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The metric system is a
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 ...
that succeeded the decimalised system based on the metre that had been introduced in France in the 1790s. The historical development of these systems culminated in the definition of the International System of Units (SI) in the mid-20th century, under the oversight of an international standards body. Adopting the metric system is known as ''
metrication Metrication or metrification is the act or process of converting to the metric system of measurement. All over the world, countries have transitioned from local and traditional units of measurement to the metric system. This process began in ...
''. The historical evolution of metric systems has resulted in the recognition of several principles. Each of the fundamental dimensions of nature is expressed by a single base unit of measure. The definition of base units has increasingly been realised from natural principles, rather than by copies of physical artefacts. For quantities derived from the fundamental base units of the system, units derived from the base units are used—e.g., the square metre is the derived unit for area, a quantity derived from length. These derived units are coherent, which means that they involve only products of powers of the base units, without empirical factors. For any given quantity whose unit has a special name and symbol, an extended set of smaller and larger units is defined that are related by factors of powers of ten. The unit of time should be the second; the unit of length should be either the metre or a decimal multiple of it; and the unit of mass should be the gram or a decimal multiple of it. Metric systems have evolved since the 1790s, as science and technology have evolved, in providing a single universal measuring system. Before and in addition to the SI, some other examples of metric systems are the following: the MKS system of units and the MKSA systems, which are the direct forerunners of the SI; the centimetre–gram–second (CGS) system and its subtypes, the CGS electrostatic (cgs-esu) system, the CGS electromagnetic (cgs-emu) system, and their still-popular blend, the Gaussian system; the metre–tonne–second (MTS) system; and the gravitational metric systems, which can be based on either the metre or the centimetre, and either the gram(-force) or the kilogram(-force). The SI has been adopted as the official system of weights and measures by nearly all nations in the world.

Background

The
French Revolution The French Revolution ( ) was a period of radical political and societal change in France that began with the Estates General of 1789 and ended with the formation of the French Consulate in coup of 18 Brumaire, November 1799. Many of its ...
(1789–99) provided an opportunity for the French to reform their unwieldy and archaic system of many local weights and measures. Charles Maurice de Talleyrand championed a new system based on natural units, proposing to the French National Assembly in 1790 that such a system be developed. Talleyrand had ambitions that a new natural and standardised system would be embraced worldwide, and was keen to involve other countries in its development.
Great Britain Great Britain is an island in the North Atlantic Ocean off the northwest coast of continental Europe. With an area of , it is the largest of the British Isles, the largest European island and the ninth-largest island in the world. It i ...
ignored invitations to co-operate, so the French Academy of Sciences decided in 1791 to go it alone and they set up a commission for the purpose. The commission decided that the standard of length should be based on the
size of the Earth Figure of the Earth is a term of art in geodesy that refers to the size and shape used to model Earth. The size and shape it refers to depend on context, including the precision needed for the model. A sphere is a well-known historical approxima ...
. They defined that length to be the 'metre' and its length as one ten-millionth of the length of an Earth quadrant, the length of the meridian arc on the Earth's surface from the equator to the north pole. In 1799, after the
arc measurement Arc measurement, sometimes degree measurement (german: Gradmessung), is the astrogeodetic technique of determining of the radius of Earth – more specifically, the local Earth radius of curvature of the figure of the Earth – by relating the la ...
had been surveyed, the new system was launched in France. The units of the metric system, originally taken from observable features of nature, are now defined by seven physical constants being given exact numerical values in terms of the units. In the modern form of the International System of Units (SI), the seven
base units A base unit (also referred to as a fundamental unit) is a unit adopted for measurement of a '' base quantity''. A base quantity is one of a conventionally chosen subset of physical quantities, where no quantity in the subset can be expressed in ter ...
are: '' metre'' for length, '' kilogram'' for mass, '' second'' for time, '' ampere'' for electric current, '' kelvin'' for temperature, ''
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 t ...
'' for luminous intensity and ''
mole Mole (or Molé) may refer to: Animals * Mole (animal) or "true mole", mammals in the family Talpidae, found in Eurasia and North America * Golden moles, southern African mammals in the family Chrysochloridae, similar to but unrelated to Talpida ...
'' for amount of substance. These, together with their derived units, can measure any physical quantity. Derived units may have their own unit name, such as the
watt The watt (symbol: W) is the unit of power or radiant flux in the International System of Units (SI), equal to 1 joule per second or 1 kg⋅m2⋅s−3. It is used to quantify the rate of energy transfer. The watt is named after James ...
(J/s) and lux (cd/m2), or may just be expressed as combinations of base units, such as velocity (m/s) and acceleration (m/s2). The metric system was designed to have properties that make it easy to use and widely applicable, including units based on the natural world, decimal ratios, prefixes for multiples and sub-multiples, and a structure of base and derived units. It is also a
coherent system A coherent system of units is a system of units of measurement used to express physical quantities that are defined in such a way that the equations relating the numerical values expressed in the units of the system have exactly the same form, inc ...
, which means that its units do not introduce conversion factors not already present in equations relating quantities. It has a property called ''rationalisation'' that eliminates certain constants of proportionality in equations of physics. The metric system is extensible, and new derived units are defined as needed in fields such as radiology and chemistry. For example, 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 catalyst ...
, a derived unit for catalytic activity equivalent to one
mole Mole (or Molé) may refer to: Animals * Mole (animal) or "true mole", mammals in the family Talpidae, found in Eurasia and North America * Golden moles, southern African mammals in the family Chrysochloridae, similar to but unrelated to Talpida ...
per second (1 mol/s), was added in 1999.

