpleonasm.Someexamplesofsuchpleonasticusageincludethelistof'alternatetitles'intheEncyclopediaBritannicaarticleontheSI,[4]thelastparagraphinaneditorialinthejournalNature,[5]andthefootnote1toTable5inthestylemanualoftheInternationalAstronomicalUnion.[6] ^Inadecimalsystem,differentunitsforagivenkindofphysicalquantityarerelatedbyfactorsof10,sothat,withinsuchasystem,unitconversionsinvolvethesimpleprocessofmovingthedecimalpointtotherightortotheleft.[9]Soinsteadofrelationslike1mile=1760yards,aswehaveinimperialandUScustomarymeasurementsystems(whicharenotdecimal),intheSI(whichisdecimal)weinsteadhave1kilometre=1000metres.Herethekilometreiscomparableinsizetothemile(1 km≈0.6 mi)andthemetretotheyard(1 m≈1.1 yd). ^Oroneofitsdecimalmultiplesorsubmiltiples,likethecentimetre. ^Oroneofitsdecimalmultiplesorsubmiltiples,likethegram. ^Oroneofitsdecimalmultiplesorsubmiltiples,likethegram-force. ^Ametricsystemofunitsisanysystemofweightsandmeasuresthatisdecimal[c]andbasedonthemetre[d]astheunitoflengthandeitherthekilogram[e]astheunitofmassorthekilogram-force[f]astheunitofforce. ^Asof19 January 2021.[update] ^abThelattergroupincludeseconomicunionssuchastheCaribbeanCommunity(CARICOM). ^Thisisaninternationalorganizationwith[h]63memberstatesand39AssociateStatesandEconomiesoftheGeneralConference.[i][13]Itwasestablishedin1875underthetermsoftheMetreConvention.[12][14] ^abcFromFrench:Conférencegénéraledespoidsetmesures. ^abItshallbelawfulthroughouttheUnitedStatesofAmericatoemploytheweightsandmeasuresofthemetricsystem;andnocontractordealing,orpleadinginanycourt,shallbedeemedinvalidorliabletoobjectionbecausetheweightsormeasuresexpressedorreferredtothereinareweightsormeasuresofthemetricsystem.(15 U.S.C. § 204) ^Here'officialstatus'meansthattheSIisrecognizedinsomewaybythelawsandregulationsofthecountry.Inmanycountries,thismeansthatusingtheSIunitsismandatoryformostcommercialandadministrativepurposes(e.g.intheEuropeanUnion).Ontheotherhand,whenitcomestotheUS,'officialstatus'meansthatfederallawspecificallyallows,butdoesn'trequire,theSIunitstobeused.[l]Infact,federallawevenstatesthatitisthedeclaredpolicyoftheUnitedStatestodesignatethemetricsystemofmeasurementasthepreferredsystemofweightsandmeasuresforUnitedStatestradeandcommerce(15 U.S.C. § 205b).Seemetricationformoreinformation. ^ThisincludestheUnitedStates,Canada,andtheUnitedKingdom,despitethefactthesethreecountriesalsocontinuetousetheircustomarysystemstovariousdegrees. ^Althoughtheprecisedefinitionofcoherenceiscomplicated,thebasicideaisthatmathematicalrelationsbetweentheunitsforquantitiesshouldmirrorthemathematicalrelationsbetweenthecorrespondingquantitiesthemselves.Forexample,thecoherentunitofvolumeisequaltothevolumeofacubewhosesidesareoneunitoflength;thecoherentunitofpressureisequaltothepressureexertedbyaunit-magnitudeforceoverasurfaceofunitarea;etc.Asanexampleoflackofcoherence,considerhow,intheUScustomarysystem,theunitsoffluidvolumearerelatedtotheunitsoflength.Theprincipalunitsoflengthareinches,feet,yards,andmiles;meanwhile,theprincipalunitsoffluidvolumearebasedonthe(US)gallon,which,at231cubicinches,isnotacubicinch,oracubicfoot,oracubicyard,oracubicmile(notethat231=3×7×11). ^Forexample,theSIunitofvelocityisthemetrepersecond,m⋅s−1;ofaccelerationisthemetrepersecondsquared,m⋅s−2;etc.Thesecanalsobewrittenasm/sandm/s2,respectively. ^Forexamplethenewton(N),theunitofforce,equivalenttokg⋅m⋅s−2;thejoule(J),theunitofenergy,equivalenttokg⋅m2⋅s−2,etc.Themostrecentlynamedderivedunit,thekatal,wasdefinedin1999. ^Forexample,therecommendedunitfortheelectricfieldstrengthisthevoltpermetre,V/m,wherethevoltisthederivedunitforelectricpotentialdifference.Thevoltpermetreisequaltokg⋅m⋅s−3⋅A−1whenexpressedintermsofbaseunits. ^Thismustbeoneof29coherentunitswithaseparatenameandsymbol,i.e.eitheroneofthesevenbaseunitsoroneofthe22coherentderivedunitswithspecialnamesandsymbols. ^Forexample,thecoherentSIunitoflengthisthemetre,abouttheheightofkitchencounter(justover3 ft).Butfordrivingdistances,onewouldnormallyusekilometres,whereonekilometreis1000metres;herethemetricprefix'kilo-'(symbol'k')standsforafactorof1000.Ontheotherhand,fortailoringmeasurements,onewouldusuallyusecentimetres,whereonecentimetreis1/100ofametre;herethemetricprefix'centi-'(symbol'c')standsforafactorof1/100. ^Non-coherent,customarysystemshaveanothertendency,well-illustratedbytheU.S.customarysystem.Inthatsystem,someliquidcommoditiesaremeasuredneitherinthecoherentunitsofvolume(e.g.cubicinches)noringallons,butinbarrels.Furthermore,thesizeofthebarreldependsonthecommodity:itmeans31USgallonsforbeer,[15]but42gallonsforpetroleum.[16] Sodifferentunitsforoneandthesamequantity(e.g.volume)areuseddependingonwhatisbeingmeasured,andthesedifferentunitsmaynotberelatedtoeachotherinanyobviousway—eveniftheyhavethesamename. ^Meaningthatdifferentunitsforagivenquantity,suchaslength,arerelatedbyfactorsof10.Therefore,calculationsinvolvethesimpleprocessofmovingthedecimalpointtotherightortotheleft.