"SI" redirects here. For the chemical element with symbol Si, seeSilicon. For other uses, seeSI (disambiguation).
TheInternational System of Units, internationally known by the abbreviationSI (from FrenchSystème international d'unités), is the modern form of themetric system and the world's most widely usedsystem of measurement. It is the only system of measurement with official status in nearly every country in the world, employed in science, technology, industry, and everyday commerce. The SI system is coordinated by theInternational Bureau of Weights and Measures, which is abbreviated BIPM fromFrench:Bureau international des poids et mesures.
The seven base units and the 22 coherent derived units with special names and symbols may be used in combination to express other coherent derived units. Since the sizes of coherent units will be convenient for only some applications and not for others, the SI provides twenty-fourprefixes which, when added to the name and symbol of a coherent unit produce twenty-four additional (non-coherent) SI units for the same quantity; these non-coherent units are always decimal (i.e. power-of-ten) multiples and sub-multiples of the coherent unit.
The current way of defining the SI is a result of a decades-long move towards increasingly abstract and idealised formulation in which therealisations of the units are separated conceptually from the definitions. A consequence is that as science and technologies develop, new and superior realisations may be introduced without the need to redefine the unit. One problem with artefacts is that they can be lost, damaged, or changed; another is that they introduce uncertainties that cannot be reduced by advancements in science and technology.
The original motivation for the development of the SI was the diversity of units that had sprung up within thecentimetre–gram–second (CGS) systems (specifically the inconsistency between the systems ofelectrostatic units andelectromagnetic units) and the lack of coordination between the variousdisciplines that used them. The General Conference on Weights and Measures (French:Conférence générale des poids et mesures – CGPM), which was established by theMetre Convention of 1875, brought together many international organisations to establish the definitions and standards of a new system and to standardise the rules for writing and presenting measurements. The system was published in 1960 as a result of an initiative that began in 1948, and is based on themetre–kilogram–second system of units (MKS) combined with ideas from the development of the CGS system.
The International System of Units consists of a set of seven defining constants with seven corresponding base units, derived units, and a set of decimal-based multipliers that are used as prefixes.[1]: 125
The seven defining constants are the most fundamental feature of the definition of the system of units.[1]: 125 The magnitudes of all SI units are defined by declaring that seven constants have certain exact numerical values when expressed in terms of their SI units. These defining constants are thespeed of light in vacuumc, thehyperfine transition frequency of caesiumΔνCs, thePlanck constanth, theelementary chargee, theBoltzmann constantk, theAvogadro constantNA, and theluminous efficacyKcd. The nature of the defining constants ranges from fundamental constants of nature such asc to the purely technical constantKcd. The values assigned to these constants were fixed to ensure continuity with previous definitions of the base units.[1]: 128
The SI selects seven units to serve asbase units, corresponding to seven base physical quantities. They are thesecond, with the symbols, which is the SI unit of the physical quantity oftime; themetre, symbolm, the SI unit oflength;kilogram (kg, the unit ofmass);ampere (A,electric current);kelvin (K,thermodynamic temperature);mole (mol,amount of substance); andcandela (cd,luminous intensity).[1]The base units are defined in terms of the defining constants. For example, the kilogram is defined by taking the Planck constanth to be6.62607015×10−34 J⋅s, giving the expression in terms of the defining constants[1]: 131
1 kg =(299792458)2/(6.62607015×10−34)(9192631770)hΔνCs/c2.
All units in the SI can be expressed in terms of the base units, and the base units serve as a preferred set for expressing or analysing the relationships between units. The choice of which and even how many quantities to use as base quantities is not fundamental or even unique – it is a matter of convention.[1]: 126
The duration of9192631770 periods of the radiation corresponding to the transition between the twohyperfine levels of theground state of thecaesium-133 atom.
The kelvin is defined by setting the fixed numerical value of theBoltzmann constantk to1.380649×10−23 J⋅K−1, (J = kg⋅m2⋅s−2), given the definition of the kilogram, the metre, and the second.
The amount of substance of6.02214076×1023 elementary entities.[n 2] This number is the fixed numerical value of theAvogadro constant,NA, when expressed in the unit mol−1.
The luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency5.4×1014 hertz and that has a radiant intensity in that direction of1/683 watt persteradian.
