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The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form41
/sup> of the
metric system The metric system is a that succeeded the decimalised system based on the introduced in France in the 1790s. The historical development of these systems culminated in the definition of the (SI), under the oversight of an international stan ...

metric system
and the world's most widely used
system of measurement A system of measurement is a collection of units of measurement and rules relating them to each other. Systems of measurement have historically been important, regulated and defined for the purposes of science and commerce. Systems of measurement in ...
.252
/sup> Established and maintained by the
General Conference on Weights and Measures The General Conference on Weights and Measures (GCWM; french: Conférence Générale des Poids et Mesures, CGPM) is the supreme authority of the International Bureau of Weights and Measures The International Bureau of Weights and Measures (fr ...
(CGPM), it is the only system of measurement with an official status in nearly every country in the world, employed in science, technology, industry, and everyday commerce. The SI comprises a coherent system of
units of measurement A unit of measurement is a definite magnitude Magnitude may refer to: Mathematics *Euclidean vector, a quantity defined by both its magnitude and its direction *Magnitude (mathematics), the relative size of an object *Norm (mathematic ...
starting with seven s, which are the
second The second (symbol: s, also abbreviated: sec) is the base unit of time Time is the continued sequence of existence and event (philosophy), events that occurs in an apparently irreversible process, irreversible succession from the past, th ...
(symbol s, the unit of
time Time is the continued sequence of existence and event (philosophy), events that occurs in an apparently irreversible process, irreversible succession from the past, through the present, into the future. It is a component quantity of various me ...

time
),
metre The metre ( Commonwealth spelling) or meter (American spelling Despite the various English dialects spoken from country to country and within different regions of the same country, there are only slight regional variations in English ...
(m,
length Length is a measure of distance Distance is a numerical measurement ' Measurement is the number, numerical quantification (science), quantification of the variable and attribute (research), attributes of an object or event, which can be us ...

length
),
kilogram The kilogram (also kilogramme) is the base unit of mass Mass is the physical quantity, quantity of ''matter'' in a physical body. It is also a measure (mathematics), measure of the body's ''inertia'', the resistance to acceleration (change ...
(kg,
mass Mass is the quantity Quantity is a property that can exist as a multitude or magnitude, which illustrate discontinuity and continuity. Quantities can be compared in terms of "more", "less", or "equal", or by assigning a numerical value ...
),
ampere The ampere (, ; symbol: A), often shortened to "amp",SI supports only the use of symbols and deprecates the use of abbreviations for units. is the base unit of electric current An electric current is a stream of charged particles, such as ele ...

ampere
(A,
electric current An electric current is a stream of charged particle In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies matter, ...
),
kelvin The kelvin is the base unit of temperature Temperature ( ) is a physical quantity that expresses hot and cold. It is the manifestation of thermal energy Thermal radiation in visible light can be seen on this hot metalwork. Thermal en ...

kelvin
(K,
thermodynamic temperature Thermodynamic temperature is a quantity defined in thermodynamics as distinct from Kinetic theory of gases, kinetic theory or statistical mechanics. A thermodynamic temperature reading of zero is of particular importance for the third law of therm ...

thermodynamic temperature
),
mole Mole (or Molé) may refer to: Animals * Mole (animal) or "true mole", mammals in the family Talpidae, found in Eurasia and North America * Golden moles, southern African mammals in the family Chrysochloridae, similar to but unrelated to Talpidae ...
(mol,
amount of substance In chemistry Chemistry is the study of the properties and behavior of . It is a that covers the that make up matter to the composed of s, s and s: their composition, structure, properties, behavior and the changes they undergo during a ...
), and
candela The candela ( or ; symbol: cd) is the of in the (SI); that is, luminous power per unit emitted by a point light source in a particular direction. Luminous intensity is analogous to , but instead of simply adding up the contributions of ever ...

candela
(cd,
luminous intensity In photometryPhotometry can refer to: * Photometry (optics), the science of measurement of visible light in terms of its perceived brightness to human vision * Photometry (astronomy), the measurement of the flux or intensity of an astronomical o ...
). The system can accommodate coherent units for an unlimited number of additional quantities. These are called coherent derived units, which can always be represented as products of powers of the base units. Twenty-two coherent derived units have been provided with special names and symbols. 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
prefix A prefix is an affix In linguistics Linguistics is the scientific study of language A language is a structured system of communication used by humans, including speech (spoken language), gestures (Signed language, sign language) ...
es which, when added to the name and symbol of a coherent unit produce twenty 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 SI is intended to be an evolving system; units and prefixes are created and unit definitions are modified through international agreement as the technology of
measurement Measurement is the quantification (science), quantification of variable and attribute (research), attributes of an object or event, which can be used to compare with other objects or events. The scope and application of measurement are dependen ...

measurement
progresses and the precision of measurements improves. Since 2019, the magnitudes of all SI units have been defined by declaring that seven ''defining constants'' have certain exact numerical values when expressed in terms of their SI units. These defining constants are the
speed of light The speed of light in vacuum A vacuum is a space Space is the boundless three-dimensional Three-dimensional space (also: 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called paramet ...
in vacuum , the hyperfine transition frequency of caesium , the
Planck constant The Planck constant, or Planck's constant, is a fundamental physical constant A physical constant, sometimes fundamental physical constant or universal constant, is a physical quantity that is generally believed to be both universal in nature an ...
, the
elementary charge The elementary charge, usually denoted by or sometimes e is the electric charge Electric charge is the physical property of matter that causes it to experience a force when placed in an electromagnetic field. Electric charge can be ''positive' ...
, the
Boltzmann constant The Boltzmann constant ( or ) is the proportionality factor In mathematics, two varying quantities are said to be in a Binary relation, relation of proportionality, Multiplication, multiplicatively connected to a Constant (mathematics), c ...
, the
Avogadro constant The Avogadro constant (''N''A or ''L'') is the proportionality factor that relates the number of constituent particles (usually molecule File:Pentacene on Ni(111) STM.jpg, A scanning tunneling microscopy image of pentacene molecules, which ...
, and the
luminous efficacy Luminous efficacy is a measure of how well a light source produces visible light. It is the ratio of luminous flux up Integrating sphere used for measuring the luminous flux of a light source. In photometry (optics), photometry, luminous flux or ...
. The nature of the defining constants ranges from fundamental constants of nature such as to the purely technical constant . Prior to 2019, , , , and were not defined a priori but were rather very precisely measured quantities. In 2019, their values were fixed by definition to their best estimates at the time, ensuring continuity with previous definitions of the base units. 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 last artefact used by the SI was the
International Prototype of the Kilogram The International Prototype of the Kilogram (referred to by metrologists as the IPK or Le Grand K; sometimes called the '' ur-kilogram,'' or ''urkilogram,'' particularly by German-language authors writing in English) is an object that was used to ...
, a cylinder of platinum-iridium. 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
discipline Discipline is action ACTION is a bus operator in Canberra Canberra ( ) is the capital city of Australia. Founded following the Federation of Australia, federation of the colonies of Australia as the seat of government for the new n ...
s that used them. The
General Conference on Weights and Measures The General Conference on Weights and Measures (GCWM; french: Conférence Générale des Poids et Mesures, CGPM) is the supreme authority of the International Bureau of Weights and Measures The International Bureau of Weights and Measures (fr ...
(French: ' – CGPM), which was established by the
Metre Convention The Metre Convention (french: link=no, Convention du Mètre), also known as the Treaty of the Metre, is an international treaty A treaty is a formal, legally binding written agreement between actors in international law International ...

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, so it is based on the
metre–kilogram–second system of units The MKS system of units is a physical system of measurement that uses the metre, kilogram, and second (MKS) as Base unit (measurement), base units. Adopted in 1889, use of the MKS system of units succeeded the centimetre–gram–second system of ...
(MKS) rather than any variant of the CGS.


Introduction

The International System of Units, or SI, is a decimal and
metric METRIC (Mapping EvapoTranspiration at high Resolution with Internalized Calibration) is a computer model Computer simulation is the process of mathematical modelling, performed on a computer, which is designed to predict the behaviour of or th ...

metric
system of units A system of measurement is a collection of units of measurement A unit of measurement is a definite magnitude Magnitude may refer to: Mathematics *Euclidean vector, a quantity defined by both its magnitude and its direction *Magnitude ...
established in 1960 and periodically updated since then. The SI has an in most countries, including
the United States The United States of America (U.S.A. or USA), commonly known as the United States (U.S. or US) or America, is a country Continental United States, primarily located in North America. It consists of 50 U.S. state, states, a Washington, D.C., ...
,
Canada Canada is a country in the northern part of North America North America is a continent A continent is any of several large landmasses. Generally identified by convention (norm), convention rather than any strict criteria, ...
, and
the United Kingdom The United Kingdom of Great Britain and Northern Ireland, commonly known as the United Kingdom (UK) or Britain,Usage is mixed. The Guardian' and Telegraph' use Britain as a synonym for the United Kingdom. Some prefer to use Britain as shortha ...
, although these three countries are amongst a 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 Imperial is that which relates to an empire, emperor, or imperialism. Imperial or The Imperial may also refer to: Places United States * Imperial, California * Imperial, Missouri * Imperial, Nebraska * Imperial, Pennsylvania * Imperial, Texas * ...
, and they are legally defined in terms of the SI. There are other, less widespread systems of measurement that are occasionally used in particular regions of the world. In addition, there are many individual non-SI units that don't belong to any comprehensive system of units, but that are nevertheless still regularly used in particular fields and regions. Both of these categories of unit are also typically defined legally in terms of SI units.