[9]Forexample,thecoherentSIunitoflengthisthemetre,whichisabouttheheightofthekitchencounter.ButifonewishestotalkaboutdrivingdistancesusingtheSIunits,onewillnormallyusekilometres,whereonekilometreis1000metres.Ontheotherhand,tailoringmeasurementswouldusuallybeexpressedincentimetres,whereonecentimetreis1/100ofametre. ^AlthoughthetermsthemetricsystemandtheSIareoftenusedassynonyms,thereareinfactmanymutuallyincompatiblemetricsystems.Moreover,thereexistmetricunitsthatarenotrecognisedbyanylargermetricsystem.See§ MetricunitsthatarenotrecognisedbytheSI,below. ^AsofMay 2020[update],onlyforthefollowingcountriesisituncertainwhethertheSIhasanyofficialstatus:Myanmar,Liberia,theFederatedStatesofMicronesia,theMarshallIslands,Palau,andSamoa. ^IntheUS,thehistoryoflegislationbeginswiththeMetricActof1866,whichlegallyprotecteduseofthemetricsystemincommerce.ThefirstsectionisstillpartofUSlaw(15 U.S.C. § 204).[l]In1875,theUSbecameoneoftheoriginalsignatoriesoftheMetreConvention.In1893,theMendenhallOrderstatedthattheOfficeofWeightsandMeasures...willinthefutureregardtheInternationalPrototypeMetreandKilogrammeasfundamentalstandards,andthecustomaryunits—theyardandthepound—willbederivedtherefrominaccordancewiththeActofJuly28,1866.In1954,theUSadoptedtheInternationalNauticalMile,whichisdefinedasexactly1852 m,inlieuoftheU.S.NauticalMile,definedas6080.20 ft=1853.248 m.In1959,theU.S.NationalBureauofStandardsofficiallyadaptedtheInternationalyardandpound,whicharedefinedexactlyintermsofthemetreandthekilogram.In1968,theMetricStudyAct(Pub.L.90-472,August9,1968,82Stat.693)authorisedathree-yearstudyofsystemsofmeasurementintheU.S.,withparticularemphasisonthefeasibilityofadoptingtheSI.TheMetricConversionActof1975followed,lateramendedbytheOmnibusTradeandCompetitivenessActof1988,theSavingsinConstructionActof1996,andtheDepartmentofEnergyHigh-EndComputingRevitalizationActof2004.Asaresultofalltheseacts,theUScurrentlaw(15 U.S.C. § 205b)statesthatItisthereforethedeclaredpolicyoftheUnitedStates- (1)todesignatethemetricsystemofmeasurementasthepreferredsystemofweightsandmeasuresforUnitedStatestradeandcommerce; (2)torequirethateachFederalagency,byadatecertainandtotheextenteconomicallyfeasiblebytheendofthefiscalyear1992,usethemetricsystemofmeasurementinitsprocurements,grants,andotherbusiness-relatedactivities,excepttotheextentthatsuchuseisimpracticalorislikelytocausesignificantinefficienciesorlossofmarketstoUnitedStatesfirms,suchaswhenforeigncompetitorsareproducingcompetingproductsinnon-metricunits; (3)toseekoutwaystoincreaseunderstandingofthemetricsystemofmeasurementthrougheducationalinformationandguidanceandinGovernmentpublications;and (4)topermitthecontinueduseoftraditionalsystemsofweightsandmeasuresinnon-businessactivities. ^AndhavebeendefinedintermsoftheSI'smetricpredecessorssinceatleastthe1890s. ^Seee.g.hereforthevariousdefinitionsofthecatty,atraditionalChineseunitofmass,invariousplacesacrossEastandSoutheastAsia.Similarly,seethisarticleonthetraditionalJapaneseunitsofmeasurement,aswellasthisoneonthetraditionalIndianunitsofmeasurement. ^abfromFrench:Comitéinternationaldespoidsetmesures ^abTheSIBrochureforshort.AsofMay 2020[update],thelatesteditionistheninth,publishedin2019.ItisRef.[2]ofthisarticle. ^abfromFrench:Bureauinternationaldespoidsetmesures ^ThelatterareformalisedintheInternationalSystemofQuantities(ISQ).[2]: 129  ^Thechoiceofwhichandevenhowmanyquantitiestouseasbasequantitiesisnotfundamentalorevenunique–itisamatterofconvention.[2]: 126 Forexample,fourbasequantitiescouldhavebeenchosenasvelocity,angularmomentum,electricchargeandenergy. ^HerearesomeexamplesofcoherentderivedSIunits:theunitofvelocity,whichisthemetrepersecond,withthesymbolm/s;theunitofacceleration,whichisthemetrepersecondsquared,withthesymbolm/s2;etc. ^Ausefulpropertyofacoherentsystemisthatwhenthenumericalvaluesofphysicalquantitiesareexpressedintermsoftheunitsofthesystem,thentheequationsbetweenthenumericalvalueshaveexactlythesameform,includingnumericalfactors,asthecorrespondingequationsbetweenthephysicalquantities;[17]: 6 