Notes
^Despite the prefix "kilo-", the kilogram is the coherent base unit of mass, and is used in the definitions of derived units. Nonetheless, prefixes for the unit of mass are determined as if the gram were the base unit.
^When the mole is used, the elementary entities must be specified and may beatoms,molecules,ions,electrons, other particles, or specified groups of such particles.
The system allows for an unlimited number of additional units, calledderived units, which can always be represented as products of powers of the base units, possibly with a nontrivial numeric multiplier. When that multiplier is one, the unit is called acoherent derived unit. For example, the coherent derived SI unit ofvelocity is themetre per second, with the symbolm/s.[1]: 139 The base and coherent derived units of the SI together form a coherent system of units (the set of coherent SI units). A useful property of a coherent system is that when the numerical values of physical quantities are expressed in terms of the units of the system, then the equations between the numerical values have exactly the same form, including numerical factors, as the corresponding equations between the physical quantities.[3]: 6
Twenty-two coherent derived units have been provided with special names and symbols as shown in the table below. The radian and steradian have no base units but are treated as derived units for historical reasons.[1]: 137
The 22 SI derived units with special names and symbols[1]: 137
^abThe radian and steradian are defined as dimensionless derived units.
^abIn photometry, the steradian is usually retained in expressions for units.
The derived units in the SI are formed by powers, products, or quotients of the base units and are unlimited in number.[1]: 138 [4]: 14, 16
Arrangement of the principal measurements in physics based on the mathematical manipulation of length, time, and mass
Derived units apply to somederived quantities, which may by definition be expressed in terms ofbase quantities, and thus are not independent; for example,electrical conductance is the inverse ofelectrical resistance, with the consequence that the siemens is the inverse of the ohm, and similarly, the ohm and siemens can be replaced with a ratio of an ampere and a volt, because those quantities bear a defined relationship to each other.[b] Other useful derived quantities can be specified in terms of the SI base and derived units that have no named units in the SI, such as acceleration, which has the SI unit m/s2.[1]: 139
A combination of base and derived units may be used to express a derived unit. For example, the SI unit offorce is thenewton (N), the SI unit ofpressure is thepascal (Pa) – and the pascal can be defined as one newton per square metre (N/m2).[5]
Like all metric systems, the SI usesmetric prefixes to systematically construct, for the same physical quantity, a set of units that are decimal multiples of each other over a wide range. For example, driving distances are normally given inkilometres (symbolkm) rather than in metres. Here the metric prefix 'kilo-' (symbol 'k') stands for a factor of 1000; thus,1 km =1000 m.
The SI provides twenty-four metric prefixes that signify decimal powers ranging from 10−30 to 1030, the most recent being adopted in 2022.[1]: 143–144 [6][7][8] Most prefixes correspond to integer powers of 1000; the only ones that do not are those for 10, 1/10, 100, and 1/100.The conversion between different SI units for one and the same physical quantity is always through a power of ten. This is why the SI (and metric systems more generally) are calleddecimal systems of measurement units.[9]
The grouping formed by a prefix symbol attached to a unit symbol (e.g. 'km', 'cm') constitutes a new inseparable unit symbol. This new symbol can be raised to a positive or negative power. It can also be combined with other unit symbols to formcompound unit symbols.[1]: 143 For example,g/cm3 is an SI unit ofdensity, wherecm3 is to be interpreted as (cm)3.