Controlling body

The SI was established and is maintained by the
General Conference on Weights and Measures The General Conference on Weights and Measures (GCWM; french: Conférence Générale des Poids et Mesures, CGPM) is the supreme authority of the International Bureau of Weights and Measures The International Bureau of Weights and Measures (fr ...
(CGPM). In practice, the CGPM follows the recommendations of the Consultative Committee for Units (CCU), which is the actual body conducting technical deliberations concerning new scientific and technological developments related to the definition of units and the SI. The CCU reports to the
International Committee for Weights and Measures The General Conference on Weights and Measures (GCWM; french: Conférence Générale des Poids et Mesures, CGPM) is the supreme authority of the International Bureau of Weights and Measures (BIPM), the intergovernmental organization established in ...
(CIPM ), which, in turn, reports to the CGPM. See
below Below may refer to: *Earth *Ground (disambiguation) *Soil *Floor *Bottom (disambiguation) *Less than *Temperatures below freezing *Hell or underworld People with the surname *Fred Below (1926–1988), American blues drummer *Fritz von Below (1853 ...
for more details. All the decisions and recommendations concerning units are collected in a brochure called ''The International System of Units (SI)'', which is published by the
International Bureau of Weights and Measures The International Bureau of Weights and Measures (french: Bureau international des poids et mesures, BIPM) is an intergovernmental organisation An intergovernmental organization (IGO) is an organization composed primarily of sovereign state ...
(BIPM ) and periodically updated.


Overview of the units


SI base units

The SI selects seven units to serve as s, corresponding to seven base physical quantities. They are the
second The second (symbol: s, also abbreviated: sec) is the base unit of time Time is the continued sequence of existence and event (philosophy), events that occurs in an apparently irreversible process, irreversible succession from the past, th ...
, with the symbol , which is the SI unit of the physical quantity of
time Time is the continued sequence of existence and event (philosophy), events that occurs in an apparently irreversible process, irreversible succession from the past, through the present, into the future. It is a component quantity of various me ...

time
; the
metre The metre ( Commonwealth spelling) or meter (American spelling Despite the various English dialects spoken from country to country and within different regions of the same country, there are only slight regional variations in English ...
, symbol , the SI unit of
length Length is a measure of distance Distance is a numerical measurement ' Measurement is the number, numerical quantification (science), quantification of the variable and attribute (research), attributes of an object or event, which can be us ...

length
;
kilogram The kilogram (also kilogramme) is the base unit of mass Mass is the physical quantity, quantity of ''matter'' in a physical body. It is also a measure (mathematics), measure of the body's ''inertia'', the resistance to acceleration (change ...
(, the unit of
mass Mass is the quantity Quantity is a property that can exist as a multitude or magnitude, which illustrate discontinuity and continuity. Quantities can be compared in terms of "more", "less", or "equal", or by assigning a numerical value ...
);
ampere The ampere (, ; symbol: A), often shortened to "amp",SI supports only the use of symbols and deprecates the use of abbreviations for units. is the base unit of electric current An electric current is a stream of charged particles, such as ele ...

ampere
(,
electric current An electric current is a stream of charged particle In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies matter, ...
);
kelvin The kelvin is the base unit of temperature Temperature ( ) is a physical quantity that expresses hot and cold. It is the manifestation of thermal energy Thermal radiation in visible light can be seen on this hot metalwork. Thermal en ...

kelvin
(,
thermodynamic temperature Thermodynamic temperature is a quantity defined in thermodynamics as distinct from Kinetic theory of gases, kinetic theory or statistical mechanics. A thermodynamic temperature reading of zero is of particular importance for the third law of therm ...

thermodynamic temperature
);
mole Mole (or Molé) may refer to: Animals * Mole (animal) or "true mole", mammals in the family Talpidae, found in Eurasia and North America * Golden moles, southern African mammals in the family Chrysochloridae, similar to but unrelated to Talpidae ...
(,
amount of substance In chemistry Chemistry is the study of the properties and behavior of . It is a that covers the that make up matter to the composed of s, s and s: their composition, structure, properties, behavior and the changes they undergo during a ...
); and
candela The candela ( or ; symbol: cd) is the of in the (SI); that is, luminous power per unit emitted by a point light source in a particular direction. Luminous intensity is analogous to , but instead of simply adding up the contributions of ever ...

candela
(,
luminous intensity In photometryPhotometry can refer to: * Photometry (optics), the science of measurement of visible light in terms of its perceived brightness to human vision * Photometry (astronomy), the measurement of the flux or intensity of an astronomical o ...
). 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.


SI derived units

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. The base and coherent derived units of the SI together form a coherent system of units (''the set of coherent SI units''). Twenty-two coherent derived units have been provided with special names and symbols. The seven base units and the 22 derived units with special names and symbols may be used in combination to express other derived units, which are adopted to facilitate measurement of diverse quantities.


Why SI kept the distinction between base and derived units

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 ISO 80000 or IEC 80000 is an international standard An international standard is a technical standard developed by one or more international standards organization, standards organizations. International standards are available for consideration ...
series of standards specifies base and derived quantities that necessarily have the corresponding SI units.


SI metric prefixes and the decimal nature of the SI

Like all metric systems, the SI uses
metric prefix A metric prefix is a unit prefix that precedes a basic unit of measure to indicate a multiple (mathematics), multiple or submultiple of the unit. All metric prefixes used today are decimal, decadic. Each prefix has a unique symbol that is prepende ...
es 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, while the coherent unit of length is the metre, the SI provides a full range of smaller and larger units of length, any of which may be more convenient for any given application – for example, driving distances are normally given in
kilometre The kilometre (SI symbol: km; or ), spelt kilometer in American English, is a unit of length in the metric system, equal to one thousand metres (kilo- being the SI prefix for ). It is now the measurement unit used for expressing distances betw ...
s (symbol ) rather than in metres. Here the metric prefix '
kilo- Kilo is a decimal prefix, decimal metric prefix, unit prefix in the metric system denoting multiplication by one thousand (103). It is used in the International System of Units, where it has the symbol k, in lower case. The prefix ''kilo'' is der ...
' (symbol 'k') stands for a factor of 1000; thus, = . The current version of the SI provides twenty metric prefixes that signify decimal powers ranging from 10−24 to 1024. Most prefixes correspond to integer powers of 1000; the only ones that do not are those for 10, 1/10, 100, and 1/100. In general, given any coherent unit with a separate name and symbol, one forms a new unit by simply adding an appropriate metric prefix to the name of the coherent unit (and a corresponding prefix symbol to the coherent unit's symbol). Since the metric prefix signifies a particular power of ten, the new unit is always a power-of-ten multiple or sub-multiple of the coherent unit. Thus, 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''. 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 and can be combined with other unit symbols to form compound unit symbols. For example, is an SI unit of
density The density (more precisely, the volumetric mass density; also known as specific mass), of a substance is its per unit . The symbol most often used for density is ''ρ'' (the lower case Greek letter ), although the Latin letter ''D'' can also ...

density
, where is to be interpreted as ().


