The International System of Units, internationally known by the abbreviation SI (from French French: Système international d'unités), is the modern form of the metric system and the world's most widely used system of measurement. Coordinated by the International Bureau of Weights and Measures (abbreviated BIPM from French: Bureau international des poids et mesures) 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.
| Name | Quantity | ||
|---|---|---|---|
| s | |||
| m | |||
| kg | |||
| A | |||
| K | |||
| mol | |||
| cd | candela |
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-four prefixes 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 the realisations 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 the centimetre–gram–second (CGS) systems (specifically the inconsistency between the systems of electrostatic units and electromagnetic units) and the lack of coordination between the various disciplines that used them. The General Conference on Weights and Measures (French: French: Conférence générale des poids et mesures – CGPM), which was established by the Metre 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 the metre–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 defining constants with corresponding base units, derived units, and a set of decimal-based multipliers that are used as prefixes.
| Defining constant | Exact value | ||
|---|---|---|---|
| luminous efficacy of radiation |
See main article: SI base unit.
The SI selects seven units to serve as base units, corresponding to seven base physical quantities. They are the second, with the symbol, which is the SI unit of the physical quantity of time; the metre, symbol, the SI unit of length; kilogram (the unit of mass); ampere (electric current); kelvin (thermodynamic temperature); mole (amount of substance); and candela (luminous intensity).The base units are defined in terms of the defining constants. For example, the kilogram is defined by taking the Planck constant to be, giving the expression in terms of the defining constants
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.
| Unit name | Unit symbol | Typical symbols | Definition | |||
|---|---|---|---|---|---|---|
| s | T | t | The duration of periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom. | |||
| m | L | l x r | The distance travelled by light in vacuum in second. | |||
| kilogram[1] | kg | M | m | The kilogram is defined by setting the Planck constant to, given the definitions of the metre and the second.[2] | ||
| A | I | I, i | The flow of times the elementary charge per second, which is approximately elementary charges per second. | |||
| K | \Theta | T | The kelvin is defined by setting the fixed numerical value of the Boltzmann constant to,, given the definition of the kilogram, the metre, and the second. | |||
| mol | N | n | The amount of substance of elementary entities.[3] This number is the fixed numerical value of the Avogadro constant,, when expressed in the unit mol−1. | |||
| cd | J | I\rm | The luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency and that has a radiant intensity in that direction of watt per steradian. | |||
| ||||||
See main article: SI derived unit. The system allows for an unlimited number of additional units, called derived 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 a coherent derived unit. For example, the coherent derived SI unit unit of velocity is the metre per second, with the symbol . 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.[4]
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.
| Name | Symbol | Quantity | In SI base units | In other SI units | |
|---|---|---|---|---|---|
| radian[5] | rad | plane angle | m/m | 1 | |
| steradian | sr | solid angle | 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 = J/m3 | |
| joule | J | energy, work, heat | kg⋅m2⋅s−2 | N⋅m = Pa⋅m3 | |
| watt | W | power, radiant flux | kg⋅m2⋅s−3 | J/s | |
| coulomb | C | electric charge | s⋅A | ||
| volt | V | electric potential, 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 | electrical conductance | kg−1⋅m−2⋅s3⋅A2 | Ω−1 | |
| weber | Wb | magnetic flux | kg⋅m2⋅s−2⋅A−1 | V⋅s | |
| tesla | T | magnetic flux density | kg⋅s−2⋅A−1 | Wb/m2 | |
| henry | H | inductance | kg⋅m2⋅s−2⋅A−2 | Wb/A | |
| degree Celsius | °C | temperature relative to 273.15 K | K | ||
| lumen | lm | luminous flux | cd⋅m2/m2 | cd⋅sr | |
| lux | lx | illuminance | cd⋅m2/m4 | lm/m2 = cd⋅sr⋅m−2 | |
| becquerel | Bq | activity referred to a radionuclide (decays per unit time) | s−1 | ||
| gray | Gy | absorbed dose (of ionising radiation) | m2⋅s−2 | J/kg | |
| sievert | Sv | equivalent dose (of ionising radiation) | m2⋅s−2 | J/kg | |
| katal | kat < | -- Note: this is the last row, there are exactly 22 in the ref --> | catalytic activity | mol⋅s−1 | |
| Notes | |||||
The derived units in the SI are formed by powers, products, or quotients of the base units and are potentially unlimited in number.
Derived units apply to some derived quantities, which may by definition be expressed in terms of base quantities, and thus are not independent; for example, electrical conductance is the inverse of electrical 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. 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.
A combination of base and derived units may be used to express a derived unit. For example, the SI unit of force is the newton (N), the SI unit of pressure is the pascal (Pa) – and the pascal can be defined as one newton per square metre (N/m2).[6]
See main article: Metric prefix.
Like all metric systems, the SI uses metric 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 in kilometres (symbol) rather than in metres. Here the metric prefix 'kilo-' (symbol 'k') stands for a factor of 1000; thus, = .