Prefixes are added to unit names to produce multiples andsubmultiples of the original unit. All of these are integer powers of ten, and above a hundred or below a hundredth all are integer powers of a thousand. For example,kilo- denotes a multiple of a thousand andmilli- denotes a multiple of a thousandth, so there are one thousand millimetres to the metre and one thousand metres to the kilometre. The prefixes are never combined, so for example a millionth of a metre is amicrometre, not amillimillimetre. Multiples of the kilogram are named as if the gram were the base unit, so a millionth of a kilogram is amilligram, not amicrokilogram.[10]: 122 [11]: 14
The BIPM specifies 24 prefixes for the International System of Units (SI):
The base units and the derived units formed as the product of powers of the base units with a numerical factor of one form acoherent system of units. Every physical quantity has exactly one coherent SI unit. For example,1 m/s = (1 m) / (1 s) is the coherent derived unit for velocity.[1]: 139 With the exception of the kilogram (for which the prefix kilo- is required for a coherent unit), when prefixes are used with the coherent SI units, the resulting units are no longer coherent, because the prefix introduces a numerical factor other than one.[1]: 137 For example, the metre, kilometre, centimetre, nanometre, etc. are all SI units of length, though only the metre is acoherent SI unit. The complete set of SI units consists of both the coherent set and the multiples and sub-multiples of coherent units formed by using the SI prefixes.[1]: 138
The kilogram is the only coherent SI unit whose name and symbol include a prefix. For historical reasons, the names and symbols for multiples and sub-multiples of the unit of mass are formed as if thegram were the base unit. Prefix names and symbols are attached to the unit namegram and the unit symbol g respectively. For example,10−6 kg is writtenmilligram andmg, notmicrokilogram andμkg.[1]: 144
Several different quantities may share the same coherent SI unit. For example, the joule per kelvin (symbolJ/K) is the coherent SI unit for two distinct quantities:heat capacity andentropy; another example is the ampere, which is the coherent SI unit for bothelectric current andmagnetomotive force. This illustrates why it is important not to use the unit alone to specify the quantity. As theSI Brochure states,[1]: 140 "this applies not only to technical texts, but also, for example, to measuring instruments (i.e. the instrument read-out needs to indicate both the unit and the quantity measured)".
Furthermore, the same coherent SI unit may be a base unit in one context, but a coherent derived unit in another. For example, the ampere is a base unit when it is a unit of electric current, but a coherent derived unit when it is a unit of magnetomotive force.[1]: 140
Examples of coherent derived units in terms of base units[4]: 17
Example of lexical conventions. In the expression of acceleration due to gravity, a space separates the value and the units, both the 'm' and the 's' are lowercase because neither the metre nor the second are named after people, and exponentiation is represented with asuperscript '2'.
According to the SI Brochure,[1]: 148 unit names should be treated ascommon nouns of the context language. This means that they should be typeset in the same character set as other common nouns (e.g.Latin alphabet in English,Cyrillic script in Russian, etc.), following the usual grammatical andorthographical rules of the context language. For example, in English and French, even when the unit is named after a person and its symbol begins with a capital letter, the unit name in running text should start with a lowercase letter (e.g., newton, hertz, pascal) and iscapitalised only at the beginning of a sentence and inheadings and publication titles. As a nontrivial application of this rule, the SI Brochure notes[1]: 148 that the name of the unit with the symbol°C is correctly spelled as 'degreeCelsius': the first letter of the name of the unit, 'd', is in lowercase, while the modifier 'Celsius' is capitalised because it is a proper name.[1]: 148
The English spelling and even names for certain SI units, prefixes and non-SI units depend on the variety of English used.US English uses the spellingdeka-,meter, andliter, andInternational English usesdeca-,metre, andlitre. The name of the unit whose symbol is t and which is defined by1 t =103 kg is 'metric ton' in US English and 'tonne' in International English.[4]: iii
Symbols of SI units are intended to be unique and universal, independent of the context language.[10]: 130–135 The SI Brochure has specific rules for writing them.[10]: 130–135
In addition, the SI Brochure provides style conventions for among other aspects of displaying quantities units: the quantity symbols, formatting of numbers and the decimal marker, expressing measurement uncertainty, multiplication and division of quantity symbols, and the use of pure numbers and various angles.[1]: 147
In the United States, the guideline produced by theNational Institute of Standards and Technology (NIST)[11]: 37 clarifies language-specific details for American English that were left unclear by the SI Brochure, but is otherwise identical to the SI Brochure.[14] For example, since 1979, thelitre may exceptionally be written using either an uppercase "L" or a lowercase "l", a decision prompted by the similarity of the lowercase letter "l" to the numeral "1", especially with certain typefaces or English-style handwriting. NIST recommends that within the United States, "L" be used rather than "l".[11]
Metrologists carefully distinguish between the definition of a unit and its realisation. The SI units are defined by declaring that sevendefining constants[1]: 125–129 have certain exact numerical values when expressed in terms of their SI units. The realisation of the definition of a unit is the procedure by which the definition may be used to establish the value and associated uncertainty of a quantity of the same kind as the unit.[1]: 135
For each base unit the BIPM publishes amises en pratique, (French for 'putting into practice; implementation',[16]) describing the current best practical realisations of the unit.[17] The separation of the defining constants from the definitions of units means that improved measurements can be developed leading to changes in themises en pratique as science and technology develop, without having to revise the definitions.