Coherent and non-coherent SI units

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. The one exception is the kilogram, the only coherent SI unit whose name and symbol, for historical reasons, include a prefix. 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. For example, the metre, kilometre, centimetre, nanometre, etc. are all SI units of length, though only the metre is a ''coherent'' SI unit. A similar statement holds for derived units: for example, , , , /, etc. are all SI units of density, but of these, only is a ''coherent'' SI unit. Moreover, the metre is the ''only'' coherent SI unit of length. Every physical quantity has exactly one coherent SI unit, although this unit may be expressible in different forms by using some of the special names and symbols. For example, the coherent SI unit of
linear momentum In Newtonian mechanics, linear momentum, translational momentum, or simply momentum ( pl. momenta) is the product of the mass Mass is both a property Property (''latin: Res Privata'') in the Abstract and concrete, abstract is what ...

linear momentum
may be written as either or as , and both forms are in use (e.g. compare respectively here205
/sup> and here135
/sup>). On the other hand, several different quantities may share same coherent SI unit. For example, the joule per kelvin (symbol ) is the coherent SI unit for two distinct quantities:
heat capacity Heat capacity or thermal capacity is a physical property A physical property is any property Property is a system of rights that gives people legal control of valuable things, and also refers to the valuable things themselves. Depending on t ...
and
entropy Entropy is a scientific concept as well as a measurable physical property that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynamic ...

entropy
; another example is the ampere, which is the coherent SI unit for both
electric current An electric current is a stream of charged particle In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies matter, ...
and
magnetomotive force In physics, the magnetomotive force (mmf) is a quantity appearing in the equation for the magnetic flux in a magnetic circuit, often called Ohm's law for magnetic circuits. It is the property of certain substances or phenomena that give rise to ma ...
. This is why it is important not to use the unit alone to specify the quantity. 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. As perhaps a more familiar example, consider
rainfall Rain is liquid water in the form of droplet Rain water flux from a canopy. Among the forces that govern drop formation: cohesion, Van der Waals force">Cohesion_(chemistry).html" ;"title="surface tension, Cohesion (chemistry)">cohesion, ...
, defined as volume of rain (measured in ) that fell per unit area (measured in ). Since /, it follows that the coherent ''derived'' SI unit of rainfall is the metre, even though the metre is also the ''base'' SI unit of length.


Permitted non-SI units

There is a special group of units that are called "non-SI units that are accepted for use with the SI". See
Non-SI units mentioned in the SI This is a list of units that are not defined as part of the International System of Units International is an adjective (also used as a noun) meaning "between nations". International may also refer to: Music Albums * International (Kevin Michael a ...
for a full list. Most of these, 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 of 60 s/min, since 1 min ), the hour (), and the day (); the degree (for measuring plane angles, and the
electronvolt In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular suc ...
(a unit of energy,


New units

The SI is intended to be an evolving system; units and prefixes are created and unit definitions are modified through international agreement as the technology of
measurement Measurement is the quantification (science), quantification of variable and attribute (research), attributes of an object or event, which can be used to compare with other objects or events. The scope and application of measurement are dependen ...

measurement
progresses and the precision of measurements improves.


Defining magnitudes of units

Since 2019, the magnitudes of all SI units have been defined in an abstract way, which is conceptually separated from any practical realisation of them. Namely, the SI units are defined by declaring that seven ''defining constants'' have certain exact numerical values when expressed in terms of their SI units. Probably the most widely known of these constants is the
speed of light The speed of light in vacuum A vacuum is a space Space is the boundless three-dimensional Three-dimensional space (also: 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called paramet ...
in vacuum, , which in the SI by definition has the exact value of = . The other six constants are , the hyperfine transition frequency of caesium; , the
Planck constant The Planck constant, or Planck's constant, is a fundamental physical constant A physical constant, sometimes fundamental physical constant or universal constant, is a physical quantity that is generally believed to be both universal in nature an ...
; , the
elementary charge The elementary charge, usually denoted by or sometimes e is the electric charge Electric charge is the physical property of matter that causes it to experience a force when placed in an electromagnetic field. Electric charge can be ''positive' ...
; , the
Boltzmann constant The Boltzmann constant ( or ) is the proportionality factor In mathematics, two varying quantities are said to be in a Binary relation, relation of proportionality, Multiplication, multiplicatively connected to a Constant (mathematics), c ...
; A, the
Avogadro constant The Avogadro constant (''N''A or ''L'') is the proportionality factor that relates the number of constituent particles (usually molecule File:Pentacene on Ni(111) STM.jpg, A scanning tunneling microscopy image of pentacene molecules, which ...
; and cd, the
luminous efficacy Luminous efficacy is a measure of how well a light source produces visible light. It is the ratio of luminous flux up Integrating sphere used for measuring the luminous flux of a light source. In photometry (optics), photometry, luminous flux or ...
of monochromatic radiation of frequency . The nature of the defining constants ranges from fundamental constants of nature such as to the purely technical constant cd. Prior to 2019, , , , and were not defined a priori but were rather very precisely measured quantities. In 2019, their values were fixed by definition to their best estimates at the time, ensuring continuity with previous definitions of the base units. As far as realisations, what are believed to be the current best practical realisations of units are described in the so-called ''mises en pratique'', which are also published by the BIPM. The abstract nature of the definitions of units is what makes it possible to improve and change the ''mises en pratique'' as science and technology develop without having to change the actual definitions themselves. In a sense, this way of defining the SI units is no more abstract than the way derived units are traditionally defined in terms of the base units. Consider a particular derived unit, for example, the joule, the unit of energy. Its definition in terms of the base units is ⋅/. Even if the practical realisations of the metre, kilogram, and second are available, a practical realisation of the joule would require some sort of reference to the underlying physical definition of work or energy—some actual physical procedure for realising the energy in the amount of one joule such that it can be compared to other instances of energy (such as the energy content of gasoline put into a car or of electricity delivered to a household). The situation with the defining constants and all of the SI units is analogous. In fact, purely ''mathematically'' speaking, the SI units are defined ''as if'' we declared that it is the defining constant's units that are now the base units, with all other SI units being derived units. To make this clearer, first note that each defining constant can be taken as determining the magnitude of that defining constant's unit of measurement; for example, the definition of defines the unit as = ('the speed of one metre per second is equal to one th of the speed of light'). In this way, the defining constants directly define the following seven units: Further, one can show, using
dimensional analysis In engineering Engineering is the use of scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encompasses a broad range ...
, that every coherent SI unit (whether base or derived) can be written as a unique product of powers of the units of the SI defining constants (in complete analogy to the fact that every coherent derived SI unit can be written as a unique product of powers of the base SI units). For example, the kilogram can be written as Thus, the kilogram is defined in terms of the three defining constants , , and because, on the one hand, these three defining constants respectively define the units , , and , while, on the other hand, the kilogram can be written in terms of these three units, namely, While the question of how to actually realise the kilogram in practice would, at this point, still be open, that is not really different from the fact that the question of how to actually realise the joule in practice is still in principle open even once one has achieved the practical realisations of the metre, kilogram, and second.


Specifying fundamental constants vs. other methods of definition

The current way of defining the SI is the 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. The great advantage of doing it this way is that as science and technologies develop, new and superior realisations may be introduced without the need to redefine the units. Units can now be realised with 'an accuracy that is ultimately limited only by the quantum structure of nature and our technical abilities but not by the definitions themselves. Any valid equation of physics relating the defining constants to a unit can be used to realise the unit, thus creating opportunities for innovation... with increasing accuracy as technology proceeds.' In practice, the CIPM Consultative Committees provide so-called "''mises en pratique'' (practical techniques), which are the descriptions of what are currently believed to be best experimental realisations of the units. This system lacks the conceptual simplicity of using artefacts (referred to as ''prototypes'') as realisations of units to define those units: with prototypes, the definition and the realisation are one and the same. However, using artefacts has two major disadvantages that, as soon as it is technologically and scientifically feasible, result in abandoning them as means for defining units. One major disadvantage is that artefacts can be lost, damaged, or changed. The other is that they largely cannot benefit from advancements in science and technology. The last artefact used by the SI was the International Prototype Kilogram (IPK), a particular cylinder of platinum-iridium; from 1889 to 2019, the kilogram was by definition equal to the mass of the IPK. Concerns regarding its stability on the one hand, and progress in precise measurements of the Planck constant and the Avogadro constant on the other, led to a revision of the definition of the base units, put into effect on 20 May 2019. This was the biggest change in the SI since it was first formally defined and established in 1960, and it resulted in the definitions described above. In the past, there were also various other approaches to the definitions of some of the SI units. One made use of a specific physical state of a specific substance (the
triple point of water In thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, radiation, and physical properties of matter. The behavior of these quantities is governed ...

triple point of water
, which was used in the definition of the kelvin); others referred to idealised experimental prescriptions (as in the case of the former SI definition of the ampere and the former SI definition (originally enacted in 1979) ). In the future, the set of defining constants used by the SI may be modified as more stable constants are found, or if it turns out that other constants can be more precisely measured.


History

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
discipline Discipline is action ACTION is a bus operator in Canberra Canberra ( ) is the capital city of Australia. Founded following the Federation of Australia, federation of the colonies of Australia as the seat of government for the new n ...
s that used them. The
General Conference on Weights and Measures The General Conference on Weights and Measures (GCWM; french: Conférence Générale des Poids et Mesures, CGPM) is the supreme authority of the International Bureau of Weights and Measures The International Bureau of Weights and Measures (fr ...
(French: ' – CGPM), which was established by the
Metre Convention The Metre Convention (french: link=no, Convention du Mètre), also known as the Treaty of the Metre, is an international treaty A treaty is a formal, legally binding written agreement between actors in international law International ...