The current version of the SI provides twenty-four metric prefixes that signify decimal powers ranging from 10−30 to 1030, the most recent being adopted in 2022.[7] [8] [9] 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 called decimal systems of measurement units.[10]
The grouping formed by a prefix symbol attached to a unit symbol (e.g. '', '') 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 form compound unit symbols. For example, is an SI unit of density, where is to be interpreted as .
Prefixes are added to unit names to produce multiples and submultiples 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 and milli- 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 a micrometre, not a millimillimetre. Multiples of the kilogram are named as if the gram were the base unit, so a millionth of a kilogram is a milligram, not a microkilogram.
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 a coherent system of units. Every physical quantity has exactly one coherent SI unit. For example, is the coherent derived unit for velocity. 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. For example, the metre, kilometre, centimetre, nanometre, etc. are all SI units of length, though only the metre is a 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.
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 the gram were the base unit. Prefix names and symbols are attached to the unit name gram and the unit symbol g respectively. For example, is written milligram and, not microkilogram and .
Several different quantities may share the same coherent SI unit. For example, the joule per kelvin (symbol) is the coherent SI unit for two distinct quantities: heat capacity and entropy; another example is the ampere, which is the coherent SI unit for both electric current and magnetomotive force. This illustrates why it is important not to use the unit alone to specify the quantity. As the SI Brochure states, "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.
| Name | Symbol | Derived quantity | Typical symbol | |
|---|---|---|---|---|
| square metre | area | |||
| cubic metre | volume | |||
| metre per second | speed, velocity | |||
| metre per second squared | acceleration | |||
| reciprocal metre | wavenumber | , | ||
| vergence (optics) | , 1/ | |||
| kilogram per cubic metre | density | |||
| kilogram per square metre | surface density | |||
| cubic metre per kilogram | specific volume | |||
| ampere per square metre | current density | |||
| ampere per metre | magnetic field strength | |||
| mole per cubic metre | concentration | |||
| kilogram per cubic metre | mass concentration | , | ||
| candela per square metre | luminance |
| Name | Symbol | Quantity | In SI base units | |
|---|---|---|---|---|
| pascal-second | Pa⋅s | dynamic viscosity | m−1⋅kg⋅s−1 | |
| newton-metre | N⋅m | moment of force | m2⋅kg⋅s−2 | |
| newton per metre | N/m | surface tension | kg⋅s−2 | |
| radian per second | rad/s | angular velocity, angular frequency | s−1 | |
| radian per second squared | rad/s2 | angular acceleration | s−2 | |
| watt per square metre | W/m2 | heat flux density, irradiance | kg⋅s−3 | |
| joule per kelvin | J/K | entropy, heat capacity | m2⋅kg⋅s−2⋅K−1 | |
| joule per kilogram-kelvin | J/(kg⋅K) | specific heat capacity, specific entropy | m2⋅s−2⋅K−1 | |
| joule per kilogram | J/kg | specific energy | m2⋅s−2 | |
| watt per metre-kelvin | W/(m⋅K) | thermal conductivity | m⋅kg⋅s−3⋅K−1 | |
| joule per cubic metre | J/m3 | energy density | m−1⋅kg⋅s−2 | |
| volt per metre | V/m | electric field strength | m⋅kg⋅s−3⋅A−1 | |
| coulomb per cubic metre | C/m3 | electric charge density | m−3⋅s⋅A | |
| coulomb per square metre | C/m2 | surface charge density, electric flux density, electric displacement | m−2⋅s⋅A | |
| farad per metre | F/m | permittivity | m−3⋅kg−1⋅s4⋅A2 | |
| henry per metre | H/m | permeability | m⋅kg⋅s−2⋅A−2 | |
| joule per mole | J/mol | molar energy | m2⋅kg⋅s−2⋅mol−1 | |
| joule per mole-kelvin | J/(mol⋅K) | molar entropy, molar heat capacity | m2⋅kg⋅s−2⋅K−1⋅mol−1 | |
| coulomb per kilogram | C/kg | exposure (x- and γ-rays) | kg−1⋅s⋅A | |
| gray per second | Gy/s | absorbed dose rate | m2⋅s−3 | |
| watt per steradian | W/sr | radiant intensity | m2⋅kg⋅s−3 | |
| watt per square metre-steradian | W/(m2⋅sr) | radiance | kg⋅s−3 | |
| katal per cubic metre | kat/m3 | catalytic activity concentration | m−3⋅s−1⋅mol |
According to the SI Brochure, unit names should be treated as common 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 and orthographical 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 is capitalised only at the beginning of a sentence and in headings and publication titles. As a nontrivial application of this rule, the SI Brochure notes that the name of the unit with the symbol is correctly spelled as 'degree Celsius': 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.
The English spelling and even names for certain SI units and metric prefixes depend on the variety of English used. US English uses the spelling deka-, meter, and liter, and International English uses deca-, metre, and litre. The name of the unit whose symbol is t and which is defined according to is 'metric ton' in US English and 'tonne' in International English.
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.
In the United States, the guideline produced by the National Institute of Standards and Technology (NIST)[11] clarifies language-specific details for American English that were left unclear by the SI Brochure, but is otherwise identical to the SI Brochure.[12] For example, since 1979, the litre 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. The American NIST recommends that within the United States "L" be used rather than "l".