The publishedmise en pratique is not the only way in which a base unit can be determined: the SI Brochure states that "any method consistent with the laws of physics could be used to realise any SI unit".[10]: 111 Various consultative committees of theCIPM decided in 2016 that more than onemise en pratique would be developed for determining the value of each unit.[18] These methods include the following:
At least three separate experiments be carried out yielding values having a relativestandard uncertainty in the determination of thekilogram of no more than5×10−8 and at least one of these values should be better than2×10−8. Both theKibble balance and theAvogadro project should be included in the experiments and any differences between these be reconciled.[19][20]
The definition of thekelvin measured with a relative uncertainty of theBoltzmann constant derived from two fundamentally different methods such as acoustic gasthermometry and dielectric constant gas thermometry be better than one part in10−6 and that these values be corroborated by other measurements.[21]
The International System of Units, or SI,[1]: 123 is adecimal andmetricsystem of units established in 1960 and periodically updated since then. The SI has anofficial status in most countries, includingthe United States,Canada, andthe United Kingdom, although these three countries are among the handful of nations that, to various degrees, also continue to use their customary systems. Nevertheless, with this nearly universal level of acceptance, the SI "has been used around the world as the preferred system of units, the basic language for science, technology, industry, and trade."[1]: 123, 126
The quantities and equations that provide the context in which the SI units are defined are now referred to as theInternational System of Quantities (ISQ).The ISQ is based on thequantities underlying each of theseven base units of the SI. Other quantities, such asarea,pressure, andelectrical resistance, are derived from these base quantities by clear, non-contradictory equations. The ISQ defines the quantities that are measured with the SI units.[23] The ISQ is formalised, in part, in the international standardISO/IEC 80000, which was completed in 2009 with the publication ofISO 80000-1,[24] and has largely been revised in 2019–2020.[25]
The SI is regulated and continually developed by three international organisations that were established in 1875 under the terms of theMetre Convention. They are theGeneral Conference on Weights and Measures (CGPM[c]),[26] the International Committee for Weights and Measures (CIPM[d]), and theInternational Bureau of Weights and Measures (BIPM[e]).All the decisions and recommendations concerning units are collected in a brochure calledThe International System of Units (SI),[1] which is published in French and English by the BIPM and periodically updated. The writing and maintenance of the brochure is carried out by one of the committees of the CIPM. The definitions of the terms "quantity", "unit", "dimension", etc. that are used in theSI Brochure are those given in theinternational vocabulary of metrology.[27] The brochure leaves some scope for local variations, particularly regarding unit names and terms in different languages. For example, the United States'National Institute of Standards and Technology (NIST) has produced a version of the CGPM document (NIST SP 330), which clarifies usage for English-language publications that useAmerican English.[4]
Closeup of the National Prototype Metre, serial number 27, allocated to the United States
The concept of a system of units emerged a hundred years before the SI.In the 1860s,James Clerk Maxwell,William Thomson (later Lord Kelvin), and others working under the auspices of theBritish Association for the Advancement of Science, building on previous work ofCarl Gauss, developed thecentimetre–gram–second system of units or cgs system in 1874. The systems formalised the concept of a collection of related units called acoherent system of units. In a coherent system,base units combine to definederived units without extra factors.[4]: 2 For example, using metre per second is coherent in a system that uses metre for length and second for time, but kilometre per hour is not coherent. The principle of coherence was successfully used to define a number of units of measure based on the CGS, including theerg forenergy, thedyne forforce, thebarye forpressure, thepoise fordynamic viscosity and thestokes forkinematic viscosity.[29]
A French-inspired initiative for international cooperation inmetrology led to the signing in 1875 of theMetre Convention, also called Treaty of the Metre, by 17 nations.[f][30]: 353–354 TheGeneral Conference on Weights and Measures (French:Conférence générale des poids et mesures – CGPM), which was established by the Metre Convention,[29] brought together many international organisations to establish the definitions and standards of a new system and to standardise the rules for writing and presenting measurements.[31]: 37 [32] Initially the convention only covered standards for the metre and the kilogram. This became the foundation of the MKS system of units.[4]: 2