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. Adopted in 1889, use of the MKS system of units succeeded the
centimetre–gram–second system of units The centimetre–gram–second system of units (abbreviated CGS or cgs) is a variant of the metric system The metric system is a that succeeded the decimalised system based on the introduced in France in the 1790s. The historical develo ...
(CGS) in
commerce Commerce is the exchange of goods and services, especially on a large scale. Etymology The English-language word ''commerce'' has been derived from the Latin word ''commercium'', from ''com'' ("together") and ''merx'' ("merchandise"). History ...

commerce
and
engineering Engineering is the use of scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encompasses a broad range of more speciali ...

engineering
. The metre and kilogram system served as the basis for the development of the International System of Units (abbreviated SI), which now serves as the international standard. Because of this, the standards of the CGS system were gradually replaced with metric standards incorporated from the MKS system. In 1901,
Giovanni Giorgi Giovanni Giorgi (27 November 1871 – 19 August 1950) was an Italian physicist A physicist is a scientist A scientist is a person who conducts Scientific method, scientific research to advance knowledge in an Branches of science, area of int ...

Giovanni Giorgi
proposed to the (AEI) that this system, extended with a fourth unit to be taken from the units of
electromagnetism Electromagnetism is a branch of physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in ...

electromagnetism
, be used as an international system. This system was strongly promoted by electrical engineer George A. Campbell. The International System was published in 1960, based on the MKS units, as a result of an initiative that began in 1948.


Controlling authority

The SI is regulated and continually developed by three international organisations that were established in 1875 under the terms of the
Metre Convention The Metre Convention (french: link=no, Convention du Mètre), also known as the Treaty of the Metre, is an international treaty A treaty is a formal, legally binding written agreement between actors in international law International ...

Metre Convention
. They are the
General Conference on Weights and Measures The General Conference on Weights and Measures (GCWM; french: Conférence Générale des Poids et Mesures, CGPM) is the supreme authority of the International Bureau of Weights and Measures The International Bureau of Weights and Measures (fr ...
(CGPM), the International Committee for Weights and Measures (CIPM), and the
International Bureau of Weights and Measures The International Bureau of Weights and Measures (french: Bureau international des poids et mesures, BIPM) is an intergovernmental organisation An intergovernmental organization (IGO) is an organization composed primarily of sovereign state ...
(BIPM). The ultimate authority rests with the CGPM, which is a plenary body through which its Member States act together on matters related to measurement science and measurement standards; it usually convenes every four years. The CGPM elects the CIPM, which is an 18-person committee of eminent scientists. The CIPM operates based on the advice of a number of its Consultative Committees, which bring together the world's experts in their specified fields as advisers on scientific and technical matters. One of these committees is the Consultative Committee for Units (CCU), which is responsible for ''matters related to the development of the International System of Units (SI), preparation of successive editions of the SI brochure, and advice to the CIPM on matters concerning units of measurement.'' It is the CCU which considers in detail all new scientific and technological developments related to the definition of units and the SI. In practice, when it comes to the definition of the SI, the CGPM simply formally approves the recommendations of the CIPM, which, in turn, follows the advice of the CCU. The CCU has the following as members: national laboratories of the Member States of the CGPM charged with establishing national standards; relevant intergovernmental organisations and international bodies; international commissions or committees; scientific unions; personal members; and, as an
ex officio member An ''ex officio'' member is a member of a body (notably a board, committee, council) who is part of it by virtue of holding another office. The term ''ex officio An ''ex officio'' member is a member of a body (notably a board, committee, council) ...
of all Consultative Committees, the Director of the BIPM. All the decisions and recommendations concerning units are collected in a brochure called ''The International System of Units (SI)'', which is published by the BIPM and periodically updated.


Units and prefixes

The International System of Units consists of a set of s, derived units, and a set of decimal-based multipliers that are used as
prefix A prefix is an affix In linguistics Linguistics is the scientific study of language A language is a structured system of communication used by humans, including speech (spoken language), gestures (Signed language, sign language) ...
es. The units, excluding prefixed units, form a coherent system of units, which is based on a system of quantities in such a way that the equations between the numerical values expressed in coherent units have exactly the same form, including numerical factors, as the corresponding equations between the quantities. For example, 1 N = 1 kg × 1 m/s2 says that ''one'' newton is the force required to
accelerate In mechanics Mechanics (Ancient Greek, Greek: ) is the area of physics concerned with the motions of physical objects, more specifically the relationships among force, matter, and motion. Forces applied to objects result in Displacement ( ...

accelerate
a mass of ''one'' kilogram at ''one''
metre per second squared The metre per second squared is the unit Unit may refer to: Arts and entertainment * UNIT, a fictional military organization in the science fiction television series ''Doctor Who'' * Unit of action, a discrete piece of action (or beat) in a theatr ...
, as related through the principle of coherence to the equation relating the corresponding quantities: . Derived units apply to derived quantities, which may by definition be expressed in terms of base quantities, and thus are not independent; for example,
electrical conductance The electrical resistance of an object is a measure of its opposition to the flow of electric current. Its Multiplicative inverse, reciprocal quantity is , measuring the ease with which an electric current passes. Electrical resistance shares so ...
is the inverse of
electrical resistance The electrical resistance of an object is a measure of its opposition to the flow of electric current An electric current is a stream of charged particle In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epi ...
, 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 is defined in SI units as m/s2.


Base units

The SI base units are the building blocks of the system and all the other units are derived from them.


Derived units

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 are associated with derived quantities; for example,
velocity The velocity of an object is the Time derivative, rate of change of its Position (vector), position with respect to a frame of reference, and is a function of time. Velocity is equivalent to a specification of an object's speed and direction ...

velocity
is a quantity that is derived from the base quantities of time and length, and thus the SI derived unit is metre per second (symbol m/s). The dimensions of derived units can be expressed in terms of the dimensions of the base units. Combinations of base and derived units may be used to express other derived units. For example, the SI unit of
force In physics, a force is an influence that can change the motion (physics), motion of an Physical object, object. A force can cause an object with mass to change its velocity (e.g. moving from a Newton's first law, state of rest), i.e., to acce ...

force
is the
newton Newton most commonly refers to: * Isaac Newton (1642–1726/1727), English scientist * Newton (unit), SI unit of force named after Isaac Newton Newton may also refer to: Arts and entertainment * Newton (film), ''Newton'' (film), a 2017 Indian fil ...
(N), the SI unit of
pressure Pressure (symbol: ''p'' or ''P'') is the force In physics, a force is an influence that can change the motion (physics), motion of an Physical object, object. A force can cause an object with mass to change its velocity (e.g. moving fr ...

pressure
is the
pascal Pascal, Pascal's or PASCAL may refer to: People and fictional characters * Pascal (given name), including a list of people with the name * Pascal (surname), including a list of people and fictional characters with the name ** Blaise Pascal, French ...
(Pa)—and the pascal can be defined as one newton per square metre (N/m2).


Prefixes

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. When prefixes are used to form multiples and submultiples of SI base and derived units, the resulting units are no longer coherent. The BIPM specifies 20 prefixes for the International System of Units (SI): :


Non-SI units accepted for use with 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 This is a list of units that are not defined as part of the International System of Units International is an adjective (also used as a noun) meaning "between nations". International may also refer to: Music Albums * International (Kevin Michael a ...
: Some units of time, angle, and legacy non-SI units have a long history of use. Most societies have used the solar day and its non-decimal subdivisions as a basis of time and, unlike the
foot The foot (plural: feet) is an anatomical Anatomy (Greek ''anatomē'', 'dissection') is the branch of biology Biology is the natural science that studies life and living organisms, including their anatomy, physical structure, Biochemis ...
or the
pound Pound or Pounds may refer to: Units * Pound (currency) A pound is any of various units of currency A currency, "in circulation", from la, currens, -entis, literally meaning "running" or "traversing" in the most specific sense is money Im ...
, these were the same regardless of where they were being measured. The
radian The radian, denoted by the symbol \text, is the SI unit for measuring angle In Euclidean geometry, an angle is the figure formed by two Ray (geometry), rays, called the ''sides'' of the angle, sharing a common endpoint, called the ''verte ...

radian
, being of a revolution, has mathematical advantages but is rarely used for navigation. Further, the units used in navigation around the world are similar. The
tonne The tonne ( or ; symbol: t) is a metric unit of mass equal to 1,000 kilogram The kilogram (also kilogramme) is the base unit of mass Mass is the physical quantity, quantity of ''matter'' in a physical body. It is also a meas ...
,
litre The litre (British English British English (BrE) is the standard dialect A standard language (also standard variety, standard dialect, and standard) is a language variety that has undergone substantial codification of grammar and ...

litre
, and
hectare The hectare (; SI symbol: ha) is a non-SI metric unit of area Area is the quantity Quantity is a property that can exist as a multitude or magnitude, which illustrate discontinuity and continuity. Quantities can be compared in terms o ...

hectare
were adopted by the CGPM in 1879 and have been retained as units that may be used alongside SI units, having been given unique symbols. The catalogued units are given below: These units are used in combination with SI units in common units such as the kilowatt-hour (1 kW⋅h = 3.6 MJ).