See main article: Realisation (metrology). Metrologists carefully distinguish between the definition of a unit and its realisation. The SI units are defined by declaring that seven defining constants 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.
For each base unit the BIPM publishes a French: mises en pratique, (French for 'putting into practice; implementation',[13]) describing the current best practical realisations of the unit.[14] The separation of the defining constants from the definitions of units means that improved measurements can be developed leading to changes in the French: mises en pratique as science and technology develop, without having to revise the definitions.
The published French: mise 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". Various consultative committees of the CIPM decided in 2016 that more than one French: mise en pratique would be developed for determining the value of each unit.[15] These methods include the following:
The International System of Units, or SI, is a decimal and metric system of units established in 1960 and periodically updated since then. The SI has an official status in most countries, including the United States, Canada, and the 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."
The only other types of measurement system that still have widespread use across the world are the imperial and US customary measurement systems. The international yard and pound are defined in terms of the SI.[19]
See main article: International System of Quantities. The quantities and equations that provide the context in which the SI units are defined are now referred to as the International System of Quantities (ISQ).The ISQ is based on the quantities underlying each of the seven base units of the SI. Other quantities, such as area, pressure, and electrical resistance, are derived from these base quantities by clear, non-contradictory equations. The ISQ defines the quantities that are measured with the SI units.[20] The ISQ is formalised, in part, in the international standard ISO/IEC 80000, which was completed in 2009 with the publication of ISO 80000-1,[21] and has largely been revised in 2019–2020.[22]
See main article: General Conference on Weights and Measures and International Bureau of Weights and Measures. The SI is regulated and continually developed by three international organisations that were established in 1875 under the terms of the Metre Convention. They are the General Conference on Weights and Measures (CGPM),[23] the International Committee for Weights and Measures (CIPM), and the International Bureau of Weights and Measures (BIPM).All the decisions and recommendations concerning units are collected in a brochure called The International System of Units (SI), 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 the SI Brochure are those given in the international vocabulary of metrology.[24] 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 use American English.[25]
See also: CGS system of units.
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 the British Association for the Advancement of Science, building on previous work of Carl Gauss, developed the centimetre–gram–second system of units or cgs system in 1874. The systems formalised the concept of a collection of related units called a coherent system of units. In a coherent system, base units combine to define derived units without extra factors.[25] For example, using meters per second is coherent in a system that uses meter for length and seconds 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 the erg for energy, the dyne for force, the barye for pressure, the poise for dynamic viscosity and the stokes for kinematic viscosity.[26]
See main article: Metre Convention and MKS system of units. A French-inspired initiative for international cooperation in metrology led to the signing in 1875 of the Metre Convention, also called Treaty of the Metre, by 17 nations.[27] The General Conference on Weights and Measures (French: French: Conférence générale des poids et mesures – CGPM), which was established by the Metre Convention,[28] 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.[29] Initially the convention only covered standards for the metre and the kilogram. This became the foundation of the MKS system of units.[25]
At the close of the 19th century three different systems of units of measure existed for electrical measurements: a CGS-based system for electrostatic units, also known as the Gaussian or ESU system, a CGS-based system for electromechanical units (EMU), and an International system based on units defined by the Metre Convention[30] for electrical distribution systems.Attempts to resolve the electrical units in terms of length, mass, and time using dimensional analysis was beset with difficulties – the dimensions depended on whether one used the ESU or EMU systems.[31] This anomaly was resolved in 1901 when Giovanni 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 be electric current, voltage, or electrical resistance.[32]
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.[25]
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".[33] This working document was Practical 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.[34] 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.
The 10th CGPM in 1954 resolved to create an international system of units[35] andin 1960, the 11th CGPM adopted the International System of Units, abbreviated SI from the French name French: Le Système international d'unités, which included a specification for units of measurement.
The International Bureau of Weights and Measures (BIPM) has described SI as "the modern form of metric system". In 1971 the mole became the seventh base unit of the SI.[25]
See main article: 2019 redefinition of the SI base units.
After the metre was redefined in 1960, the International 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.[36] 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. During extraordinary 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.[37] By avoiding the use of an artifact to define units, all issues with the loss, damage, and change of the artifact are avoided.
A proposal was made that:[38]
The new definitions were adopted at the 26th CGPM on 16 November 2018, and came into effect on 20 May 2019.[39] The change was adopted by the European Union through Directive (EU) 2019/1258.[40]
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 the ISO/IEC 80000 series of standards, which define the International System of Quantities (ISQ), specifies base and derived quantities that necessarily have the corresponding SI units.
See main article: Non-SI units mentioned in the SI.
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, including the hour, minute, degree of angle, litre, and decibel.
See main article: List of metric units. Although the term metric system is often used as an informal alternative name for the International System of Units,[41] 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 individual metric units such as the sverdrup and the darcy 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."Instances include: "watt-peak" and "watt RMS"; "geopotential metre" and "vertical metre"; "standard cubic metre"; "atomic second", "ephemeris second", and "sidereal second".