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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 form of the
metric system The metric system is a system of measurement that succeeded the Decimal, decimalised system based on the metre that had been introduced in French Revolution, France in the 1790s. The historical development of these systems culminated in the d ...
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 i ...
. 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 (BIPM), the intergovernmental organization established i ...
(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 (mathematics), magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity. Any other quantity of that kind can ...
starting with seven base units, which are the
second The second (symbol: s) is the unit of Time in physics, time in the International System of Units (SI), historically defined as of a day – this factor derived from the division of the day first into 24 hours, then to 60 minutes and finally t ...
(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 ...
),
metre The metre (British English, British spelling) or meter (American English, American spelling; American and British English spelling differences#-re, -er, see spelling differences) (from the French unit , from the Greek language, Greek noun , "m ...
(m,
length Length is a measure of distance. In the International System of Quantities, length is a quantity with Dimension (physical quantity), dimension distance. In most Measurement system, systems of measurement a Base unit (measurement), base unit f ...
),
kilogram The kilogram (also kilogramme) is the unit of mass in the International System of Units (SI), having the unit symbol kg. It is a widely used measure in science, engineering and commerce worldwide, and is often simply called a kilo colloquially. ...
(kg,
mass Mass is an Intrinsic and extrinsic properties, intrinsic property of a body. It was traditionally believed to be related to the physical quantity, quantity of matter in a Physical object, physical body, until the discovery of the atom and par ...
),
ampere The ampere (, ; symbol: A), often Clipping (morphology), shortened to amp,SI supports only the use of symbols and deprecates the use of abbreviations for units. is the unit of electric current in the International System of Units (SI). One amp ...
(A,
electric current An electric current is a stream of charged particles, such as electrons or ions, moving through an electrical conductor or space. It is measured as the net rate of flow of electric charge through a surface or into a control volume. The moving par ...
),
kelvin The kelvin, symbol K, is the primary unit of temperature in the International System of Units (SI), used alongside its metric prefix, prefixed forms and the degree Celsius. It is named after the Belfast-born and University of Glasgow-based eng ...
(K,
thermodynamic temperature Thermodynamic temperature is a quantity defined in thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of ...
), mole (mol,
amount of substance In chemistry, the amount of substance ''n'' in a given sample of matter is defined as the countable quantity, quantity or particle number, number of discrete atomic-scale particles in it divided by the Avogadro constant ''N''A. The particles or ent ...
), and
candela The candela ( or ; symbol: cd) is the unit of luminous intensity in the International System of Units (SI). It measures luminous power per unit solid angle emitted by a light source in a particular direction. Luminous intensity is analogous to ...
(cd,
luminous intensity In Photometry (optics), photometry, luminous intensity is a measure of the wavelength-weighted Power (physics), power emitted by a light source in a particular direction per unit solid angle, based on the luminosity function, a standardized model ...
). 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-four
prefix A prefix is an affix which is placed before the Word stem, stem of a word. Adding it to the beginning of one word changes it into another word. For example, when the prefix ''un-'' is added to the word ''happy'', it creates the word ''unhappy'' ...
es which, when added to the name and symbol of a coherent unit produce twenty-four additional (non-coherent) SI units for the same quantity; these non-coherent units are always decimal (i.e. power-of-ten) multiples and sub-multiples of the coherent unit. The 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. In other words, measurement is a process of determi ...
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, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special relativity, special theory of relativity, is ...
in vacuum , the hyperfine transition frequency of caesium , the
Planck constant The Planck constant, or Planck's constant, is a fundamental physical constant of foundational importance in quantum mechanics. The constant gives the relationship between the energy of a photon and its frequency, and by the mass-energy equivalenc ...
, the
elementary charge The elementary charge, usually denoted by is the electric charge carried by a single proton or, equivalently, the magnitude of the negative electric charge carried by a single electron, which has charge −1 . This elementary charge is a fundame ...
, the
Boltzmann constant The Boltzmann constant ( or ) is the proportionality factor that relates the average relative kinetic energy of particles in a ideal gas, gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin and the gas ...
, the Avogadro constant , 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 to power, measured in lumens per watt The watt (symbol: W) is the unit of power or radiant flux in the International Sys ...
. 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 metrology, metrologists as the IPK or Le Grand K; sometimes called the ''wiktionary:ur-#Prefix, ur-kilogram,'' or ''urkilogram,'' particularly by German-language authors writing in Engli ...
, 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 The electrostatic system of units (CGS-ESU) is a system of units used to measure quantities of electric charge, electric current, and voltage within the centimetre–gram–second (or "CGS") system of metric units. In electrostatic units, electrical ...
and
electromagnetic units In physics, electromagnetism is an interaction that occurs between particles with electric charge. It is the second-strongest of the four fundamental interactions, after the strong force, and it is the dominant force in the interactions of a ...
) and the lack of coordination between the various
discipline Discipline refers to rule following behavior, to regulate, order, control and authority. It may also refer to punishment. Discipline is used to create habits, routines, and automatic mechanisms such as blind obedience. It may be inflicted on ot ...
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 (BIPM), the intergovernmental organization established i ...
(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 that was signed in Paris on 20 May 1875 by representatives of 17 nations (Argentina, Austria-Hungary, Belgium, Brazi ...
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 (MKS) rather than any variant of the CGS.