Anexamplemaybeusefultoclarifythis.Supposewearegivenanequationrelatingsomephysicalquantities,e.g.T=1/2{m}{v}2,expressingthekineticenergyTintermsofthemassmandthevelocityv.Chooseasystemofunits,andlet{T},{m},and{v}bethenumericalvaluesofT,m,andvwhenexpressedinthatsystemofunits.Ifthesystemiscoherent,thenthenumericalvalueswillobeythesameequation(includingnumericalfactors)asthephysicalquantities,i.e.wewillhavethatT=1/2{m}{v}2.Ontheotherhand,ifthechosensystemofunitsisnotcoherent,thispropertymayfail.Forexample,thefollowingisnotacoherentsystem:onewhereenergyismeasuredincalories,whilemassandvelocityaremeasuredintheirSIunits.Afterall,inthatcase,1/2{m}{v}2willgiveanumericalvaluewhosemeaningisthekineticenergywhenexpressedinjoules,andthatnumericalvalueisdifferent,byafactorof4.184,fromthenumericalvaluewhenthekineticenergyisexpressedincalories.Thus,inthatsystem,theequationsatisfiedbythenumericalvaluesisinstead{T}=1/4.1841/2{m}{v}2. ^Forexamplethenewton(N),theunitofforce,equaltokg⋅m⋅s−2whenwrittenintermsofthebaseunits;thejoule(J),theunitofenergy,equaltokg⋅m2⋅s−2,etc.Themostrecentlynamedderivedunit,thekatal,wasdefinedin1999. ^Forexample,therecommendedunitfortheelectricfieldstrengthisthevoltpermetre,V/m,wherethevoltisthederivedunitforelectricpotentialdifference.Thevoltpermetreisequaltokg⋅m⋅s−3⋅A−1whenexpressedintermsofbaseunits. ^WhichdefinetheInternationalSystemofQuantities(ISQ). ^ItiscorrecttosaythatanSIbaseunit(likethemetre)isacoherentunitforitscorrespondingphysicalquantity.RecallthatthesetofcoherentSIunitsconsistsofthebaseunitsandthecoherentderivedunits.Thisusageisconsistentwiththedefinitionofacoherentunitasonethatisequalto'aproductofpowersofthebaseunitswithaprefactorof1'.Afterall,eachbaseunitisobviouslysorepresentable—itisequaltoitselftothepowerof1andwithaprefactorof1. ^Onekilometreisabout0.62 miles,alengthequaltoabouttwoandahalflapsaroundatypicalathletictrack.Walkingatamoderatepaceforonehour,anadulthumanwillcoveraboutfivekilometres(aboutthreemiles).ThedistancefromLondon,UK,toParis,Franceisabout350 km;fromLondontoNewYork,5600 km. ^Inotherwords,givenanybaseunitoranycoherentderivedunitwithaspecialnameandsymbol. ^Except—forhistoricalreasons—inthecaseoftheunitsofmass.Eventhoughthecoherentunitofmassisthekilogram,kg,themetricprefixesareaddedtothegram.SotheSIunitequalto10−6 kgisamilligram,mg,ratherthana'microkilogram','μkg'.[2]: 144  ^ThislaststatementinfactappliestoallSIunits,notonlythosewithspecialnamesandsymbols.ConsidertheexampleoftheSIunitsoftorque.BecausetheSIdoesnothaveaunitwithaspecialnameandsymbolfortorque,itscoherentSIunitisthenewton-metre,N⋅m.Thefollowingaresomeexamplesofnon-coherentSIunitsoftorque:N⋅mm,kN⋅μm,mN⋅cm,etc.Notethatthesenon-coherentunitsareobtainedfromtheoriginalcoherentunitbyreplacingsome(orall)oftheunitswithspecialnamesandsymbolsthatarepresentintheoriginalcoherentunitbytheirdecimalmultiplesorsubmultiples.Butthenthesedifferentpowersoftencombineintooneoverallpoweroften.Forexample,kN⋅μm=(103N)⋅(10−6m)=103-6N⋅m=10−3N⋅m. ^Note,however,thatthereisaspecialgroupofunitsthatarecallednon-SIunitsacceptedforusewithSI,mostofwhicharenotdecimalmultiplesofthecorrespondingSIunits;seebelow. ^Namesandsymbolsfordecimalmultiplesandsub-multiplesoftheunitofmassareformedasifitisthegramwhichisthebaseunit,i.e.byattachingprefixnamesandsymbols,respectively,totheunitname"gram"andtheunitsymbol"g".Forexample,10−6 kgiswrittenasmilligram,mg,notasmicrokilogram,μkg.[2]: 144  ^AstheSIBrochurestates,[2]: 140 thisappliesnotonlytotechnicaltexts,butalso,forexample,tomeasuringinstruments(i.e.theinstrumentread-outneedstoindicateboththeunitandthequantitymeasured). ^Customarily,however,rainfallismeasuredinnon-coherentSIunitssuchasmillimetresinheightcollectedoneachsquaremetreduringacertainperiod,equivalenttolitrespersquaremetre. ^Evenbaseunits;themolewasaddedasabaseSIunitonlyin1971.[2]: 156  ^Seethenextsectionforwhythistypeofdefinitionisconsideredadvantageous. ^Theirexactlydefinedvaluesareasfollows:[2]: 128  Δ ν Cs {\displaystyle\Delta\nu_{\text{Cs}}} =9192631770 Hz c {\displaystylec} =299792458 m/s h {\displaystyleh} =6.62607015×10−34 J⋅s e {\displaystylee} =1.602176634×10−19 C k {\displaystylek} =1.380649×10−23 J/K N A {\displaystyleN_{\text{A}}} =6.02214076×1023 mol−1 K cd {\displaystyleK_{\text{cd}}} =683 lm/W. ^AmiseenpratiqueisFrenchfor'puttingintopractice;implementation'.[21][22] ^abThesoleexceptionisthedefinitionofthesecond,whichisstillgivennotintermsoffixedvaluesoffundamentalconstantsbutintermsofaparticularpropertyofaparticularnaturallyoccurringobject,thecaesiumatom.Andindeed,ithasbeenclearforsometimethatrelativelysoon,byusingatomsotherthancaesium,itwillbepossibletohavedefinitionsofthesecondthataremoreprecisethanthecurrentone.Takingadvantageofthesemoreprecisemethodswillnecessitatethechangeinthedefinitionofthesecond,probablysometimearoundtheyear2030.[28]: 196  ^abAgain,exceptforthesecond,asexplainedinthepreviousnote. Thesecondmayeventuallygetfixedbydefininganexactvalueforyetanotherfundamentalconstant(whosederivedunitincludesthesecond),forexampletheRydbergconstant.Forthistohappen,theuncertaintyinthemeasurementofthatconstantmustbecomesosmallastobedominatedbytheuncertaintyinthemeasurementofwhateverclocktransitionfrequencyisbeingusedtodefinethesecondatthatpoint.Oncethathappens,thedefinitionswillbereversed:thevalueoftheconstantwillbefixedbydefinitiontoanexactvalue,namelyitsmostrecentbestmeasuredvalue,whiletheclocktransitionfrequencywillbecomeaquantitywhosevalueisnolongerfixedbydefinitionbutwhichhastobemeasured.Unfortunately,itisunlikelythatthiswillhappenintheforeseeablefuture,becausepresentlytherearenopromisingstrategiesformeasuringanyadditionalfundamentalconstantswiththenecessaryprecision.