Common notions of the metric units

The basic units of the metric system, as originally defined, represented common quantities or relationships in nature. They still do – the modern precisely defined quantities are refinements of definition and methodology, but still with the same magnitudes. In cases where laboratory precision may not be required or available, or where approximations are good enough, the original definitions may suffice. *A second is 1/60 of a minute, which is 1/60 of an hour, which is 1/24 of a day, so a second is 1/86400 of a day (the use of base 60 dates back to Babylonian times); a second is the time it takes a dense object to freely fall 4.9 metres from rest. *The length of the
equator The Equator is a circle of latitude, about in circumference, that divides Earth into the Northern Hemisphere, Northern and Southern Hemisphere, Southern hemispheres. It is an imaginary line located at 0 degrees latitude, halfway between the N ...

equator
is close to (more precisely ). In fact, the dimensions of our planet were used by the French Academy in the original definition of the metre. *The metre is close to the length of a pendulum that has a period of 2 seconds; most dining tabletops are about 0.75 metres high; a very tall human (basketball forward) is about 2 metres tall. *The kilogram is the mass of a litre of cold water; a cubic centimetre or millilitre of water has a mass of one gram; a 1-euro coin weighs 7.5 g; a Sacagawea US 1-dollar coin weighs 8.1 g; a UK 50-pence coin weighs 8.0 g. *A candela is about the luminous intensity of a moderately bright candle, or 1 candle power; a 60 W tungsten-filament
incandescent light bulb An incandescent light bulb, incandescent lamp or incandescent light globe is an with a wire heated until it glows. The filament is enclosed in a glass bulb with a vacuum or inert gas to protect the filament from . Current is supplied to the ...

incandescent light bulb
has a luminous intensity of about 64 candelas. *A mole of a substance has a mass that is its
molecular mass The molecular mass (''m'') is the mass of a given molecule: it is measured in dalton Dalton may refer to: Science * Dalton (crater), a lunar crater * Dalton (program), chemistry software * Dalton (unit) (Da), the atomic mass unit Entertainment ...
expressed in units of grams; the mass of a mole of carbon is 12.0 g, and the mass of a mole of table salt is 58.4 g. *Since all gases have the same volume per mole at a given temperature and pressure far from their points of liquefaction and solidification (see
Perfect gasIn physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies matter, its Motion (physics), motion and behavior through Spac ...
), and air is about 1/5 oxygen (molecular mass 32) and 4/5 nitrogen (molecular mass 28), the density of any near-perfect gas relative to air can be obtained to a good approximation by dividing its molecular mass by 29 (because 4/5 × 28 + 1/5 × 32 = 28.8 ≈ 29). For example,
carbon monoxide Carbon monoxide (chemical formula CO) is a colorless, odorless, tasteless, flammable gas that is slightly less dense than air. Carbon monoxide consists of one carbon atom and one oxygen atom. It is the simplest molecule of the oxocarbon family. In ...

carbon monoxide
(molecular mass 28) has almost the same density as air. *A temperature difference of one kelvin is the same as one degree Celsius: 1/100 of the temperature differential between the freezing and boiling points of water at sea level; the absolute temperature in kelvins is the temperature in degrees Celsius plus about 273;
human body temperature Normal human body-temperature (normothermia, euthermia) is the typical temperature Temperature is a physical quantity that expresses hot and cold. It is the manifestation of thermal energy, present in all matter, which is the source of th ...
is about 37 °C or 310 K. *A 60 W incandescent light bulb rated at 120 V (US mains voltage) consumes 0.5 A at this voltage. A 60 W bulb rated at 240 V (European mains voltage) consumes 0.25 A at this voltage.


Lexicographic conventions


Unit names

According to the SI Brochure, unit names should be treated as
common noun A noun () is a word In linguistics, a word of a spoken language can be defined as the smallest sequence of phonemes that can be uttered in isolation with semantic, objective or pragmatics, practical meaning (linguistics), meaning. In many l ...
s of the context language. This means that they should be typeset in the same character set as other common nouns (e.g.
Latin alphabet The Latin alphabet or Roman alphabet is the collection of letters originally used by the ancient Romans In historiography Historiography is the study of the methods of historian ( 484– 425 BC) was a Greek historian who lived ...

Latin alphabet
in English,
Cyrillic script The Cyrillic script ( ) is a writing system used for various languages across Eurasia and is used as the national script in various Slavic languages, Slavic, Turkic languages, Turkic, Mongolic languages, Mongolic, Uralic languages, Uralic, Caucas ...
in Russian, etc.), normally in upright (i.e. not italic) type, 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 capitalized 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 capitalized 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 American English (AmE, AE, AmEng, USEng, en-US), sometimes called United States English or U.S. English, is the set of varieties Variety may refer to: Science and technology Mathematics * Algebraic variety, the set of solutions of a syst ...
uses the spelling ''deka-'', ''meter'', and ''liter'', whilst
International English International English is the concept of the English language English is a West Germanic languages, West Germanic language first spoken in History of Anglo-Saxon England, early medieval England, which has eventually become the World lang ...
uses ''deca-'', ''metre'', and ''litre''. Additionally, the name of the unit whose symbol is t and which is defined according to is 'metric ton' US English but 'tonne' in International English.


Unit symbols and the values of quantities

Symbols of SI units are intended to be unique and universal, independent of the context language. The SI Brochure has specific rules for writing them. The guideline produced by the
National Institute of Standards and Technology The National Institute of Standards and Technology (NIST) is a physical sciences Physical science is a branch of natural science that studies abiotic component, non-living systems, in contrast to life science. It in turn has many branches, e ...
(NIST) clarifies language-specific details for American English that were left unclear by the SI Brochure, but is otherwise identical to the SI Brochure.


General rules

General rules for writing SI units and quantities apply to text that is either handwritten or produced using an automated process: * The value of a quantity is written as a number followed by a space (representing a multiplication sign) and a unit symbol; e.g., 2.21 kg, , 22 K. This rule explicitly includes the percent sign (%) and the symbol for degrees Celsius (°C). Exceptions are the symbols for plane angular degrees, minutes, and seconds (°, ′, and ″, respectively), which are placed immediately after the number with no intervening space. * Symbols are mathematical entities, not abbreviations, and as such do not have an appended period/full stop (.), unless the rules of grammar demand one for another reason, such as denoting the end of a sentence. * A prefix is part of the unit, and its symbol is prepended to a unit symbol without a separator (e.g., k in km, M in MPa, G in GHz, μ in μg). Compound prefixes are not allowed. A prefixed unit is atomic in expressions (e.g., km2 is equivalent to (km)2). * Unit symbols are written using roman (upright) type, regardless of the type used in the surrounding text. * Symbols for derived units formed by multiplication are joined with a centre dot (⋅) or a non-breaking space; e.g., N⋅m or N m. * Symbols for derived units formed by division are joined with a
solidus Solidus (Latin Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally spoken in the area around Rome, known as Latium. Through the power of the Roman Republi ...
(/), or given as a negative
exponent Exponentiation is a mathematical Mathematics (from Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Southeast Europ ...
. E.g., the "metre per second" can be written m/s, m s−1, m⋅s−1, or . A solidus followed without parentheses by a centre dot (or space) or a solidus is ambiguous and must be avoided; e.g., kg/(m⋅s2) and kg⋅m−1⋅s−2 are acceptable, but kg/m/s2 is ambiguous and unacceptable. * The first letter of symbols for units derived from the name of a person is written in
upper case Letter case is the distinction between the letters Letter, letters, or literature may refer to: Characters typeface * Letter (alphabet) A letter is a segmental symbol A symbol is a mark, sign, or word that indicates, signifies, or i ...
; otherwise, they are written in
lower case Letter case is the distinction between the letters Letter, letters, or literature may refer to: Characters typeface * Letter (alphabet) A letter is a segmental symbol A symbol is a mark, sign, or word that indicates, signifies, or ...
. E.g., the unit of
pressure Pressure (symbol: ''p'' or ''P'') is the force In physics, a force is an influence that can change the motion (physics), motion of an Physical object, object. A force can cause an object with mass to change its velocity (e.g. moving fr ...

pressure
is named after
Blaise Pascal Blaise Pascal ( , , ; ; 19 June 1623 – 19 August 1662) was a French mathematician, physicist, inventor, philosopher, writer and Catholic Church, Catholic theologian. He was a child prodigy who was educated by his father, a tax collector i ...