Introduction

The International System of Units, or SI, is a decimal and
metric Metric or metrical may refer to: * Metric system, an internationally adopted decimal system of measurement * An adjective indicating relation to measurement in general, or a noun describing a specific type of measurement Mathematics In mathema ...
system of units established in 1960 and periodically updated since then. The SI has an official status 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 North America. Its Provinces and territories of Canada, ten provinces and three territories extend from the Atlantic Ocean to the Pacific Ocean and northward into the Arctic Ocean, covering over , making it the world ...
, and
the United Kingdom The United Kingdom of Great Britain and Northern Ireland, commonly known as the United Kingdom (UK) or Britain, is a country in Europe, off the north-western coast of the European mainland, continental mainland. It comprises England, Scotlan ...
, 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 The imperial and US customary measurement systems are both derived from an earlier English units, English system of measurement which in turn can be traced back to Ancient Roman units of measurement, and Carolingian Renaissance, Carolingian and S ...
, 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 (BIPM), the intergovernmental organization established i ...
(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 i ...
(CIPM ), which, in turn, reports to the CGPM. See below 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 List of intergovernmental organizations, intergovernmental organisation, through which its 59 member-states act together on measur ...
(BIPM ) and periodically updated.


Overview of the units


SI base units

The SI selects seven units to serve as base units, corresponding to seven base physical quantities. They are the
second The second (symbol: s) is the unit of Time in physics, time in the International System of Units (SI), historically defined as of a day – this factor derived from the division of the day first into 24 hours, then to 60 minutes and finally t ...
, 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 ...
; the
metre The metre (British English, British spelling) or meter (American English, American spelling; American and British English spelling differences#-re, -er, see spelling differences) (from the French unit , from the Greek language, Greek noun , "m ...
, symbol , the SI unit of
length Length is a measure of distance. In the International System of Quantities, length is a quantity with Dimension (physical quantity), dimension distance. In most Measurement system, systems of measurement a Base unit (measurement), base unit f ...
;
kilogram The kilogram (also kilogramme) is the unit of mass in the International System of Units (SI), having the unit symbol kg. It is a widely used measure in science, engineering and commerce worldwide, and is often simply called a kilo colloquially. ...
(, the unit of
mass Mass is an Intrinsic and extrinsic properties, intrinsic property of a body. It was traditionally believed to be related to the physical quantity, quantity of matter in a Physical object, physical body, until the discovery of the atom and par ...
);
ampere The ampere (, ; symbol: A), often Clipping (morphology), shortened to amp,SI supports only the use of symbols and deprecates the use of abbreviations for units. is the unit of electric current in the International System of Units (SI). One amp ...
(,
electric current An electric current is a stream of charged particles, such as electrons or ions, moving through an electrical conductor or space. It is measured as the net rate of flow of electric charge through a surface or into a control volume. The moving par ...
);
kelvin The kelvin, symbol K, is the primary unit of temperature in the International System of Units (SI), used alongside its metric prefix, prefixed forms and the degree Celsius. It is named after the Belfast-born and University of Glasgow-based eng ...
(,
thermodynamic temperature Thermodynamic temperature is a quantity defined in thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of ...
); mole (,
amount of substance In chemistry, the amount of substance ''n'' in a given sample of matter is defined as the countable quantity, quantity or particle number, number of discrete atomic-scale particles in it divided by the Avogadro constant ''N''A. The particles or ent ...
); and
candela The candela ( or ; symbol: cd) is the unit of luminous intensity in the International System of Units (SI). It measures luminous power per unit solid angle emitted by a light source in a particular direction. Luminous intensity is analogous to ...
(,
luminous intensity In Photometry (optics), photometry, luminous intensity is a measure of the wavelength-weighted Power (physics), power emitted by a light source in a particular direction per unit solid angle, based on the luminosity function, a standardized model ...
). 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 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 or submultiple of the unit. All metric prefixes used today are decadic. Each prefix has a unique symbol that is prepended to any unit symbol. The pr ...
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 International System of Units (SI), equal to one thousand metres (kilo- being the SI prefix for ). It is now the measurement unit used for exp ...
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 Letter case, lowercase. The prefix ' ...
' (symbol 'k') stands for a factor of 1000; thus, = . The current version of the SI provides twenty-four metric prefixes that signify decimal powers ranging from 10−30 to 1030, the most recent being adopted in 2022. 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 Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek language, Greek letter Rho (letter), rho), although the Latin letter ''D'' ca ...
, 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, momentum (more specifically linear momentum or translational momentum) is the product of the mass Mass is an Intrinsic and extrinsic properties, intrinsic property of a body. It was traditionally believed to ...
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 the 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 quantity, physical property of matter, defined as the amount of heat to be supplied to an object to produce a unit change in its temperature. The International System of Units, SI unit of heat ca ...
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 thermodynam ...
; another example is the ampere, which is the coherent SI unit for both
electric current An electric current is a stream of charged particles, such as electrons or ions, moving through an electrical conductor or space. It is measured as the net rate of flow of electric charge through a surface or into a control volume. The moving par ...
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 ...
. 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 water drop (liquid), droplets that have condensation, condensed from Water vapor#In Earth's atmosphere, atmospheric water vapor and then Precipitation, fall under gravity. Rain is a major component of the water cycle and is responsib ...
, 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 The International System of Units, known by the international abbreviation SI in all languages and sometimes Pleonasm#Acronyms and initialisms, pleona ...
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, an electronvolt (symbol eV, also written electron-volt and electron volt) is the measure of an amount of kinetic energy gained by a single electron accelerating from rest through an Voltage, electric potential difference of one volt i ...
(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. In other words, measurement is a process of determi ...
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, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special relativity, special theory of relativity, is ...
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 of foundational importance in quantum mechanics. The constant gives the relationship between the energy of a photon and its frequency, and by the mass-energy equivalenc ...
; , the
elementary charge The elementary charge, usually denoted by is the electric charge carried by a single proton or, equivalently, the magnitude of the negative electric charge carried by a single electron, which has charge −1 . This elementary charge is a fundame ...
; , the
Boltzmann constant The Boltzmann constant ( or ) is the proportionality factor that relates the average relative kinetic energy of particles in a ideal gas, gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin and the gas ...
; A, the Avogadro constant; 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 to power, measured in lumens per watt The watt (symbol: W) is the unit of power or radiant flux in the International Sys ...
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 , 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 and science, dimensional analysis is the analysis of the relationships between different physical quantities by identifying their base quantity, base quantities (such as length, mass, time, and electric current) and units of measur ...
, 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 Water () is a Chemical polarity, polar inorganic compound that is at room temperature a tasteless and odorless liquid, which is nearly colorless apart from Color of water, an inherent hint of blue. It is by far the most studied chemical compou ...
, 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) of the candela). 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 The electrostatic system of units (CGS-ESU) is a system of units used to measure quantities of electric charge, electric current, and voltage within the centimetre–gram–second (or "CGS") system of metric units. In electrostatic units, electrical ...
and
electromagnetic units In physics, electromagnetism is an interaction that occurs between particles with electric charge. It is the second-strongest of the four fundamental interactions, after the strong force, and it is the dominant force in the interactions of a ...
) and the lack of coordination between the various
discipline Discipline refers to rule following behavior, to regulate, order, control and authority. It may also refer to punishment. Discipline is used to create habits, routines, and automatic mechanisms such as blind obedience. It may be inflicted on ot ...
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 (BIPM), the intergovernmental organization established i ...
(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 that was signed in Paris on 20 May 1875 by representatives of 17 nations (Argentina, Austria-Hungary, Belgium, Brazi ...
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 based on the centimetre as the unit of length, the gram as the unit of mass, and the second as the unit of time. All CGS mechanics, mechani ...
(CGS) in
commerce Commerce is the large-scale organized system of activities, functions, procedures and institutions directly and indirectly related to the exchange (buying and selling) of goods and services among two or more parties within local, regional, nation ...
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 specializ ...
. 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 proposed to the (AEI) that this system, extended with a fourth unit to be taken from the units of
electromagnetism In physics, electromagnetism is an interaction that occurs between particles with electric charge. It is the second-strongest of the four fundamental interactions, after the strong force, and it is the dominant force in the interactions of a ...
, 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 that was signed in Paris on 20 May 1875 by representatives of 17 nations (Argentina, Austria-Hungary, Belgium, Brazi ...
. 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 (BIPM), the intergovernmental organization established i ...
(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 List of intergovernmental organizations, intergovernmental organisation, through which its 59 member-states act together on measur ...
(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 ''List of Latin phrases (E)#ex officio, ex officio'' is Latin, meaning literally 'from the office' ...
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 base units, derived units, and a set of decimal-based multipliers that are used as
prefix A prefix is an affix which is placed before the Word stem, stem of a word. Adding it to the beginning of one word changes it into another word. For example, when the prefix ''un-'' is added to the word ''happy'', it creates the word ''unhappy'' ...
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, acceleration is the rate of change of the velocity of an object with respect to time. Accelerations are vector quantities (in that they have magnitude and direction). The orientation of an object's acceleration is given by ...
a mass of ''one'' kilogram at ''one''
metre per second squared The metre per second squared is the Units of measurement, unit of acceleration in the International System of Units (SI). As a SI derived unit, derived unit, it is composed from the SI base units of length, the metre, and time, the second. Its sy ...
, 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 s ...
is the inverse of
electrical resistance 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 s ...
, 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 Velocity is the directional derivative, directional speed of an physical object, object in motion as an indication of its time derivative, rate of change in position (vector), position as observed from a particular frame of reference and as m ...
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 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 accelerate. Force can ...
is the newton (N), the SI unit of
pressure Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and e ...
is the pascal (Pa)—and the pascal can be defined as one newton per square metre (N/m2).