Giovanni Giorgi and the problem of electrical units
At the close of the 19th century three different systems of units of measure existed for electrical measurements: aCGS-based system for electrostatic units, also known as the Gaussian or ESU system, aCGS-based system for electromechanical units (EMU), and an International system based on units defined by the Metre Convention[33] for electrical distribution systems. Attempts to resolve the electrical units in terms of length, mass, and time usingdimensional analysis was beset with difficulties – the dimensions depended on whether one used the ESU or EMU systems.[34] This anomaly was resolved in 1901 whenGiovanni Giorgi published a paper in which he advocated using a fourth base unit alongside the existing three base units. The fourth unit could be chosen to beelectric current,voltage, orelectrical resistance.[35]
Electric current with named unit 'ampere' was chosen as the base unit, and the other electrical quantities derived from it according to the laws of physics. When combined with the MKS the new system, known as MKSA, was approved in 1946.[4]
In 1948, the 9th CGPM commissioned a study to assess the measurement needs of the scientific, technical, and educational communities and "to make recommendations for a single practical system of units of measurement, suitable for adoption by all countries adhering to the Metre Convention".[36] This working document wasPractical system of units of measurement. Based on this study, the 10th CGPM in 1954 defined an international system derived six base units: the metre, kilogram, second, ampere, degree Kelvin, and candela.
The 9th CGPM also approved the first formal recommendation for the writing of symbols in the metric system when the basis of the rules as they are now known was laid down.[37] These rules were subsequently extended and now cover unit symbols and names, prefix symbols and names, how quantity symbols should be written and used, and how the values of quantities should be expressed.[10]: 104, 130
The 10th CGPM in 1954 resolved to create an international system of units[31]: 41 and in 1960, the 11th CGPM adopted theInternational System of Units, abbreviated SI from the French nameLe Système international d'unités, which included a specification for units of measurement.[10]: 110
Reverse dependencies of the SI base units on sevenphysical constants, which are assigned exact numerical values in the2019 redefinition. Unlike in the previous definitions, the base units are all derived exclusively from constants of nature. Here, means that is used to define.
After themetre was redefined in 1960, theInternational Prototype of the Kilogram (IPK) was the only physical artefact upon which base units (directly the kilogram and indirectly the ampere, mole and candela) depended for their definition, making these units subject to periodic comparisons of national standard kilograms with the IPK.[38] During the 2nd and 3rd Periodic Verification of National Prototypes of the Kilogram, a significant divergence had occurred between the mass of the IPK and all of its official copies stored around the world: the copies had all noticeably increased in mass with respect to the IPK. Duringextraordinary verifications carried out in 2014 preparatory to redefinition of metric standards, continuing divergence was not confirmed. Nonetheless, the residual and irreducible instability of a physical IPK undermined the reliability of the entire metric system to precision measurement from small (atomic) to large (astrophysical) scales.[39]By avoiding the use of an artefact to define units, all issues with the loss, damage, and change of the artefact are avoided.[1]: 125
The current definitions of the kilogram, ampere, kelvin, and mole be revised
The wording of base unit definitions should change emphasis from explicit unit to explicit constant definitions.
The new definitions were adopted at the 26th CGPM on 16 November 2018, and came into effect on 20 May 2019.[41] The change was adopted by the European Union through Directive (EU) 2019/1258.[42]
Prior to its redefinition in 2019, the SI was defined through the seven base units from which the derived units were constructed as products of powers of the base units. After the redefinition, the SI is defined by fixing the numerical values of seven defining constants. This has the effect that the distinction between the base units and derived units is, in principle, not needed, since all units, base as well as derived, may be constructed directly from the defining constants. Nevertheless, the distinction is retained because "it is useful and historically well established", and also because theISO/IEC 80000 series of standards, which define theInternational System of Quantities (ISQ), specifies base and derived quantities that necessarily have the corresponding SI units.[1]: 129
While not an SI-unit, the litre may be used with SI units. It is equivalent to(10 cm)3 = (1 dm)3 =10−3 m3.