Blaise Pascal
, so its symbol is written "Pa", but the symbol for mole is written "mol". Thus, "T" is the symbol for tesla, a measure of
magnetic field strength A magnetic field is a vector field In vector calculus and physics, a vector field is an assignment of a vector to each point in a subset of space. For instance, a vector field in the plane can be visualised as a collection of arrows with a ...
, and "t" the symbol for
tonne The tonne ( or ; symbol: t) is a metric unit of mass equal to 1,000 kilogram The kilogram (also kilogramme) is the base unit of mass Mass is the physical quantity, quantity of ''matter'' in a physical body. It is also a meas ...
, a measure of
mass Mass is the quantity Quantity is a property that can exist as a multitude or magnitude, which illustrate discontinuity and continuity. Quantities can be compared in terms of "more", "less", or "equal", or by assigning a numerical value ...
. Since 1979, the
litre The litre (British English British English (BrE) is the standard dialect A standard language (also standard variety, standard dialect, and standard) is a language variety that has undergone substantial codification of grammar and ...

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". * Symbols do not have a plural form, e.g., 25 kg, but not 25 . * Uppercase and lowercase prefixes are not interchangeable. E.g., the quantities 1 mW and 1 MW represent two different quantities (milliwatt and megawatt). * The symbol for the decimal marker is either a full stop, point or comma on the line. In practice, the decimal point is used in most English-speaking countries and most of Asia, and the comma in most of Latin America and in continental List of sovereign states and dependent territories in Europe, European countries. * Spaces should be used as a thousands separator () in contrast to commas or periods (1,000,000 or 1.000.000) to reduce confusion resulting from the variation between these forms in different countries. * Any line-break inside a number, inside a compound unit, or between number and unit should be avoided. Where this is not possible, line breaks should coincide with thousands separators. * Because the value of "billion" and "trillion" Long and short scales, varies between languages, the dimensionless terms "ppb" (parts per long and short scales, billion) and "ppt" (parts per long and short scales, trillion) should be avoided. The SI Brochure does not suggest alternatives.


Printing SI symbols

The rules covering printing of quantities and units are part of ISO 80000-1:2009. Further rules are specified in respect of production of text using printing presses, word processors, typewriters, and the like.


International System of Quantities

:::::SI Brochure The CGPM publishes a brochure that defines and presents the SI. Its official version is in French, in line with the
Metre Convention The Metre Convention (french: link=no, Convention du Mètre), also known as the Treaty of the Metre, is an international treaty A treaty is a formal, legally binding written agreement between actors in international law International ...

Metre Convention
. It leaves some scope for local variations, particularly regarding unit names and terms in different languages. The writing and maintenance of the CGPM brochure is carried out by one of the committees of the International Committee for Weights and Measures (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.
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 Quantity#Quantity in physical science, quantities underlying each of the SI base units, seven base units of the SI. Other quantities, such as area,
pressure Pressure (symbol: ''p'' or ''P'') is the force In physics, a force is an influence that can change the motion (physics), motion of an Physical object, object. A force can cause an object with mass to change its velocity (e.g. moving fr ...

pressure
, and
electrical resistance The electrical resistance of an object is a measure of its opposition to the flow of electric current An electric current is a stream of charged particle In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epi ...
, are derived from these base quantities by clear non-contradictory equations. The ISQ defines the quantities that are measured with the SI units. The ISQ is formalised, in part, in the international standard
ISO/IEC 80000 ISO 80000 or IEC 80000 is an international standard An international standard is a technical standard developed by one or more international standards organization, standards organizations. International standards are available for consideration ...
, which was completed in 2009 with the publication of ISO 80000-1, and has largely been revised in 2019–2020 with the remainder being under review.


Realisation of units

Metrologists carefully distinguish between the definition of a unit and its realisation. The definition of each base unit of the SI is drawn up so that it is unique and provides a sound theoretical basis on which the most accurate and reproducible measurements can be made. 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. A description of the ''mise en pratique'' of the base units is given in an electronic appendix to the SI Brochure. The published ''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." In the current (2016) exercise to New SI definitions, overhaul the definitions of the base units, various consultative committees of the CIPM have required that more than one ''mise en pratique'' shall be developed for determining the value of each unit. In particular: * At least three separate experiments be carried out yielding values having a relative Uncertainty#Measurements, standard uncertainty in the determination of the
kilogram The kilogram (also kilogramme) is the base unit of mass Mass is the physical quantity, quantity of ''matter'' in a physical body. It is also a measure (mathematics), measure of the body's ''inertia'', the resistance to acceleration (change ...
of no more than and at least one of these values should be better than . Both the Kibble balance and the Avogadro project should be included in the experiments and any differences between these be reconciled. *When the
kelvin The kelvin is the base unit of temperature Temperature ( ) is a physical quantity that expresses hot and cold. It is the manifestation of thermal energy Thermal radiation in visible light can be seen on this hot metalwork. Thermal en ...

kelvin
is being determined, the relative uncertainty of the
Boltzmann constant The Boltzmann constant ( or ) is the proportionality factor In mathematics, two varying quantities are said to be in a Binary relation, relation of proportionality, Multiplication, multiplicatively connected to a Constant (mathematics), c ...
derived from two fundamentally different methods such as acoustic gas thermometry and dielectric constant gas thermometry be better than one part in and that these values be corroborated by other measurements.


Evolution of the SI


Changes to the SI

The
International Bureau of Weights and Measures The International Bureau of Weights and Measures (french: Bureau international des poids et mesures, BIPM) is an intergovernmental organisation An intergovernmental organization (IGO) is an organization composed primarily of sovereign state ...
(BIPM) has described SI as "the modern form of metric system". Changing technology has led to an evolution of the definitions and standards that has followed two principal strands – changes to SI itself, and clarification of how to use units of measure that are not part of SI but are still nevertheless used on a worldwide basis. Since 1960 the CGPM has made a number of changes to the SI to meet the needs of specific fields, notably chemistry and radiometry. These are mostly additions to the list of named derived units, and include the ''
mole Mole (or Molé) may refer to: Animals * Mole (animal) or "true mole", mammals in the family Talpidae, found in Eurasia and North America * Golden moles, southern African mammals in the family Chrysochloridae, similar to but unrelated to Talpidae ...
'' (symbol mol) for an amount of substance, the ''
pascal Pascal, Pascal's or PASCAL may refer to: People and fictional characters * Pascal (given name), including a list of people with the name * Pascal (surname), including a list of people and fictional characters with the name ** Blaise Pascal, French ...
'' (symbol Pa) for
pressure Pressure (symbol: ''p'' or ''P'') is the force In physics, a force is an influence that can change the motion (physics), motion of an Physical object, object. A force can cause an object with mass to change its velocity (e.g. moving fr ...

pressure
, the ''Siemens (unit), siemens'' (symbol S) for electrical conductance, the ''becquerel'' (symbol Bq) for "Radioactive decay, activity referred to a radionuclide", the ''Gray (unit), gray'' (symbol Gy) for ionising radiation, the ''sievert'' (symbol Sv) as the unit of dose equivalent radiation, and the ''katal'' (symbol kat) for catalytic activity. The range of defined prefixes pico- (10−12) to tera- (1012) was extended to 10−24 to 1024. The 1960 definition of the standard metre in terms of wavelengths of a specific emission of the krypton-86 atom was replaced with the distance that light travels in vacuum in exactly second, so that the speed of light is now an exactly specified constant of nature. A few changes to notation conventions have also been made to alleviate lexicographic ambiguities. An analysis under the aegis of CSIRO, published in 2009 by the Royal Society, has pointed out the opportunities to finish the realisation of that goal, to the point of universal zero-ambiguity machine readability.