Dimensionless units

The unit of a
dimensionless quantity A dimensionless quantity (also known as a bare quantity, pure quantity, or scalar quantity as well as quantity of dimension one) is a quantity to which no Dimension (physics), physical dimension is assigned, with a corresponding International Sys ...
is
one 1 (one, unit, unity) is a number A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words. Mo ...
(symbol 1), but it is rarely shown. The radian and steradian are also dimensionless quantities, but use the symbols rad and sr respectively.


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 24 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: 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 structure found in many vertebrates. It is the terminal portion of a limb (anatomy), limb which bears weight and allows animal locomotion, locomotion. In many animals with feet, the foot is a separate o ...
or the pound, these were the same regardless of where they were being measured. The
radian The radian, denoted by the symbol rad, is the unit of angle in the International System of Units (SI) and is the standard unit of angular measure used in many areas of mathematics. The unit was formerly an SI supplementary unit (before that c ...
, 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 unit of mass equal to 1000 kilograms. It is a International System of Units#Non-SI units accepted for use with SI, non-SI unit accepted for use with SI. It is also referred to as a metric ton to disting ...
,
litre The litre (international spelling) or liter (American English American English, sometimes called United States English or U.S. English, is the set of variety (linguistics), varieties of the English language native to the United States. ...
, and
hectare The hectare (; SI symbol: ha) is a Non-SI units mentioned in the SI, non-SI metric unit of area equal to a square with 100-metre sides (1 hm2), or 10,000 m2, and is primarily used in the measurement of land. There are 100 hectares in one ...
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 of a minute, which is of an hour, which is of a day, so a second is 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 ...
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 electric light with a wire #Filament, filament heated until it glows. The filament is enclosed in a glass bulb with a vacuum or inert gas to protect the filament ...
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 daltons (Da or u). Different molecules of the same compound may have different molecular masses because they contain different isotope Isotopes are two or more ty ...
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 gas In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its motion and behavior through Spacetime, space and time, and the related entities of energy and force. "Physical science i ...
), and air is about oxygen (molecular mass 32) and 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 ). For example,
carbon monoxide Carbon monoxide (chemical formula CO) is a colorless, poisonous, odorless, tasteless, flammable gas that is slightly less dense than air. Carbon monoxide consists of one carbon atom and one oxygen atom connected by a triple bond. It is the simple ...
(molecular mass 28) has almost the same density as air. *A temperature difference of one kelvin is the same as one degree Celsius: 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 range found in humans. The normal human body temperature range is typically stated as . Human body temperature varies. It depends on sex, age, time of day, exert ...
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 230 V (European mains voltage) consumes 0.26 A at this voltage.