[29]: 4112–3  ^Theoneexceptionbeingthedefinitionofthesecond;seeNotes[ay]and[az]inthefollowingsection. ^Toseethis,recallthatHz=s−1andJ=kg⋅m2⋅s−2.Thus,(Hz)(J⋅s)/(m/s)2=(s−1)[(kg⋅m2⋅s−2)⋅s](m⋅s−1)−2=s(−1−2+1+2)⋅m(2−2)⋅kg=kg,sinceallthepowersofmetresandsecondscancelout.Itcanfurtherbeshownthat(Hz)(J⋅s)/(m/s)2istheonlycombinationofpowersoftheunitsofthedefiningconstants(thatis,theonlycombinationofpowersofHz,m/s,J⋅s,C,J/K,mol−1,andlm/W)thatresultsinthekilogram. ^Namely,1 Hz=ΔνCs/91926317701 m/s=c/299792458,and1 J⋅s=h/6.62607015×10−34. ^TheSIBrochurepreferstowritetherelationshipbetweenthekilogramandthedefiningconstantsdirectly,withoutgoingthroughtheintermediarystepofdefining1 Hz,1 m/s,and1 J⋅s,likethis:[2]: 131 1 kg=(299792458)2/(6.62607015×10−34)(9192631770)h ΔνCs/c2. ^Forexample,from1889until1960,themetrewasdefinedasthelengthoftheInternationalPrototypeMetre,aparticularbarmadeofplatinum-iridiumalloythatwas(andstillis)keptattheInternationalBureauofWeightsandMeasures,locatedinthePavillondeBreteuilinSaint-Cloud,France,nearParis.Thefinalartefact-baseddefinitionofthemetre,whichstoodfrom1927totheredefinitionofthemetrein1960,readasfollows:[2]: 159 Theunitoflengthisthemetre,definedbythedistance,at0°,betweentheaxesofthetwocentrallinesmarkedonthebarofplatinum-iridiumkeptattheBureauInternationaldesPoidsetMesuresanddeclaredPrototypeofthemetrebythe1stConférenceGénéraledesPoidsetMesures,thisbarbeingsubjecttostandardatmosphericpressureandsupportedontwocylindersofatleastonecentimetrediameter,symmetricallyplacedinthesamehorizontalplaneatadistanceof571 mmfromeachother.The'0°'referstothetemperatureof0 °C.ThesupportrequirementsrepresenttheAirypointsoftheprototype—thepoints,separatedby4/7ofthetotallengthofthebar,atwhichthebendingordroopofthebarisminimised.[31] ^Thelatterwascalledthe'quadrant',thelengthofameridianfromtheequatortotheNorthPole.TheoriginallychosenmeridianwastheParismeridian. ^Atthetime'weight'and'mass'werenotalwayscarefullydistinguished. ^Thisvolumeis1 cm3=1 mL,whichis1×10−6 m3.Thus,theoriginaldefinitionofmassusednotthecoherentunitofvolume(whichwouldbethem3)butadecimalsubmultipleofit. ^Indeed,theoriginalideaofthemetricsystemwastodefineallunitsusingonlynaturalanduniversallyavailablemeasurablequantities.Forexample,theoriginaldefinitionoftheunitoflength,themetre,wasadefinitefraction(oneten-millionth)ofthelengthofaquarteroftheEarth'smeridian.[bf]Oncethemetrewasdefined,onecoulddefinetheunitofvolumeasthevolumeofacubewhosesidesareoneunitoflength.Andoncetheunitofvolumewasdetermined,theunitofmasscouldbedefinedasthemassofaunitofvolumeofsomeconvenientsubstanceatstandardconditions.Infact,theoriginaldefinitionofthegramwas'theabsoluteweight[bg]ofavolumeofpurewaterequaltothecubeofthehundredthpartofametre,[bh]andatthetemperatureofmeltingice.'However,itsoonbecameapparentthattheseparticular'natural'realisationsoftheunitsoflengthandmasssimplycouldnot,atthattime,beasprecise(andasconvenienttoaccess)astheneedsofscience,technology,andcommercedemanded.Therefore,prototypeswereadoptedinstead.Carewastakentomanufacturetheprototypessothattheywouldbeascloseaspossible,giventheavailablescienceandtechnologyoftheday,totheidealised'natural'realisations.Butoncetheprototypeswerecompleted,theunitsoflengthandmassbecameequalbydefinitiontotheseprototypes(seeMètredesArchivesandKilogrammedesArchives).Nevertheless,throughoutthehistoryoftheSI,onekeepsseeingexpressionsofhopethatoneday,onewouldbeabletodispensewiththeprototypesanddefineallunitsintermsofstandardsfoundinnature.Thefirstsuchstandardwasthesecond.Itwasneverdefinedusingaprototype,beingoriginallydefinedas1/86400ofthelengthofaday(sincethereare60s/min×60min/hr×24hr/day=86400s/day).Aswementioned,thevisionofdefiningallunitsintermsofuniversallyavailablenaturalstandardswasatlastfulfilledin2019,whenthesoleremainingprototypeusedbytheSI,theoneforthekilogram,wasfinallyretired. ^Thefollowingreferencesareusefulforidentifyingtheauthorsoftheprecedingreference:Ref.,,[33]Ref.,[34]andRef.