2019 redefinitions

After the History of the metre, metre was redefined in 1960, the
International Prototype of the Kilogram The International Prototype of the Kilogram (referred to by metrologists as the IPK or Le Grand K; sometimes called the '' ur-kilogram,'' or ''urkilogram,'' particularly by German-language authors writing in English) is an object that was used to ...
(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. 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. A proposal was made that: *In addition to the speed of light, four constants of nature – the
Planck constant The Planck constant, or Planck's constant, is a fundamental physical constant A physical constant, sometimes fundamental physical constant or universal constant, is a physical quantity that is generally believed to be both universal in nature an ...
, an
elementary charge The elementary charge, usually denoted by or sometimes e is the electric charge Electric charge is the physical property of matter that causes it to experience a force when placed in an electromagnetic field. Electric charge can be ''positive' ...
, the
Boltzmann constant The Boltzmann constant ( or ) is the proportionality factor In mathematics, two varying quantities are said to be in a Binary relation, relation of proportionality, Multiplication, multiplicatively connected to a Constant (mathematics), c ...
, and the
Avogadro constant The Avogadro constant (''N''A or ''L'') is the proportionality factor that relates the number of constituent particles (usually molecule File:Pentacene on Ni(111) STM.jpg, A scanning tunneling microscopy image of pentacene molecules, which ...
– be defined to have exact values *The International Prototype of the Kilogram be retired *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. The change was adopted by the European Union through Directive (EU) 2019/1258.


History


The improvisation of units

The units and unit magnitudes of the metric system which became the SI were improvised piecemeal from everyday physical quantities starting in the mid-18th century. Only later were they moulded into an orthogonal coherent decimal system of measurement. The degree centigrade as a unit of temperature resulted from the scale devised by Swedish astronomer Anders Celsius in 1742. His scale counter-intuitively designated 100 as the freezing point of water and 0 as the boiling point. Independently, in 1743, the French physicist Jean-Pierre Christin described a scale with 0 as the freezing point of water and 100 the boiling point. The scale became known as the centi-grade, or 100 gradations of temperature, scale. The metric system was developed from 1791 onwards by a committee of the French Academy of Sciences, commissioned to create a unified and rational system of measures. The group, which included preeminent French men of science, used the same principles for relating length, volume, and mass that had been proposed by the English clergyman John Wilkins in 1668 and the concept of using the Earth's Meridian (geography), meridian as the basis of the definition of length, originally proposed in 1670 by the French abbot Gabriel Mouton, Mouton. In March 1791, the Assembly adopted the committee's proposed principles for the new decimal system of measure including the metre defined to be 1/10,000,000 of the length of the quadrant of Earth's meridian passing through Paris, and authorised a survey to precisely establish the length of the meridian. In July 1792, the committee proposed the names ''
metre The metre ( Commonwealth spelling) or meter (American spelling Despite the various English dialects spoken from country to country and within different regions of the same country, there are only slight regional variations in English ...
'', ''are (unit), are'', ''
litre The litre (British English British English (BrE) is the standard dialect A standard language (also standard variety, standard dialect, and standard) is a language variety that has undergone substantial codification of grammar and ...

litre
'' and ''grave (unit), grave'' for the units of length, area, capacity, and mass, respectively. The committee also proposed that multiples and submultiples of these units were to be denoted by decimal-based prefixes such as ''centi'' for a hundredth and ''kilo'' for a thousand. Later, during the process of adoption of the metric system, the Latin ''gramme'' and ''
kilogram The kilogram (also kilogramme) is the base unit of mass Mass is the physical quantity, quantity of ''matter'' in a physical body. It is also a measure (mathematics), measure of the body's ''inertia'', the resistance to acceleration (change ...
me'', replaced the former provincial terms ''gravet'' (1/1000 ''grave'') and ''grave''. In June 1799, based on the results of the meridian survey, the standard ''mètre des Archives'' and ''kilogramme des Archives'' were deposited in the Archives nationales (France), French National Archives. Subsequently, that year, the metric system was adopted by law in France. The French system was short-lived due to its unpopularity. Napoleon ridiculed it, and in 1812, introduced a replacement system, the ''mesures usuelles'' or "customary measures" which restored many of the old units, but redefined in terms of the metric system. During the first half of the 19th century there was little consistency in the choice of preferred multiples of the base units: typically the myriametre ( metres) was in widespread use in both France and parts of Germany, while the kilogram ( grams) rather than the myriagram was used for mass. In 1832, the German mathematician Carl Friedrich Gauss, assisted by Wilhelm Eduard Weber, Wilhelm Weber, implicitly defined the second as a base unit when he quoted the Earth's magnetic field in terms of millimetres, grams, and seconds. Prior to this, the strength of the Earth's magnetic field had only been described in Relative change and difference, relative terms. The technique used by Gauss was to equate the torque induced on a suspended magnet of known mass by the Earth's magnetic field with the torque induced on an equivalent system under gravity. The resultant calculations enabled him to assign dimensions based on mass, length and time to the magnetic field. A candlepower as a unit of illuminance was originally defined by an 1860 English law as the light produced by a pure spermaceti candle weighing pound (76 grams) and burning at a specified rate. Spermaceti, a waxy substance found in the heads of sperm whales, was once used to make high-quality candles. At this time the French standard of light was based upon the illumination from a Carcel lamp, Carcel oil lamp. The unit was defined as that illumination emanating from a lamp burning pure rapeseed oil at a defined rate. It was accepted that ten standard candles were about equal to one Carcel lamp.


Metre Convention

A French-inspired initiative for international cooperation in metrology led to the signing in 1875 of the
Metre Convention The Metre Convention (french: link=no, Convention du Mètre), also known as the Treaty of the Metre, is an international treaty A treaty is a formal, legally binding written agreement between actors in international law International ...

Metre Convention
, also called Treaty of the Metre, by 17 nations. Initially the convention only covered standards for the metre and the kilogram. In 1921, the Metre Convention was extended to include all physical units, including the ampere and others thereby enabling the CGPM to address inconsistencies in the way that the metric system had been used. A set of 30 prototypes of the metre and 40 prototypes of the kilogram,The text "''Des comparaisons périodiques des étalons nationaux avec les prototypes internationaux''" ( en, the periodic comparisons of national standards with the international prototypes) in article 6.3 of th
Metre Convention
distinguishes between the words "standard"
OED: "The legal magnitude of a unit of measure or weight"
and "prototype"
OED: "an original on which something is modelled"
.
in each case made of a 90% platinum-10% iridium alloy, were manufactured by ''British metallurgy specialty firm'' and accepted by the CGPM in 1889. One of each was selected at random to become the International prototype metre and International prototype kilogram that replaced the ''mètre des Archives'' and ''kilogramme des Archives'' respectively. Each member state was entitled to one of each of the remaining prototypes to serve as the national prototype for that country. The treaty also established a number of international organisations to oversee the keeping of international standards of measurement.


The CGS and MKS systems

In the 1860s, James Clerk Maxwell, William Thomson, 1st Baron Kelvin, William Thomson (later Lord Kelvin) and others working under the auspices of the British Association for the Advancement of Science, built on Gauss's work and formalised the concept of a coherent system of units with base units and derived units christened the
centimetre–gram–second system of units The centimetre–gram–second system of units (abbreviated CGS or cgs) is a variant of the metric system The metric system is a that succeeded the decimalised system based on the introduced in France in the 1790s. The historical develo ...
in 1874. 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 In physics, a force is an influence that can change the motion (physics), motion of an Physical object, object. A force can cause an object with mass to change its velocity (e.g. moving from a Newton's first law, state of rest), i.e., to acce ...

force
, the barye for
pressure Pressure (symbol: ''p'' or ''P'') is the force In physics, a force is an influence that can change the motion (physics), motion of an Physical object, object. A force can cause an object with mass to change its velocity (e.g. moving fr ...

pressure
, the Poise (unit), poise for dynamic viscosity and the Stokes (unit), stokes for kinematic viscosity. In 1879, the CIPM published recommendations for writing the symbols for length, area, volume and mass, but it was outside its domain to publish recommendations for other quantities. Beginning in about 1900, physicists who had been using the symbol "μ" (mu) for "micrometre" or "micron", "λ" (lambda) for "microlitre", and "γ" (gamma) for "microgram" started to use the symbols "μm", "μL" and "μg". 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. for electrical distribution systems. Attempts to resolve the electrical units in terms of length, mass, and time using
dimensional analysis In engineering Engineering is the use of scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encompasses a broad range ...
was beset with difficulties—the dimensions depended on whether one used the ESU or EMU systems. This anomaly was resolved in 1901 when
Giovanni Giorgi Giovanni Giorgi (27 November 1871 – 19 August 1950) was an Italian physicist A physicist is a scientist A scientist is a person who conducts Scientific method, scientific research to advance knowledge in an Branches of science, area of int ...

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 An electric current is a stream of charged particle In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies matter, ...
, voltage, or
electrical resistance The electrical resistance of an object is a measure of its opposition to the flow of electric current An electric current is a stream of charged particle In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epi ...
. 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. This became the foundation of the MKS system of units. In the late 19th and early 20th centuries, a number of non-coherent units of measure based on the gram/kilogram, centimetre/metre, and second, such as the ''Pferdestärke'' (metric horsepower) for Power (physics), power, the darcy (unit), darcy for Permeability (earth sciences), permeability and "Torr#Manometric units of pressure, millimetres of mercury" for Atmospheric pressure, barometric and blood pressure were developed or propagated, some of which incorporated standard gravity in their definitions. At the end of the Second World War, a number of different systems of measurement were in use throughout the world. Some of these systems were metric system variations; others were based on Systems of measurement, customary systems of measure, like the U.S customary system and Imperial system of the UK and British Empire.