Lexicographic conventions


Unit names

According to the SI Brochure, unit names should be treated as common nouns of the context language. This means that they should be typeset in the same character set as other common nouns (e.g.
Latin alphabet The Latin alphabet or Roman alphabet is the collection of letters originally used by the Ancient Rome, ancient Romans to write the Latin language. Largely unaltered with the exception of extensions (such as diacritics), it used to write Eng ...
in English,
Cyrillic script The Cyrillic script ( ), Slavonic script or the Slavic script, is a writing system used for various languages across Eurasia. It is the designated national script in various Slavic languages, Slavic, Turkic languages, Turkic, Mongolic languages, ...
in Russian, etc.), following the usual grammatical and orthographical rules of the context language. For example, in English and French, even when the unit is named after a person and its symbol begins with a capital letter, the unit name in running text should start with a lowercase letter (e.g., newton, hertz, pascal) and is 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, sometimes called United States English or U.S. English, is the set of variety (linguistics), varieties of the English language native to the United States. English is the Languages of the United States, most widely spoken lan ...
uses the spelling ''deka-'', ''meter'', and ''liter'', whilst
International English International English is the concept of using the English language English is a West Germanic languages, West Germanic language of the Indo-European language family, with its earliest forms spoken by the inhabitants of early medieval ...
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 an agency of the United States Department of Commerce whose mission is to promote American innovation and industrial competitiveness. NIST's activities are organized into Outline of p ...
(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 (/), or given as a negative
exponent Exponentiation is a mathematics, mathematical operation (mathematics), operation, written as , involving two numbers, the ''Base (exponentiation), base'' and the ''exponent'' or ''power'' , and pronounced as " (raised) to the (power of) ". W ...
. E.g., the "metre per second" can be written m/s, m s−1, m⋅s−1, or . In cases where a solidus is followed by a centre dot (or space), or more than one solidus is present, parentheses must be used to avoid ambiguity; e.g., kg/(m⋅s2), kg⋅m−1⋅s−2, and (kg/m)/s2 are acceptable, but kg/m/s2 and kg/m⋅s2 are 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 Letter (alphabet), letters that are in larger uppercase or capitals (or more formally ''majuscule'') and smaller lowercase (or more formally ''minuscule'') in the written representation of certain lang ...
; otherwise, they are written in
lower case Letter case is the distinction between the Letter (alphabet), letters that are in larger uppercase or capitals (or more formally ''majuscule'') and smaller lowercase (or more formally ''minuscule'') in the written representation of certain lang ...
. E.g., the unit of
pressure Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and e ...
is named after
Blaise Pascal Blaise Pascal ( , , ; ; 19 June 1623 – 19 August 1662) was a French mathematician, physicist, inventor, philosopher, and Catholic Church, Catholic writer. He was a child prodigy who was educated by his father, a tax collector in Rouen. Pa ...
, 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 that describes the magnetic influence on moving electric charge Electric charge is the physical property of matter that causes charged matter to experience a force when placed in an electromagnetic ...
, and "t" the symbol for
tonne The tonne ( or ; symbol: t) is a unit of mass equal to 1000 kilograms. It is a International System of Units#Non-SI units accepted for use with SI, non-SI unit accepted for use with SI. It is also referred to as a metric ton to disting ...
, a measure of
mass Mass is an Intrinsic and extrinsic properties, intrinsic property of a body. It was traditionally believed to be related to the physical quantity, quantity of matter in a Physical object, physical body, until the discovery of the atom and par ...
. Since 1979, the
litre The litre (international spelling) or liter (American English American English, sometimes called United States English or U.S. English, is the set of variety (linguistics), varieties of the English language native to the United States. ...
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, 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 point or
comma The comma is a punctuation mark that appears in several variants in different languages. It has the same shape as an apostrophe or single closing quotation mark () in many typefaces, but it differs from them in being placed on the baseline (t ...
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 Latin America or * french: Amérique Latine, link=no * ht, Amerik Latin, link=no * pt, América Latina, link=no, name=a, sometimes referred to as LatAm is a large cultural region in the Americas where Romance languages — languages derived f ...
and in continental
European countries The list below includes all entities falling even partially under any of the regions of Europe, various common definitions of Europe, geographical or political. Fifty generally recognised sovereign states, Kosovo with limited, but substantial, ...
. * Spaces should be used as a
thousands separator A decimal separator is a symbol used to separate the integer part from the fractional part of a number written in decimal form (e.g., "." in 12.45). Different countries officially designate different symbols for use as the separator. The choi ...
() 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" varies between languages, the dimensionless terms "ppb" (parts per
billion Billion is a word for a large number, and it has two distinct definitions: * 1,000,000,000, i.e. one thousand million, or (ten to the ninth power), as defined on the short scale. This is its only current meaning in English. * 1,000,000,000,000, ...
) and "ppt" (parts per
trillion ''Trillion'' is a number with two distinct definitions: *1,000,000,000,000, i.e. one million 1,000,000, million, or (ten to the twelfth Exponentiation, power), as defined on the long and short scales, short scale. This is now the meaning in bot ...
) 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 press A printing press is a mechanical device for applying pressure to an inked surface resting upon a printing, print medium (such as paper or cloth), thereby transferring the ink. It marked a dramatic improvement on earlier printing methods in wh ...
es,
word processor A word processor (WP) is a device or computer program that provides for input, editing, formatting, and output of text, often with some additional features. Early word processors were stand-alone devices dedicated to the function, but current ...
s,
typewriter A typewriter is a machine, mechanical or electromechanical machine for typing characters. Typically, a typewriter has an array of Button (control), keys, and each one causes a different single character to be produced on paper by striking ...
s, 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 that was signed in Paris on 20 May 1875 by representatives of 17 nations (Argentina, Austria-Hungary, Belgium, Brazi ...
. 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 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 i ...
(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 The International System of Quantities (ISQ) consists of the Quantity, quantities used in physics and in modern science in general, starting with basic quantities such as length and mass, and the relationships between those quantities. This syste ...
'' (ISQ). The ISQ is based on the
quantities Quantity or amount is a property that can exist as a Counting, multitude or Magnitude (mathematics), magnitude, which illustrate discontinuity (mathematics), discontinuity and continuum (theory), continuity. Quantities can be compared in terms o ...
underlying each of the seven base units of the SI. Other quantities, such as
