SI units - NPL - National Physical Laboratory

The globally-agreed system of measurement units was formally named the 'International System of Units' (SI) in 1960. The SI covers units for every type of ... 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Findoutmore Home Resources SIunits Resources SIunits TheSIbaseunits Theglobally-agreedsystemofmeasurementunitswasformallynamedthe'InternationalSystemofUnits'(SI)in1960.TheSIcoversunitsforeverytypeofmeasurement,butattheheartoftheSIisasetofsevenunitsknownasthe‘baseunits’. kilogram(kg) Unitofmass metre(m) Unitoflength second(s) Unitoftime ampere(A) Unitofelectriccurrent kelvin(K) Unitofthermodynamictemperature mole(mol) Unitofamountofsubstance candela(cd) Unitofluminousintensity ThisInternationalSystemofUnitsisnecessarytoensurethatoureverydaymeasurements remaincomparableandconsistentworldwide.Standardisingsuchmeasurementsnotonlyhelpstokeepthemconsistentandaccurate,butalsohelpssocietyhaveconfidenceininformation.Forinstance,massismeasuredeveryday,andhavingagreementonthedefinitionofthekilogrammeans thatconsumerscantrustthattheshopisreallyprovidingthemasstheysaytheyare.Equally,havingreliableinformationonclimatechange,pollutionandmedicaldiagnosticsisimportanttosocietyandbuildstrustandallowseffectivedecisionstobemade. Findoutmoreabouttheredefinitionofthe SIunits Howaretheunitsofmeasurementdefined? Historically,unitsofmeasurementweredefinedbyphysicalobjectsorpropertiesofmaterials.Forexample,themetrewasdefinedbythelengthbetweenlinesengravedonametalbarandthekilogramwasdefinedasthemassofasinglecylinderofplatinum-iridiummetal–theInternationalPrototypeoftheKilogram(IPK). Inthesetwoexamples,thedefinitionwasalsotherealisation–thephysicalform–oftheunit.However,thesephysicalrepresentationscanchangeovertimeandaresusceptibletodamageorloss.So,overtheyears,thedefinitionshaveevolvedtodependonconstantsof naturethataremorestableandreproducible,andtomeettheneedsoftoday’sresearchandtechnologicalapplications. Duringthelastcentury,scientistsmeasuredconstantsofnature,suchasthespeedoflightandthePlanckconstant,withincreasingaccuracy.Theydiscoveredthattheseweremorestablethanphysicalobjects.ItbecameclearthattheseconstantsofnaturecouldofferanewandmorestablefoundationfortheSI. FindoutaboutourcurrentresearchonSIunits WewelcometheopportunitytodelivertechnicallecturesonmetrologyandSIunitsatuniversitiesandotherorganisations,pleasecontactustodiscussyourrequirements. SIderivedunits Derivedunitsareunitswhichmaybeexpressedintermsofbaseunitsbymeansofmathematicalsymbolsofmultiplicationanddivision. Certainderivedunitshavebeengivenspecialnamesandsymbols,andthesespecialnamesandsymbolsmaythemselvesbeusedincombinationwiththeSIandotherderivedunitstoexpresstheunitsofotherquantities. ExamplesofSIderivedunitsexpressedintermsofbaseunits DerivedQuantity SIderivedunit   Name Symbol area squaremetre m2 volume cubicmetre m3 speed,velocity metrepersecond m/s acceleration metrepersecondsquared m/s2 wavenumber 1permetre m-1 density,massdensity kilogrampercubicmetre kg/m3 specificvolume cubicmetreperkilogram m3/kg currentdensity amperepersquaremetre A/m2 magneticfieldstrength amperepermetre A/m concentration (ofamountofsubstance) molepercubicmetre mol/m3 luminance candelapersquaremetre cd/m2 refractiveindex (thenumber)one 1(a) (a)Thesymbol'1'isgenerallyomittedincombinationwithanumericalvalue. SIprefixes SIprefixesareusedtoformdecimalmultiplesandsubmultiplesofSIunits. Theyshouldbeusedtoavoidverylargeorverysmallnumericvalues. Theprefixattachesdirectlytothenameofaunit,andaprefixsymbolattachesdirectlytothesymbolforaunit. MultiplyingFactor SIPrefix ScientificNotation 1000000000000000000000000 yotta(Y) 1024 1000000000000000000000 zetta(Z) 1021 1000000000000000000 exa(E) 1018 1000000000000000 peta(P) 1015 1000000000000 tera(T) 1012 1000000000 giga(G) 109 1000000 mega(M) 106 1000 kilo(k) 103 100 hecto(h) 102 10 deca(da) 101 1   100 0.1 deci(d) 10-1 0.01 centi(c) 10-2 0.001 milli(m) 10-3 0.000001 micro(µ) 10-6 0.000000001 nano(n) 10-9 0.000000000001 pico(p) 10-12 0.000000000000001 femto(f) 10-15 0.000000000000000001 atto(a) 10-18 0.000000000000000000001 zepto(z) 10-21 0.000000000000000000000001 yocto(y) 10-24 SIconventions ThefollowingisalistofthekeyrecommendationswhenusingSIunits: Writingunitnamesandsymbols