[35] ^abAshappenedwithBritishstandardsforlengthandmassin1834,whentheywerelostordamagedbeyondthepointofuseabilityinagreatfireknownastheburningofParliament.Acommissionofeminentscientistswasassembledtorecommendthestepstobetakenfortherestorationofthestandards,andinitsreport,itdescribedthedestructioncausedbythefireasfollows:[32][bj] WeshallinthefirstplacedescribethestateoftheStandardsrecoveredfromtheruinsoftheHouseofCommons,asascertainedinourinspectionofthemmadeon1stJune,1838,attheJournalOffice,wheretheyarepreservedunderthecareofMr.JamesGudge,PrincipalClerkoftheJournalOffice.Thefollowinglist,takenbyourselvesfrominspection,wascomparedwithalistproducedbyMr.Gudge,andstatedbyhimtohavebeenmadebyMr.CharlesRowland,oneoftheClerksoftheJournalOffice,immediatelyafterthefire,andwasfoundtoagreewithit.Mr.GudgestatedthatnootherStandardsofLengthorWeightwereinhiscustody. No.1.Abrassbarmarked"Standard[G.II.crownemblem]Yard,1758",whichonexaminationwasfoundtohaveitsrighthandstudperfect,withthepointandlinevisible,butwithitslefthandstudcompletelymeltedout,aholeonlyremaining.Thebarwassomewhatbent,anddiscolouredineverypart. No.2.Abrassbarwithaprojectingcockateachend,formingabedforthetrialofyard-measures;discoloured. No.3.Abrassbarmarked"Standard[G.II.crownemblem]Yard,1760",fromwhichthelefthandstudwascompletelymeltedout,andwhichinotherrespectswasinthesameconditionasNo.1. No.4.Ayard-bedsimilartoNo.2;discoloured. No.5.Aweightoftheform[drawingofaweight]marked[2lb.T.1758],apparentlyofbrassorcopper;muchdiscoloured. No.6.Aweightmarkedinthesamemannerfor4lbs.,inthesamestate. No.7.AweightsimilartoNo.6,withahollowspaceatitsbase,whichappearedatfirstsighttohavebeenoriginallyfilledwithsomesoftmetalthathadbeennowmeltedout,butwhichonaroughtrialwasfoundtohavenearlythesameweightasNo.6. No.8.Asimilarweightof8lbs.,similarlymarked(withthealterationof8lbs.for4lbs.),andinthesamestate. No.9.AnotherexactlylikeNo.8. Nos.10and11.Twoweightsof16lbs.,similarlymarked. Nos.12and13.Twoweightsof32lbs.,similarlymarked. No.14.Aweightwithatriangularring-handle,marked"S.F.175917lbs.8dwts.Troy",apparentlyintendedtorepresentthestoneof14lbs.avoirdupois,allowing7008troygrainstoeachavoirdupoispound. ItappearsfromthislistthatthebaradoptedintheAct5thGeo.IV.,cap.74,sect.1,forthelegalstandardofoneyard,(No.3oftheprecedinglist),issofarinjured,thatitisimpossibletoascertainfromit,withthemostmoderateaccuracy,thestatutablelengthofoneyard.Thelegalstandardofonetroypoundismissing.WehavethereforetoreportthatitisabsolutelynecessarythatstepsbetakenfortheformationandlegalisingofnewStandardsofLengthandWeight. ^Indeed,oneofthemotivationsforthe2019redefinitionoftheSIwastheinstabilityoftheartefactthatservedasthedefinitionofthekilogram. Beforethat,oneofthereasonstheUnitedStatesstarteddefiningtheyardintermsofthemetrein1893wasthat[36]: 381 [t]hebronzeyardNo.11,whichwasanexactcopyoftheBritishimperialyardbothinformandmaterial,hadshownchangeswhencomparedwiththeimperialyardin1876and1888whichcouldnotreasonablybesaidtobeentirelyduetochangesinNo.11.SuspicionastotheconstancyofthelengthoftheBritishstandardwasthereforearoused.Intheabove,thebronzeyardNo.11isoneoftwocopiesofthenewBritishstandardyardthatweresenttotheUSin1856,afterBritaincompletedthemanufactureofnewimperialstandardstoreplacethoselostinthefireof1834(see[bk]).Asstandardsoflength,thenewyards,especiallybronzeNo.11,werefarsuperiortothestandardtheUShadbeenusinguptothatpoint,theso-calledTroughtonscale.TheywerethereforeacceptedbytheOfficeofWeightsandMeasures(apredecessorofNIST)asthestandardsoftheUnitedStates.TheyweretwicetakentoEnglandandrecomparedwiththeimperialyard,in1876andin1888,and,asmentionedabove,measurablediscrepancieswerefound.[36]: 381  In1890,asasignatoryoftheMetreConvention,theUSreceivedtwocopiesoftheInternationalPrototypeMetre,theconstructionofwhichrepresentedthemostadvancedideasofstandardsofthetime.ThereforeitseemedthatUSmeasureswouldhavegreaterstabilityandhigheraccuracybyacceptingtheinternationalmetreasfundamentalstandard,whichwasformalisedin1893bytheMendenhallOrder.[36]: 379–81  ^Asmentionedabove,itisallbutcertainthatthedefiningconstant Δ ν Cs {\displaystyle\Delta\nu_{\text{Cs}}} willhavetobereplacedrelativelysoon,asitisbecomingincreasinglyclearthatatomsotherthancaesiumcanprovidemoreprecisetimestandards.However,itisnotexcludedthatsomeoftheotherdefiningconstantswouldeventuallyhavetobereplacedaswell.Forexample,theelementarychargeecorrespondstoacouplingstrengthoftheelectromagneticforceviathefine-structureconstant α {\displaystyle\alpha} .Sometheoriespredictthat α {\displaystyle\alpha} canvaryovertime.Thepresentlyknownexperimentallimitsofthemaximumpossiblevariationof α {\displaystyle\alpha} aresolowthat'anyeffectonforeseeablepracticalmeasurementscanbeexcluded',[2]: 128 evenifoneofthesetheoriesturnsouttobecorrect.Nevertheless,ifthefine-structureconstantturnsouttoslightlyvaryovertime,scienceandtechnologymayinthefutureadvancetoapointwheresuchchangesbecomemeasurable.Atthatpoint,onemightconsiderreplacing,forthepurposesofdefiningtheSI,theelementarychargewithsomeotherquantity,thechoiceofwhichwillbeinformedbywhatwelearnaboutthetimevariationof α {\displaystyle\alpha} . ^Theofficialtermis"StatesPartiestotheMetreConvention";theterm"MemberStates"isitssynonymandusedforeasyreference.[13]Asof13 January 2020,[update].[13]thereare63MemberStatesand39AssociateStatesandEconomiesoftheGeneralConference.