area Area is the quantity that expresses the extent of a region on the plane or on a curved surface. The area of a plane region or ''plane area'' refers to the area of a shape or planar lamina, while ''surface area'' refers to the area of an o ...
,
pressure Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and e ...
, and
electrical resistance 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 s ...
, 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, 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." Various consultative committees of the CIPM decided in 2016 that more than one ''mise en pratique'' would be developed for determining the value of each unit. These methods include the following: * At least three separate experiments be carried out yielding values having a relative standard uncertainty in the determination of the
kilogram The kilogram (also kilogramme) is the unit of mass in the International System of Units (SI), having the unit symbol kg. It is a widely used measure in science, engineering and commerce worldwide, and is often simply called a kilo colloquially. ...
of no more than and at least one of these values should be better than . Both the
Kibble balance A Kibble balance is an electromechanical measuring instrument that measures the weight of a test object very precisely by the electric current and voltage needed to produce a compensating force. It is a Metrology, metrological instrument that ca ...
and the
Avogadro project The scientific community The scientific community is a diverse network of interacting scientists. It includes many "working group, sub-communities" working on particular scientific fields, and within particular institutions; interdisciplinary and ...
should be included in the experiments and any differences between these be reconciled. *The definition of the
kelvin The kelvin, symbol K, is the primary unit of temperature in the International System of Units (SI), used alongside its metric prefix, prefixed forms and the degree Celsius. It is named after the Belfast-born and University of Glasgow-based eng ...
measured with a relative uncertainty of the
Boltzmann constant The Boltzmann constant ( or ) is the proportionality factor that relates the average relative kinetic energy of particles in a ideal gas, gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin and the gas ...
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 List of intergovernmental organizations, intergovernmental organisation, through which its 59 member-states act together on measur ...
(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'' (symbol mol) for an amount of substance, the '' pascal'' (symbol Pa) for
pressure Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and e ...
, the ''
siemens Siemens AG ( ) is a German Multinational corporation, multinational Conglomerate (company), conglomerate corporation and the largest industrial manufacturing company in Europe headquartered in Munich with branch offices abroad. The principal ...
'' (symbol S) for electrical conductance, the ''
becquerel The becquerel (; symbol: Bq) is the unit of Radioactive decay, radioactivity in the International System of Units (SI). One becquerel is defined as the activity (radioactivity), activity of a quantity of radioactive material in which one atomic n ...
'' (symbol Bq) for " activity referred to a
radionuclide A radionuclide (radioactive nuclide, radioisotope or radioactive isotope) is a nuclide that has excess nuclear energy, making it unstable. This excess energy can be used in one of three ways: emitted from the nucleus as gamma radiation; transfe ...
", the ''
gray Grey (more common in British English) or gray (more common in American English) is an intermediate color between black and white. It is a neutral or achromatic color, meaning literally that it is "without color", because it can be compose ...
'' (symbol Gy) for ionising radiation, the ''
sievert The sievert (symbol: SvNot be confused with the sverdrup or the svedberg, two non-SI units that sometimes use the same symbol.) is a unit in the International System of Units (SI) intended to represent the stochastic health risk of ionizing radi ...
'' (symbol Sv) as the unit of dose equivalent radiation, and the ''
katal The katal (symbol: kat) is the unit of catalytic activity in the International System of Units (SI) used for quantifying the catalytic activity of enzymes (that is, measuring the enzymatic activity level in enzyme catalysis) and other cat ...
'' (symbol kat) for catalytic activity. The range of defined prefixes pico- (10−12) to tera- (1012) was extended to quecto- (10−30) to quetta- (1030). The 1960 definition of the standard metre in terms of wavelengths of a specific emission of the krypton-86 atom was replaced in 1983 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 The Commonwealth Scientific and Industrial Research Organisation (CSIRO) is an Australian Government agency responsible for scientific research. CSIRO works with leading organisations around the world. From its headquarters in Canberra, CSIRO ...
, published in 2009 by the
Royal Society The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences. The society fulfils a number of roles: promoting science and its benefits, ...
, 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 metre was redefined in 1960, the
International Prototype of the Kilogram The International Prototype of the Kilogram (referred to by metrology, metrologists as the IPK or Le Grand K; sometimes called the ''wiktionary:ur-#Prefix, ur-kilogram,'' or ''urkilogram,'' particularly by German-language authors writing in Engli ...
(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 of foundational importance in quantum mechanics. The constant gives the relationship between the energy of a photon and its frequency, and by the mass-energy equivalenc ...
, an
elementary charge The elementary charge, usually denoted by is the electric charge carried by a single proton or, equivalently, the magnitude of the negative electric charge carried by a single electron, which has charge −1 . This elementary charge is a fundame ...
, the
Boltzmann constant The Boltzmann constant ( or ) is the proportionality factor that relates the average relative kinetic energy of particles in a ideal gas, gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin and the gas ...
, and the Avogadro constant – 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 Anders Celsius (; 27 November 170125 April 1744) was a Swedish astronomer An astronomer is a scientist in the field of astronomy who focuses their studies on a specific question or field outside the scope of Earth. They observe astronomical ...
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 Jean-Pierre Christin (31 May 1683 – 19 January 1755) was a French physicist, mathematician, astronomer, and musician. His proposal in 1743 to reverse the Celsius The degree Celsius is the unit of temperature Temperature is a physic ...
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 The French Academy of Sciences (French: ''Académie des sciences'') is a learned society, founded in 1666 by Louis XIV of France, Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French Scientific me ...
, 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 John Wilkins, (14 February 1614 – 19 November 1672) was an Anglican ministry, Anglican clergyman, Natural philosophy, natural philosopher, and author, and was one of the founders of the Royal Society. He was Bishop of Chester from 1668 unt ...
in 1668 and the concept of using the Earth's meridian as the basis of the definition of length, originally proposed in 1670 by the French abbot 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 (British English, British spelling) or meter (American English, American spelling; American and British English spelling differences#-re, -er, see spelling differences) (from the French unit , from the Greek language, Greek noun , "m ...
'', '' are'', ''
litre The litre (international spelling) or liter (American English American English, sometimes called United States English or U.S. English, is the set of variety (linguistics), varieties of the English language native to the United States. ...
'' and ''