Many non-SI units continue to be used in the scientific, technical, and commercial literature. Some units are deeply embedded in history and culture, and their use has not been entirely replaced by their SI alternatives. The CIPM recognised and acknowledged such traditions by compiling a list of non-SI units accepted for use with SI,[10] including the hour, minute, degree of angle, litre, and decibel.
This is a list of units that are not defined as part of theInternational System of Units (SI) but are otherwise mentioned in the SI Brochure,[43] listed as being accepted for use alongside SI units, or for explanatory purposes.
The SI prefixes can be used with several of these units, but not, for example, with the non-SI units of time. Others, in order to be converted to the corresponding SI unit, require conversion factors that are not powers of ten. Some common examples of such units are the customary units of time, namely the minute (conversion factor of60 s/min, since1 min =60 s), the hour (3600 s), and the day (86400 s); the degree (for measuring plane angles,1° =(π /180) rad); and theelectronvolt (a unit of energy,1 eV =1.602176634×10−19 J).[43]
Although the termmetric system is often used as an informal alternative name for the International System of Units,[46] other metric systems exist, some of which were in widespread use in the past or are even still used in particular areas. There are also individualmetric units such as thesverdrup and thedarcy that exist outside of any system of units. Most of the units of the other metric systems are not recognised by the SI.
Sometimes, SI unit name variations are introduced, mixing information about the corresponding physical quantity or the conditions of its measurement; however, this practice is unacceptable with the SI. "Unacceptability of mixing information with units: When one gives the value of a quantity, any information concerning the quantity or its conditions of measurement must be presented in such a way as not to be associated with the unit."[10]Instances include: "watt-peak" and "watt RMS"; "geopotential metre" and "vertical metre"; "standard cubic metre"; "atomic second", "ephemeris second", and "sidereal second".
^Electric potential difference is also called "voltage" in many countries, as well as "electric tension" or simply "tension" in some countries.
^Ohm's law:1 Ω = 1 V/A from the relationshipE =I ×R, whereE is electromotive force or voltage (unit: volt),I is current (unit: ampere), andR is resistance (unit: ohm).
^FromFrench:Conférence générale des poids et mesures.
^fromFrench:Comité international des poids et mesures
^fromFrench:Bureau international des poids et mesures
^Argentina, Austria-Hungary, Belgium, Brazil, Denmark, France, German Empire, Italy, Peru, Portugal, Russia, Spain, Sweden and Norway, Switzerland, Ottoman Empire, United States, and Venezuela.
^A footnote in the 9th SI Brochure gives an exact definition of the dalton.
Attribution
[1] This article incorporatestext from this source, which is available under theCC BY 3.0 license.
^"1.16"(PDF).International vocabulary of metrology – Basic and general concepts and associated terms (VIM) (3rd ed.). International Bureau of Weights and Measures (BIPM): Joint Committee for Guides in Metrology. 2012. Retrieved28 March 2015.
^S. V. Gupta,Units of Measurement: Past, Present and Future. International System of Units, p. 16, Springer, 2009.ISBN3642007384.
^"Amtliche Maßeinheiten in Europa 1842" [Official units of measure in Europe 1842].spasslernen (in German). 1 May 2009. Archived fromthe original on 25 September 2012. Retrieved26 March 2011. Text version of Malaisé's book:Malaisé, Ferdinand von (1842).Theoretisch-practischer Unterricht im Rechnen [Theoretical and practical instruction in arithmetic] (in German). München: Verlag des Verf. pp. 307–322. Retrieved7 January 2013.
^Quinn, Terry J. (2012).From artefacts to atoms: the BIPM and the search for ultimate measurement standards. New York Oxford: Oxford University Press.ISBN978-0-19-530786-3.
^Wood, B. (3–4 November 2014)."Report on the Meeting of the CODATA Task Group on Fundamental Constants"(PDF).BIPM. p. 7.[BIPM director Martin] Milton responded to a question about what would happen if ... the CIPM or the CGPM voted not to move forward with the redefinition of the SI. He responded that he felt that by that time the decision to move forward should be seen as a foregone conclusion.
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