[i] ^AmongthetasksoftheseConsultativeCommitteesarethedetailedconsiderationofadvancesinphysicsthatdirectlyinfluencemetrology,thepreparationofRecommendationsfordiscussionattheCIPM,theidentification,planningandexecutionofkeycomparisonsofnationalmeasurementstandards,andtheprovisionofadvicetotheCIPMonthescientificworkinthelaboratoriesoftheBIPM.[43] ^AsofApril2020,theseincludethosefromSpain(CEM),Russia(FATRiM),Switzerland(METAS),Italy(INRiM),SouthKorea(KRISS),France(LNE),China(NIM),US(NIST),Japan(AIST/NIMJ),UK(NPL),Canada(NRC),andGermany(PTB). ^AsofApril2020,theseincludeInternationalElectrotechnicalCommission(IEC),InternationalOrganizationforStandardization(ISO),andInternationalOrganizationofLegalMetrology(OIML). ^AsofApril2020,theseincludeInternationalCommissiononIllumination(CIE),CODATATaskGrouponFundamentalConstants,InternationalCommissiononRadiationUnitsandMeasurements(ICRU),andInternationalFederationofClinicalChemistryandLaboratoryMedicine(IFCC). ^AsofApril2020,theseincludeInternationalAstronomicalUnion(IAU),InternationalUnionofPureandAppliedChemistry(IUPAC),andInternationalUnionofPureandAppliedPhysics(IUPAP). ^Theseareindividualswithalong-terminvolvementinmattersrelatedtounits,havingactivelycontributedtopublicationsonunits,andhavingaglobalviewandunderstandingofscienceaswellasknowledgeonthedevelopmentandfunctioningoftheInternationalSystemofUnits.[47]AsofApril2020,theseinclude[46][48]Prof.MarcHimbertandDr.TerryQuinn. ^Forhistoricalreasons,thekilogramratherthanthegramistreatedasthecoherentunit,makinganexceptiontothischaracterisation. ^Ohm'slaw:1Ω=1V/AfromtherelationshipE=I×R,whereEiselectromotiveforceorvoltage(unit:volt),Iiscurrent(unit:ampere),andRisresistance(unit:ohm). ^WhilethesecondisreadilydeterminedfromtheEarth'srotationperiod,themetre,originallydefinedintermsoftheEarth'ssizeandshape,islessamenable;however,thefactthattheEarth'scircumferenceisverycloseto40000 kmmaybeausefulmnemonic. ^Thisisevidentfromtheformulas=v0t+1/2at2withv0=0anda=9.81 m/s2. ^ThisisevidentfromtheformulaT=2π√L/g. ^A60wattlightbulbhasabout800lumens[60]whichisradiatedequallyinalldirections(i.e.4πsteradians),thusisequalto I v = 800   lm 4 π   sr ≈ 64   cd {\displaystyleI_{v}={{\frac{800\{\text{lm}}}{4\pi\{\text{sr}}}}\approx64\{\text{cd}}}} ^ThisisevidentfromtheformulaP=IV. ^TheunitisnamedafterAndersCelsius. ^abExceptwherespecificallynoted,theserulesarecommontoboththeSIBrochureandtheNISTbrochure. ^Forexample,theUnitedStates'NationalInstituteofStandardsandTechnology(NIST)hasproducedaversionoftheCGPMdocument(NISTSP330)whichclarifiesusageforEnglish-languagepublicationsthatuseAmericanEnglish ^Thistermisatranslationoftheofficial[French]textoftheSIBrochure. ^ThestrengthoftheEarth'smagneticfieldwasdesignated1 G(gauss)atthesurface(=1cm−1/2⋅g1/2⋅s−1). ^Argentina,Austria-Hungary,Belgium,Brazil,Denmark,France,GermanEmpire,Italy,Peru,Portugal,Russia,Spain,SwedenandNorway,Switzerland,OttomanEmpire,UnitedStates,andVenezuela. ^Thetext"Descomparaisonspériodiquesdesétalonsnationauxaveclesprototypesinternationaux"(English:theperiodiccomparisonsofnationalstandardswiththeinternationalprototypes)inarticle6.3oftheMetreConventiondistinguishesbetweenthewords"standard"(OED:"Thelegalmagnitudeofaunitofmeasureorweight")and"prototype"(OED:"anoriginalonwhichsomethingismodelled"). ^ Theseincluded: GeneralConferenceonWeightsandMeasures(ConférencegénéraledespoidsetmesuresorCGPM) InternationalCommitteeforWeightsandMeasures(ComitéinternationaldespoidsetmesuresorCIPM) InternationalBureauofWeightsandMeasures(BureauinternationaldespoidsetmesuresorBIPM)–aninternationalmetrologycentreatSèvresinFrancethathascustodyoftheInternationalprototypekilogram,providesmetrologyservicesfortheCGPMandCIPM. ^PferdisGermanfor"horse"andStärkeisGermanfor"strength"or"power".ThePferdestärkeisthepowerneededtoraise75 kgagainstgravityattherateofonemetrepersecond.(1PS=0.985HP). ^ItisknownastheInternationalPrototypeoftheKilogram. ^ThisobjectistheInternationalPrototypeKilogramorIPKcalledratherpoeticallyLeGrandK. ^Meaning,theyareneitherpartoftheSInoroneofthenon-SIunitsacceptedforusewiththatsystem. ^Almostinvariablyeitherthemeterorthecentimeter. ^Allmajorsystemsofunitsinwhichforceratherthanmassisabaseunitareofatypeknownasgravitationalsystem(alsoknownastechnicalorengineeringsystem).Inthemostprominentmetricexampleofsuchasystem,theunitofforceistakentobethekilogram-force(kp),whichistheweightofthestandardkilogramunderstandardgravity,g=9.80665 m/s2.Theunitofmassisthenaderivedunit,definedasthemassthatisacceleratedatarateof1 m/s2whenacteduponbyanetforceof1 kp;oftencalledthehyl,itthereforehasavalueof1 hyl=9.80665 kg,sothatitisnotadecimalmultipleofthegram. ^Havingsaidthat,someunitsarerecognisedbyallmetricsystems.Thesecondisabaseunitinallofthem.Themetreisrecognisedinallofthem,eitherasthebaseunitoflengthorasadecimalmultipleorsubmultipleofthebaseunitoflength.Ontheotherhand,noteverymetricsystemrecognisesthegramasaunit(eitherthebaseunitoradecimalmultipleofthebaseunit).Inparticular,ingravitationalmetricsystems,theunitofforce(gram-forceorkilogram-force)replacestheunitofmassasabaseunit.Theunitofmassisthenaderivedunit,definedasthemassthat,whenacteduponbyanetunitforce,isacceleratedattheunitrate(i.e.atarateof1baseunitoflength[cn]persecondsquared).