grave A grave is a location where a cadaver, dead body (typically that of a human, although sometimes that of an animal) is burial, buried or interred after a funeral. Graves are usually located in special areas set aside for the purpose of burial ...
'' 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 ''
gram The gram (originally gramme; SI unit symbol g) is a unit of mass in the International System of Units (SI) equal to one one thousandth of a kilogram. Originally defined as of 1795 as "the absolute weight of a volume Volume is a measure ...
me'' and ''
kilogram The kilogram (also kilogramme) is the unit of mass in the International System of Units (SI), having the unit symbol kg. It is a widely used measure in science, engineering and commerce worldwide, and is often simply called a kilo colloquially. ...
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 The grave, abbreviated ''gv'', is the unit of mass used in the first metric system which was implemented in France in 1793. In 1795, the grave was renamed as the kilogram The kilogram (also kilogramme) is the unit of mass in the Internationa ...
'' were deposited in the
French National Archives The Archives nationales (, "National Archives" in English; abbreviated AN) are the national archives of France. They preserve the archives of the French state, apart from the archives of the Ministry of Armed Forces and Ministry of Foreign A ...
. 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 A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...
Carl Friedrich Gauss Johann Carl Friedrich Gauss (; german: Gauß ; la, Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician and physicist who made significant contributions to many fields in mathematics and science. Sometimes refer ...
, assisted by 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 terms. The technique used by Gauss was to equate the
torque In physics and mechanics, torque is the rotational equivalent of linear force. It is also referred to as the moment of force (also abbreviated to moment). It represents the capability of a force to produce change in the rotational motion of the ...
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 Spermaceti is a waxy substance found in the head cavities of the sperm whale The sperm whale or cachalot (''Physeter macrocephalus'') is the largest of the toothed whales and the largest toothed predator. It is the only living member of ...
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 oil lamp. The unit was defined as that illumination emanating from a lamp burning pure
rapeseed oil file:CanolaBlooms.JPG, Close-up of canola blooms file:Canola Flower.jpg, Canola flower Rapeseed oil is one of the oldest known Vegetable oil, vegetable oils. There are both Edible oil, edible and industrial forms produced from rapeseed, the see ...
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 Metrology is the scientific study of measurement. It establishes a common understanding of units, crucial in linking human activities. Modern metrology has its roots in the French Revolution's political motivation to standardise units in Fran ...
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 that was signed in Paris on 20 May 1875 by representatives of 17 nations (Argentina, Austria-Hungary, Belgium, Brazi ...
, 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 Platinum is a chemical element with the Symbol (chemistry), symbol Pt and atomic number 78. It is a density, dense, malleable, ductility, ductile, highly unreactive, precious metal, precious, silverish-white transition metal. Its name origina ...
-10%
iridium Iridium is a chemical element with the Symbol (chemistry), symbol Ir and atomic number 77. A very hard, brittle, silvery-white transition metal of the platinum group, it is considered the second-densest naturally occurring metal (after osmium) ...
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 The grave, abbreviated ''gv'', is the unit of mass used in the first metric system which was implemented in France in 1793. In 1795, the grave was renamed as the kilogram The kilogram (also kilogramme) is the unit of mass in the Internationa ...
'' 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 James Clerk Maxwell (13 June 1831 – 5 November 1879) was a Scottish mathematician and scientist responsible for the classical theory of electromagnetic radiation, which was the first theory to describe electricity, magnetism and light ...
, William Thomson (later Lord Kelvin) and others working under the auspices of the
British Association for the Advancement of Science The British Science Association (BSA) is a charity and learned society founded in 1831 to aid in the promotion and development of science. Until 2009 it was known as the British Association for the Advancement of Science (BA). The current Ch ...
, 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 based on the centimetre as the unit of length, the gram as the unit of mass, and the second as the unit of time. All CGS mechanics, mechani ...
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 In physics, energy (from Ancient Greek: wikt:ἐνέργεια#Ancient_Greek, ἐνέργεια, ''enérgeia'', “activity”) is the physical quantity, quantitative physical property, property that is #Energy transfer, transferred to a phy ...
, the
dyne The dyne (symbol: dyn; ) is a derived units of measurement, unit of force (physics), force specified in the centimetre–gram–second system of units, centimetre–gram–second (CGS) system of units, a predecessor of the modern International S ...
for
force In physics, a force is an influence that can change the 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 accelerate. Force can ...
, the
barye The barye (symbol: Ba), or sometimes barad, barrie, bary, baryd, baryed, or barie, is the centimetre–gram–second (CGS) unit of pressure Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object p ...
for
pressure Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and e ...
, the poise for
dynamic viscosity The viscosity of a fluid is a measure of its drag (physics), resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quant ...
and the stokes for
kinematic viscosity The viscosity of a fluid is a measure of its drag (physics), resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quant ...
. 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 and science, dimensional analysis is the analysis of the relationships between different physical quantities by identifying their base quantity, base quantities (such as length, mass, time, and electric current) and units of measur ...
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 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 particles, such as electrons or ions, moving through an electrical conductor or space. It is measured as the net rate of flow of electric charge through a surface or into a control volume. The moving par ...
,
voltage Voltage, also known as electric pressure, electric tension, or (electric) potential difference, is the difference in electric potential between two points. In a Electrostatics, static electric field, it corresponds to the Work (electrical), w ...
, or
electrical resistance 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 s ...
. 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, the darcy for permeability and " millimetres of mercury" for barometric and
blood pressure Blood pressure (BP) is the pressure of Circulatory system, circulating blood against the walls of blood vessels. Most of this pressure results from the heart pumping blood through the circulatory system. When used without qualification, the term ...
were developed or propagated, some of which incorporated
standard gravity The standard acceleration due to gravity (or standard acceleration of free fall), sometimes abbreviated as standard gravity, usually denoted by or , is the nominal gravitational acceleration of an object in a vacuum near the surface of the Earth. ...
in their definitions. At the end of the
Second World War World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the World War II by country, vast majority of the world's countries—including all of the great power ...
, 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 customary systems of measure, like the US customary system and British Imperial system.