The ''Practical system of units''

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". This working document was ''Practical system of units of measurement''. Based on this study, the 10th CGPM in 1954 defined an international system derived from six base units including units of temperature and optical radiation in addition to those for the MKS system mass, length, and time units and Giovanni Giorgi, Giorgi's current unit. Six base units were recommended: 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. 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.


Birth of the SI

In 1960, the 11th CGPM synthesised the results of the 12-year study into a set of 16 resolutions. The system was named the ''International System of Units'', abbreviated SI from the French name, .


Historical definitions

When James Clerk Maxwell, Maxwell first introduced the concept of a coherent system, he identified three quantities that could be used as base units: mass, length, and time. Giovanni Giorgi, Giorgi later identified the need for an electrical base unit, for which the unit of electric current was chosen for SI. Another three base units (for temperature, amount of substance, and luminous intensity) were added later. The early metric systems defined a unit of weight as a base unit, while the SI defines an analogous unit of mass. In everyday use, these are mostly interchangeable, but in scientific contexts the difference matters. Mass, strictly the inertial mass, represents a quantity of matter. It relates the acceleration of a body to the applied force via Newton's laws of motion, Newton's law, : force equals mass times acceleration. A force of 1 N (newton) applied to a mass of 1 kg will accelerate it at 1 m/s2. This is true whether the object is floating in space or in a gravity field e.g. at the Earth's surface. Weight is the force exerted on a body by a gravitational field, and hence its weight depends on the strength of the gravitational field. Weight of a 1 kg mass at the Earth's surface is ; mass times the acceleration due to gravity, which is 9.81 newtons at the Earth's surface and is about 3.5 newtons at the surface of Mars. Since the acceleration due to gravity is local and varies by location and altitude on the Earth, weight is unsuitable for precision measurements of a property of a body, and this makes a unit of weight unsuitable as a base unit.


Metric units that are not recognised by the SI

Although the term ''metric system'' is often used as an informal alternative name for the International System of Units, 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_(unit), darcy that exist outside of any system of units. Most of the units of the other metric systems are not recognised by the SI. Here are some examples. The centimetre–gram–second, centimetre–gram–second (CGS) system was the dominant metric system in the physical sciences and electrical engineering from the 1860s until at least the 1960s, and is still in use in some fields. It includes such SI-unrecognised units as the Gal (unit), gal, dyne, erg, barye, etc. in its Mechanics, mechanical sector, as well as the Poise (unit), poise and Viscosity#Units, stokes in fluid dynamics. When it comes to the units for quantities in electricity and magnetism, there are several versions of the CGS system. Two of these are obsolete: the Centimetre–gram–second system of units#Electrostatic units (ESU), CGS electrostatic ('CGS-ESU', with the SI-unrecognised units of statcoulomb, statvolt, Centimetre–gram–second system of units#Electrostatic units (ESU), statampere, etc.) and the Centimetre–gram–second system of units#Electromagnetic units (EMU), CGS electromagnetic system ('CGS-EMU', with abampere, abcoulomb, oersted, Maxwell (unit), maxwell, abhenry, Gilbert (unit), gilbert, etc.). A 'blend' of these two systems is still popular and is known as the Gaussian units, Gaussian system (which includes the Gauss (unit), gauss as a special name for the CGS-EMU unit maxwell per square centimetre). In engineering (other than electrical engineering), there was formerly a long tradition of using the gravitational metric system, whose SI-unrecognised units include the kilogram-force (kilopond), technical atmosphere, Horsepower#Metric horsepower (PS, cv, hk, pk, ks, ch), metric horsepower, etc. The metre–tonne–second system of units, metre–tonne–second (mts) system, used in the Soviet Union from 1933 to 1955, had such SI-unrecognised units as the sthène, pièze, etc. Other groups of SI-unrecognised metric units are the various legacy and CGS units related to ionising radiation (Rutherford (unit), rutherford, Curie (unit), curie, Roentgen (unit), roentgen, Rad (unit), rad, Roentgen equivalent man, rem, etc.), radiometry (Langley (unit), langley, jansky), photometry (optics), photometry (phot, Lux#Non-SI units of illuminance, nox, stilb (unit), stilb, Candela per square metre, nit, metre-candle,17
/sup> Lambert (unit), lambert, apostilb, Skot (unit), skot, Bril (unit), brill, troland, Lumen second, talbot, candlepower, Candela#History, candle), thermodynamics (calorie), and spectroscopy (Wavenumber, reciprocal centimetre). The angstrom is still used in various fields. Some other SI-unrecognised metric units that don't fit into any of the already mentioned categories include the Hectare#Are, are, bar (unit), bar, barn (unit), barn, Femtometre, fermi, Gradian, gradian (gon, grad, or grade), Carat (mass), metric carat, Micrometre#SI standardization, micron, millimetre of mercury, torr, Centimetre of water, millimetre (or centimetre, or metre) of water, Nanometre#History, millimicron, Siemens (unit)#Mho, mho, stere, x unit, Gamma#Mathematics and science, (unit of mass), Gamma#Mathematics and science, (unit of magnetic flux density), and Lambda (unit), (unit of volume). In some cases, the SI-unrecognised metric units have equivalent SI units formed by combining a
metric prefix A metric prefix is a unit prefix that precedes a basic unit of measure to indicate a multiple (mathematics), multiple or submultiple of the unit. All metric prefixes used today are decimal, decadic. Each prefix has a unique symbol that is prepende ...
with a coherent SI unit. For example, , , , etc. (a related group are the correspondences such as ≘ , ≘ , etc.). Sometimes, it is not even a matter of a metric prefix: the SI-nonrecognised unit may be exactly the same as an SI coherent unit, except for the fact that the SI does not recognise the special name and symbol. For example, the Candela per square metre, nit is just an SI-unrecognised name for the SI unit candela per square metre and the talbot is an SI-unrecognised name for the SI unit lumen second. Frequently, a non-SI metric unit is related to an SI unit through a power-of-ten factor, but not one that has a metric prefix, e.g., = , = , etc. (and correspondences like ≘ ). Finally, there are metric units whose conversion factors to SI units are not powers of ten, e.g., and . Some SI-unrecognised metric units are still frequently used, e.g., the calorie (in nutrition), the rem (in the U.S.), the jansky (in radio astronomy), the gauss (in industry) and the CGS-Gaussian units more generally (in some subfields of physics), the metric horsepower (for engine power, in Europe), the kilogram-force (for rocket engine thrust, in China and sometimes in Europe), etc. Others are now rarely used, such as the sthène and the rutherford.


See also

*
Non-SI units mentioned in the SI This is a list of units that are not defined as part of the International System of Units International is an adjective (also used as a noun) meaning "between nations". International may also refer to: Music Albums * International (Kevin Michael a ...


Notes


References


Further reading

*
Unit Systems in Electromagnetism

MW Keller ''et al.''
Metrology Triangle Using a Watt Balance, a Calculable Capacitor, and a Single-Electron Tunneling Device
"The Current SI Seen From the Perspective of the Proposed New SI"
Barry N. Taylor. Journal of Research of the National Institute of Standards and Technology, Vol. 116, No. 6, Pgs. 797–807, Nov–Dec 2011. * B. N. Taylor, Ambler Thompson, ''International System of Units (SI)'',
National Institute of Standards and Technology The National Institute of Standards and Technology (NIST) is a physical sciences Physical science is a branch of natural science that studies abiotic component, non-living systems, in contrast to life science. It in turn has many branches, e ...
2008 edition, .


External links

;Official
BIPM – About the BIPM
(home page) *
BIPM – measurement units
*
BIPM brochure
(SI reference)

* [https://physics.nist.gov/cuu/Units/bibliography.html NIST On-line official publications on the SI] *
NIST Special Publication 330, 2019 Edition: The International System of Units (SI)
*
NIST Special Publication 811, 2008 Edition: Guide for the Use of the International System of Units
*
NIST Special Pub 814: Interpretation of the SI for the United States and Federal Government Metric Conversion Policy

Rules for SAE Use of SI (Metric) Units
*
EngNet Metric Conversion Chart
Online Categorised Metric Conversion Calculator ;History
LaTeX SIunits package manual
gives a historical background to the SI. ;Research
''The metrological triangle''

Recommendation of ICWM 1 (CI-2005)
{{DEFAULTSORT:International System Of Units International System of Units, Systems of units International standards