OnlyunitsoftheSIandthoseunitsrecognisedforusewiththeSIshouldbeusedtoexpressthevaluesofquantities. Allunitnamesarewritteninsmallletters(newtonorkilogram)exceptCelsius. Theunitsymbolisinlowercaseunlessthenameoftheunitisderivedfromapropername,inwhichcasethefirstletterofthesymbolisinuppercase. Unitsymbolsareunalteredintheplural. Unitsymbolsandunitnamesshouldnotbemixed. Abbreviationssuchassec(foreithersorsecond)ormps(foreitherm/sormetre persecond)arenotallowed. Forunitvaluesmorethan1orlessthan-1thepluraloftheunitisusedandasingularunitisusedforvaluesbetween1and-1. Aspaceisleftbetweenthenumericalvalueandunitsymbol(25kg,butnot25-kgor25kg).Ifthespelled-outnameofaunitisused,thenormalrulesofEnglishareapplied. Unitsymbolsareinromantype,andquantitysymbolsareinitalictypewithsuperscriptsandsubscriptsinromanoritalictypeasappropriate. Numericalnotation Aspaceshouldbeleftbetweengroupsof3digitsoneithertherightorlefthandsideofthedecimalplace(15739.01253).Infourdigitnumbersthespacemaybeomitted.Commasshouldnotbeused. Thedecimalmarkershallbeeitherthepointonthelineorthecommaontheline.Thedecimalmarkerchosenshouldbethatwhichiscustomaryinthecontextconcerned. Mathematicaloperationsshouldonlybeappliedtounitsymbols(kg/m2)andnotunitnames(kilogram/cubicmetre). Valuesofquantitiesshouldbeexpressedas2.0µsor2.0×10-6andnotintermssuchaspartspermillion. Itshouldbecleartowhichunitsymbolanumericalvaluebelongsandwhichmathematicaloperationappliestothevalueofa quantity(35cm×48cm,not35×48cm;or100g±2g,not100±2g). Thevaluemustapplytothewholesymbolandnotanyparticularunitwithinthesymbol. Non-SIunits Therearecertainunits,whichareacceptedforusewiththeSI.Itincludesunitswhichareincontinuouseverydayuse,inparticularthetraditionalunitsoftimeandofangle,togetherwithafewotherunitswhichhaveassumedincreasingtechnicalimportance. TherearealsounitswhicharecurrentlyacceptedforusewiththeSItosatisfytheneedsofcommercial,legalandspecialistscientificinterestsorareimportantfortheinterpretationofoldertexts. Non-SIunitsacceptedforusewiththeInternationalSystem Name Symbol ValueinSIUnits minute min 1min=60s hour(1) h 1h=60min=3600s day d 1d=24h=86400s degreeofarc(2) ° 1°=(π/180)rad minuteofarc ′ 1′=(1/60)°=(π/10800)rad secondofarc ″ 1″=(1/60)'=(π/648000)rad litre(3) l,L 1l=1dm3=10-3m3 tonne(4,5) t 1t=103kg neper(6,8) Np 1Np=1 bel(7,8) B 1B=(1/2)ln10(Np)(9) Notes ThesymbolofthisunitisincludedinResolution7ofthe9thCGPM(1948;CR,70). ISO31recommendsthatthedegreebesubdivideddecimallyratherthanusingtheminuteandsecond. ThisunitandthesymbollwereadoptedbyCIPMin1879(PV,1879,41).Thealternativesymbol,L,wasadoptedbythe16thCGPM(1979,Resolution6;CR,101andMetrologia,1980,16,56-57)inordertoavoidtheriskofconfusionbetweentheletterlandthenumber1.ThepresentdefinitionofthelitreisgiveninResolution6ofthe12thCGPM(1964;CR,93). ThisunitanditssymbolwereadoptedbytheCIPMin1879(PV,1879,41). InsomeEnglish-speakingcountriesthisiscalled'metricton'. Theneperisusedtoexpressvaluesofsuchlogarithmicquantitiesasfieldlevel,powerlevel,soundpressurelevel,andlogarithmicdecrement.Naturallogarithmsareusedtoobtainthenumericalvaluesofquantitiesexpressedinnepers.TheneperiscoherentwiththeSI,butnotyetadoptedbytheCGPMasanSIunit.ForfurtherinformationseeInternationalStandardISO31. Thebelisusedtoexpressvaluesofsuchlogarithmicquantitiesasfieldlevel,powerlevel,soundpressurelevel,andattenuation.Logarithmstobasetenareusedtoobtainthenumericalvaluesofquantitiesexpressedinbels.Thesubmultipledecibel,dB,iscommonlyused.ForfurtherinformationseeInternationalStandardISO31. Inusingtheseunitsitisparticularlyimportantthatthequantitybespecified.Theunitmustnotbeusedtoimplythequantity. Npisenclosedinparenthesesbecause,althoughtheneperiscoherentwiththeSI,ithasnotyetbeenadoptedbytheCGPM. Definingconstants Since20May2019,theSIunitshavebeen definedintermsofconstantsofnature, inwhich: theunperturbedgroundstatehyperfinetransitionfrequencyofthecaesium-133atomΔν is9192631770hertz,alsoknownasthe'Csfrequency' thespeedoflightinvacuum c isexactly299792458metrespersecond thePlanckconstant h isexactly6.62607015×10–34 jouleseconds theelementarycharge e isexactly1.602176634× 10–19 coulombs theBoltzmannconstant k isexactly1.380649×10–23 joulesperkelvin theAvogadroconstant NA isexactly6.02214076×1023 reciprocalmoles theluminousefficacyofmonochromaticradiationoffrequency540 ×1012 hertz Kcd,isexactly683lumensperwatt