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 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 Maxwell first introduced the concept of a coherent system, he identified three quantities that could be used as base units: mass, length, and time. 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 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 Metric units are unit of measurement, units based on the metre, gram or second and decimal (power of ten) multiples or sub-multiples of these. The most widely used examples are the units of the International System of Units (SI). By extension the ...
such as the
sverdrup In oceanography, the sverdrup (symbol: Sv) is a non-International System of Units, SI Metric_units#Volume_flow_rate, metric unit of volumetric flow rate, with equal to . It is equivalent to the SI derived unit cubic hectometer per second (symbol ...
and the darcy that exist outside of any system of units. Most of the units of the other metric systems are not recognised by the SI. Here are some examples. The centimetre–gram–second (CGS) system was the dominant metric system in the
physical science Physical science is a branch of natural science that studies non-living systems, in contrast to life science. It in turn has many branches, each referred to as a "physical science", together called the "physical sciences". Definition Phy ...
s and
electrical engineering Electrical engineering is an engineering discipline concerned with the study, design, and application of equipment, devices, and systems which use electricity, electronics, and electromagnetism. It emerged as an identifiable occupation in the l ...
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,
dyne The dyne (symbol: dyn; ) is a derived units of measurement, unit of force (physics), force specified in the centimetre–gram–second system of units, centimetre–gram–second (CGS) system of units, a predecessor of the modern International S ...
, erg,
barye The barye (symbol: Ba), or sometimes barad, barrie, bary, baryd, baryed, or barie, is the centimetre–gram–second (CGS) unit of pressure Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object p ...
, etc. in its
mechanical Mechanical may refer to: Machine * Machine (mechanical), a system of mechanisms that shape the actuator input to achieve a specific application of output forces and movement * Mechanical calculator, a device used to perform the basic operations of ...
sector, as well as the poise and 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 CGS electrostatic ('CGS-ESU', with the SI-unrecognised units of
statcoulomb The franklin (Fr) or statcoulomb (statC) electrostatic unit of charge (esu) is the units of measurement, physical unit for electrical charge used in the Centimetre–gram–second system of units#Electrostatic units (ESU), cgs-esu and Gaussian uni ...
,
statvolt The statvolt is a unit of voltage Voltage, also known as electric pressure, electric tension, or (electric) potential difference, is the difference in electric potential between two points. In a Electrostatics, static electric field, it co ...
,
statampere The statampere (statA) is the derived electromagnetic 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 ...
, etc.) and the CGS electromagnetic system ('CGS-EMU', with
abampere The abampere (abA), also called the biot (Bi) after Jean-Baptiste Biot, is the Centimetre–gram–second system of units#CGS approach to electromagnetic units, derived Electromagnetism, electromagnetic physical unit, unit of electric current in t ...
,
abcoulomb The abcoulomb (abC or aC) or electromagnetic unit of charge (emu of charge) is the derived physical unit A unit of measurement is a definite magnitude of a quantity Quantity or amount is a property that can exist as a multitude or ...
,
oersted The oersted (symbol Oe) is the coherent derived unit of the auxiliary magnetic field H in the centimetre–gram–second system of units The centimetre–gram–second system of units (abbreviated CGS or cgs) is a variant of the metric sys ...
, maxwell, abhenry, gilbert, etc.). A 'blend' of these two systems is still popular and is known as the Gaussian system (which includes the
gauss Johann Carl Friedrich Gauss (; german: Gauß ; la, Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician and physicist who made significant contributions to many fields in mathematics and science. Sometimes refer ...
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 The gravitational metric system (original French term ) is a non-standard system of units, which does not comply with the International System of Units (SI). It is built on the three base quantity, base quantities length, time and force with base u ...
, whose SI-unrecognised units include the
kilogram-force The kilogram-force (kgf or kgF), or kilopond (kp, from la, pondus, lit=weight), is a non-standard Gravitational metric system, gravitational metric unit of force. It does not comply with the International System of Units (SI) and is deprecated f ...
(kilopond),
technical atmosphere Technical may refer to: * Technical (vehicle) A technical, in professional military parlance often called a non-standard tactical vehicle (NSTV), is a light improvised fighting vehicle, typically an open-backed civilian pickup truck or four- ...
,
metric horsepower Horsepower (hp) is a unit of measurement of power, or the rate at which work is done, usually in reference to the output of engines or motors. There are many different standards and types of horsepower. Two common definitions used today are th ...
, etc. The 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 Ionizing radiation (or ionising radiation), including nuclear radiation, consists of subatomic particles or electromagnetic waves that have sufficient energy In physics, energy (from Ancient Greek: wikt:ἐνέργεια#Ancient_Greek, ...
( rutherford,
curie In computing Computing is any goal-oriented activity requiring, benefiting from, or creating computer, computing machinery. It includes the study and experimentation of algorithmic processes, and development of both computer hardware , hardware ...
, roentgen, rad, rem, etc.),