[co] ^abcInterconversionbetweendifferentsystemsofunitsisusuallystraightforward;however,theunitsforelectricityandmagnetismareanexception,andasurprisingamountofcareisrequired.Theproblemisthat,ingeneral,thephysicalquantitiesthatgobythesamenameandplaythesameroleintheCGS-ESU,CGS-EMU,andSI—e.g.'electriccharge','electricfieldstrength',etc.—donotmerelyhavedifferentunitsinthethreesystems;technicallyspeaking,theyareactuallydifferentphysicalquantities.[110]: 422 [110]: 423 Consider'electriccharge',whichineachofthethreesystemscanbeidentifiedasthequantitytwoinstancesofwhichenterinthenumeratorofCoulomb'slaw(asthatlawiswrittenineachsystem).Thisidentificationproducesthreedifferentphysicalquantities:the'CGS-ESUcharge',the'CGS-EMUcharge',andthe'SIcharge'.[111]: 35 [110]: 423 Theyevenhavedifferentdimensionswhenexpressedintermsofthebasedimensions:mass1/2×length3/2×time−1fortheCGS-ESUcharge,mass1/2×length1/2fortheCGS-EMUcharge,andcurrent×timefortheSIcharge(where,intheSI,thedimensionofcurrentisindependentofthoseofmass,length,andtime).Ontheotherhand,thesethreequantitiesareclearlyquantifyingthesameunderlyingphysicalphenomenon.Thus,wesaynotthat'oneabcoulombequalstencoulomb',butratherthat'oneabcoulombcorrespondstotencoulomb',[110]: 423 writtenas1 abC≘10 C.[111]: 35 Bythatwemean,'iftheCGS-EMUelectricchargeismeasuredtohavethemagnitudeof1 abC,thentheSIelectricchargewillhavethemagnitudeof10 C'.[111]: 35 [112]: 57–58  ^NeitherEMUnorESUunitshadsizesthatwereconvenientforpracticalworkofelectricalengineers.Itwasthereforedecidedtoestablisha'practical'systemofunits,whereeachunitisanappropriatedecimalmultipleorsubmultipleofthecorrespondingEMUunit,sothattheresultingunitshaveconvenientsizesandformacoherentsystem.Thesepracticalunitsweregivennamesderivedfromthenamesofeminentscientists,andmanyoftheseunits—boththenamesandthemagnitudes—werelaterincorporatedintotheSI:thevolt,theampere,theohm,etc. ^Forseveraldecades,theESUandEMUunitsdidnothavespecialnames;onewouldjustsay,forexample,theESUunitofresistance.In1903,A.E.KennellysuggestedthatthenamesoftheEMUunitsbeobtainedbyprefixingthenameofthecorresponding‘practicalunit'by‘ab-’(shortfor‘absolute’,givingthe‘abohm’,‘abvolt’,the‘abampere’,etc.),andthatthenamesoftheESUunitsbeanalogouslyobtainedbyusingtheprefix‘abstat-’,whichwaslatershortenedto‘stat-’(givingthe‘statohm’,‘statvolt’,‘statampere’,etc.).[113]: 534–5 Inasense,thisbringsusbackfullcircle:historically,themagnitudesofthe'practicalunits'werefirstdefinedintermsofthemagnitudesofthecorrespondingunitsoftheEMUsystem;[cr]then,KennellyproposedthatthenamesofunitsintheESUandEMUsystemsbederivedfromthecorrespondingnamesofpracticalunits.Kennelly'snamingsystemwaswidelyusedintheU.S.,but,apparently,notinEurope.[114] ^abTheCGS-GaussianunitsareablendoftheCGS-ESUandCGS-EMU,takingunitsrelatedtomagnetismfromthelatterandalltherestfromtheformer.Inaddition,thesystemintroducesthegaussasaspecialnamefortheCGS-EMUunitmaxwellpersquarecentimetre. ^Authorsoftenabusenotationslightlyandwritethesewithan'equals'sign('=')ratherthana'correspondsto'sign('≘'). 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Furtherreading[edit] InternationalUnionofPureandAppliedChemistry(1993).Quantities,UnitsandSymbolsinPhysicalChemistry,2ndedition,Oxford:BlackwellScience.ISBN 0-632-03583-8.Electronicversion. UnitSystemsinElectromagnetism MWKelleretal.MetrologyTriangleUsingaWattBalance,aCalculableCapacitor,andaSingle-ElectronTunnelingDevice "TheCurrentSISeenFromthePerspectiveoftheProposedNewSI".BarryN.Taylor.JournalofResearchoftheNationalInstituteofStandardsandTechnology,Vol.116,No.6,Pgs.797–807,Nov–Dec2011. B.N.Taylor,AmblerThompson,InternationalSystemofUnits(SI),NationalInstituteofStandardsandTechnology2008edition,ISBN 1437915582. Externallinks[edit] WikimediaCommonshasmediarelatedtoInternationalSystemofUnits. Official BIPM–AbouttheBIPM(homepage) BIPM–measurementunits BIPMbrochure(SIreference) ISO80000-1:2009Quantitiesandunits–Part1:General NISTOn-lineofficialpublicationsontheSI NISTSpecialPublication330,2019Edition:TheInternationalSystemofUnits(SI) NISTSpecialPublication811,2008Edition:GuidefortheUseoftheInternationalSystemofUnits NISTSpecialPub814:InterpretationoftheSIfortheUnitedStatesandFederalGovernmentMetricConversionPolicy RulesforSAEUseofSI(Metric)Units InternationalSystemofUnitsatCurlie EngNetMetricConversionChartOnlineCategorisedMetricConversionCalculator History LaTeXSIunitspackagemanualgivesahistoricalbackgroundtotheSI. Research Themetrologicaltriangle RecommendationofICWM1(CI-2005) vteSIunitsBaseunits ampere candela kelvin