radiometry Radiometry is a set of techniques for measuring electromagnetic radiation In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic field, electromagnetic (EM) field, which propagate through space and carry momentu ...
( langley,
jansky The jansky (symbol Jy, plural ''janskys'') is a non-SI unit of spectral flux density, or spectral irradiance, used especially in radio astronomy. It is equivalent to 10−26 watts per square metre per hertz. The ''flux density'' or ''monochr ...
), photometry (
phot A phot (ph) is a photometric unit of illuminance In photometry (optics), photometry, illuminance is the total luminous flux incident on a surface, per unit area. It is a measure of how much the incident light illuminates the surface, wavelengt ...
,
nox In atmospheric chemistry, is shorthand for nitric oxide () and nitrogen dioxide (), the nitrogen oxides that are most relevant for air pollution. These gases contribute to the formation of smog and acid rain, as well as affecting tropos ...
, stilb, nit, metre-candle,17
/sup> lambert, apostilb, skot, brill, troland, talbot,
candlepower Candlepower (abbreviated as cp or CP) is a unit of measurement for luminous intensity In Photometry (optics), photometry, luminous intensity is a measure of the wavelength-weighted Power (physics), power emitted by a light source in a particula ...
,
candle A candle is an ignitable candle wick, wick embedded in wax, or another flammable solid substance such as tallow, that provides light, and in some cases, a Aroma compound, fragrance. A candle can also provide heat or a method of keeping time. ...
), thermodynamics (
calorie The calorie is a unit of energy. For historical reasons, two main definitions of "calorie" are in wide use. The large calorie, food calorie, or kilogram calorie was originally defined as the amount of heat needed to raise the temperature of on ...
), and spectroscopy ( reciprocal centimetre). Some other SI-unrecognised metric units that don't fit into any of the already mentioned categories include the are, bar,
barn A barn is an agricultural building usually on farms and used for various purposes. In North America, a barn refers to structures that house livestock, including cattle and horses, as well as equipment and fodder, and often grain.Allen G. N ...
,
fermi Enrico Fermi (; 29 September 1901 – 28 November 1954) was an Italian (later naturalized American) physicist and the creator of the world's first nuclear reactor, the Chicago Pile-1. He has been called the "architect of the Atomic Age, nuclea ...
, gradian (gon, grad, or grade), metric carat,
micron The micrometre (American and British English spelling differences#-re, -er, international spelling as used by the International Bureau of Weights and Measures; SI symbol: μm) or micrometer (American and British English spelling differences# ...
,
millimetre of mercury A millimetre of mercury is a Pressure measurement#Liquid column (manometer), manometric Unit of measurement, unit of pressure, formerly defined as the extra pressure generated by a column of mercury (element), mercury one millimetre high, and ...
,
torr The torr (symbol: Torr) is a Pressure#Units, unit of pressure based on an absolute scale, defined as exactly of a standard atmosphere (unit), atmosphere (). Thus one torr is exactly (≈ ). Historically, one torr was intended to be the ...
, millimetre (or centimetre, or metre) of water, millimicron, mho,
stere The stere or stère (st) is a units of measurement, unit of volume in the metric system, original metric system equal to one cubic metre. The stere is typically used for measuring large quantities of firewood or other cut wood, while the cubic me ...
,
x unit : ''For the software testing tools, see xUnit.'' The x unit (symbol xu) is a Units of measurement, unit of length approximately equal to 0.1 pm (10−13 m). It is used to quote the wavelength of X-rays and gamma rays. Originally def ...
, (unit of mass), (unit of magnetic flux density), and (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 or submultiple of the unit. All metric prefixes used today are decadic. Each prefix has a unique symbol that is prepended to any unit symbol. The pr ...
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 nit is just an SI-unrecognised name for the SI unit
candela per square metre The candela per square metre (symbol: cd/m2) is the unit of luminance in the International System of Units (SI). The unit is based on the candela, the SI unit of luminous intensity, and the square metre, the SI unit of area. The nit (symbol: nt) ...
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., = , The
angstrom The angstromEntry "angstrom" in the Oxford online dictionary. Retrieved on 2019-03-02 from https://en.oxforddictionaries.com/definition/angstrom.Entry "angstrom" in the Merriam-Webster online dictionary. Retrieved on 2019-03-02 from https://www.m ...
( = ), still used in various fields, 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 US), the jansky (in
radio astronomy Radio astronomy is a subfield of astronomy that studies Astronomical object, celestial objects at radio frequency, radio frequencies. The first detection of radio waves from an astronomical object was in 1933, when Karl Jansky at Bell Telephone La ...
), the gauss (in industry) and the CGS-Gaussian units more generally (in some subfields of physics), the metric horsepower (for engine power, in most of the non-English speaking world), 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 The International System of Units, known by the international abbreviation SI in all languages and sometimes Pleonasm#Acronyms and initialisms, pleona ...


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 an agency of the United States Department of Commerce whose mission is to promote American innovation and industrial competitiveness. NIST's activities are organized into Outline of p ...
2008 edition, .


External links

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

* ttps://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)


Spelling and usage


USMA Frequently Asked Questions about SI
{{DEFAULTSORT:International System Of Units Systems of units International standards