kilogram metre mole second Derivedunitswithspecialnames becquerel coulomb degreeCelsius farad gray henry hertz joule katal lumen lux newton ohm pascal radian siemens sievert steradian tesla volt watt weber Otheracceptedunits astronomicalunit dalton day decibel degreeofarc electronvolt hectare hour litre minute minuteandsecondofarc neper tonne Seealso Conversionofunits Metricprefixes 2005–2019definition 2019redefinition Systemsofmeasurement Category vteSystemsofmeasurementCurrentGeneral InternationalSystemofUnits(SI) UKimperialsystem UScustomaryunits Specific Apothecaries' Avoirdupois Troy Astronomical Electrical EnglishEngineeringUnits(US) Natural Hartreeatomic Geometrised Lorentz–Heaviside Planck Quantumchromodynamical Stoney BackgroundMetric Overview Introduction Outline History Metrication UK/US Overview Comparison Foot–pound–second(FPS) HistoricMetric metre–kilogram–second(MKS) metre–tonne–second(MTS) centimetre–gram–second(CGS) gravitational Europe Byzantine Cornish Cypriot Czech Danish Dutch English Winchester Exchequer Estonian Finnish French Traditional Mesuresusuelles German Greek Hungarian Icelandic Irish Italian Latvian Luxembourgian Maltese Norwegian Ottoman Polish Portuguese Romanian Russian Scottish Serbian Slovak Spanish Swedish Swiss Welsh Asia Afghan Cambodian Chinese HongKong Indian Indonesian Japanese Korean Mongolian Myanmar Nepalese Omani Philippine Pegu Singaporean SriLankan Syrian Taiwanese Tatar Thai Vietnamese Africa Algerian Ethiopian Egyptian Eritrean Guinean Libyan Malagasy Mauritian Moroccan Seychellois Somali SouthAfrican Tunisian Tanzanian NorthAmerica CostaRican Cuban Haitian Honduran Mexican Nicaraguan PuertoRican SouthAmerica Argentine Bolivian Brazilian Chilean Colombian Paraguayan Peruvian Uruguayan Venezuelan Ancient Arabic BiblicalandTalmudic Egyptian Greek Hindu Indian Mesopotamian Persian Roman Listarticles Humorous Obsolete Unusual Other Absolutescale N-body Modulor AuthoritycontrolGeneral IntegratedAuthorityFile(Germany) Nationallibraries Spain France(data) UnitedStates Japan Other MicrosoftAcademic Portal:Physics Retrievedfrom"https://en.wikipedia.org/w/index.php?title=International_System_of_Units&oldid=1061985580" Categories:InternationalSystemofUnitsSystemsofunitsInternationalstandardsHiddencategories:ArticlescontainingFrench-languagetextArticlescontainingpotentiallydatedstatementsfromJanuary2021AllarticlescontainingpotentiallydatedstatementsArticlescontainingpotentiallydatedstatementsfromMay2020ArticlescontainingpotentiallydatedstatementsfromJanuary2020ArticlescontainingexplicitlycitedEnglish-languagetextCS1maint:unfitURLCS1maint:postscriptCS1German-languagesources(de)CS1French-languagesources(fr)CS1errors:missingperiodicalArticleswithshortdescriptionShortdescriptionisdifferentfromWikidataUseBritishEnglishfromMay2020UsedmydatesfromMay2020Allarticleswithspecificallymarkedweasel-wordedphrasesArticleswithspecificallymarkedweasel-wordedphrasesfromNovember2021CommonscategorylinkisonWikidataArticleswithCurlielinksArticleswithGNDidentifiersArticleswithBNEidentifiersArticleswithBNFidentifiersArticleswithLCCNidentifiersArticleswithNDLidentifiersArticleswithMAidentifiersGoodarticles Navigationmenu Personaltools NotloggedinTalkContributionsCreateaccountLogin Namespaces ArticleTalk Variants expanded collapsed Views ReadEditViewhistory More expanded collapsed Search Navigation MainpageContentsCurrenteventsRandomarticleAboutWikipediaContactusDonate Contribute HelpLearntoeditCommunityportalRecentchangesUploadfile Tools WhatlinkshereRelatedchangesUploadfileSpecialpagesPermanentlinkPageinformationCitethispageWikidataitem Print/export DownloadasPDFPrintableversion Inotherprojects WikimediaCommons Languages AfrikaansAlemannischАҧсшәаالعربيةAragonésԱրեւմտահայերէնঅসমীয়াAsturianuAzərbaycancaتۆرکجهবাংলাBân-lâm-gúБашҡортсаБеларускаяБеларуская(тарашкевіца)БългарскиBosanskiBrezhonegCatalàЧӑвашлаČeštinaCymraegDanskDeutschEestiΕλληνικάEspañolEsperantoEuskaraفارسیFijiHindiFøroysktFrançaisFryskFurlanGaeilgeGàidhligGalego贛語한국어Հայերենहिन्दीHrvatskiIdoIlokanoBahasaIndonesiaInterlinguaÍslenskaItalianoעבריתJawaಕನ್ನಡКъарачай-малкъарქართულიҚазақшаKiswahiliKreyòlayisyenKriyòlgwiyannenKurdîКыргызчаLatinaLatviešuLëtzebuergeschLietuviųLimburgsLa.lojban.LombardMagyarМакедонскиമലയാളംमराठीمصرىBahasaMelayuМонголမြန်မာဘာသာNederlandsनेपालीनेपालभाषा日本語NordfriiskNorskbokmålNorsknynorskOccitanOʻzbekcha/ўзбекчаਪੰਜਾਬੀپنجابیPatoisភាសាខ្មែរPlattdüütschPolskiPortuguêsRipoarischRomânăRunaSimiРусиньскыйРусскийSarduScotsSesothosaLeboaShqipSicilianuසිංහලSimpleEnglishSlovenčinaSlovenščinaСловѣньскъ/ⰔⰎⰑⰂⰡⰐⰠⰔⰍⰟSoomaaligaکوردیСрпски/srpskiSrpskohrvatski/српскохрватскиSundaSuomiSvenskaTagalogதமிழ்TarandíneТатарча/tatarçaతెలుగుไทยTürkçeТывадылУкраїнськаاردوVènetoTiếngViệt文言West-VlamsWinaray吴语ייִדישYorùbá粵語Žemaitėška中文 Editlinks