Principles

Although the metric system has changed and developed since its inception, its basic concepts have hardly changed. Designed for transnational use, it consisted of a basic set of
units of measurement A unit of measurement is a definite 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 be expressed as a multi ...
, now known as
base units A base unit (also referred to as a fundamental unit) is a unit adopted for measurement of a '' base quantity''. A base quantity is one of a conventionally chosen subset of physical quantities, where no quantity in the subset can be expressed in ter ...
. Derived units were built up from the base units using logical rather than empirical relationships while multiples and submultiples of both base and derived units were decimal-based and identified by a standard set of prefixes.

Realisation

The base units used in a measurement system must be realisable. Each of the definitions of the base units in the SI is accompanied by a defined ''mise en pratique'' ractical realisationthat describes in detail at least one way in which the base unit can be measured. Where possible, definitions of the base units were developed so that any laboratory equipped with proper instruments would be able to realise a standard without reliance on an artefact held by another country. In practice, such realisation is done under the auspices of a mutual acceptance arrangement. In the SI, the standard metre is defined as exactly of the distance that light travels in a second. The realisation of the metre depends in turn on precise realisation of the second. There are both astronomical observation methods and laboratory measurement methods that are used to realise units of the standard metre. Because the speed of light is now exactly defined in terms of the metre, more precise measurement of the speed of light does not result in a more accurate figure for its velocity in standard units, but rather a more accurate definition of the metre. The accuracy of the measured speed of light is considered to be within 1 m/s, and the realisation of the metre is within about 3 parts in , or a relative accuracy of . The kilogram was originally defined as the mass of one cubic decimetre of water at 4 °C, standardized as the mass of a man-made artefact of platinum–iridium held in a laboratory in France, which was used until a new definition was introduced in May 2019. Replicas made in 1879 at the time of the artefact's fabrication and distributed to signatories of the Metre Convention serve as ''de facto'' standards of mass in those countries. Additional replicas have been fabricated since as additional countries have joined the convention. The replicas were subject to periodic validation by comparison to the original, called the IPK. It became apparent that either the IPK or the replicas or both were deteriorating, and are no longer comparable: they had diverged by 50 μg since fabrication, so figuratively, the accuracy of the kilogram was no better than 5 parts in a hundred million or a relative accuracy of . The accepted redefinition of SI base units replaced the IPK with an exact definition of the Planck constant as expressed in SI units, which defines the kilogram in terms of fundamental constants.

Base and derived unit structure

The metric system base units were originally adopted because they represented fundamental orthogonal dimensions of measurement corresponding to how we perceive nature: a spatial dimension, a time dimension, one for inertia, and later, a more subtle one for the dimension of an "invisible substance" known as electricity or more generally, electromagnetism. One and only one unit in each of these dimensions was defined, unlike older systems where multiple perceptual quantities with the same dimension were prevalent, like inches, feet and yards or ounces, pounds and tons. Units for other quantities like area and volume, which are also spatial dimensional quantities, were derived from the fundamental ones by logical relationships, so that a unit of square area for example, was the unit of length squared. Many derived units were already in use before and during the time the metric system evolved, because they represented convenient abstractions of whatever base units were defined for the system, especially in the sciences. So analogous units were scaled in terms of the units of the newly established metric system, and their names adopted into the system. Many of these were associated with electromagnetism. Other perceptual units, like volume, which were not defined in terms of base units, were incorporated into the system with definitions in the metric base units, so that the system remained simple. It grew in number of units, but the system retained a uniform structure.

Decimal ratios

Some customary systems of weights and measures have duodecimal (base-12) ratios, which means quantities are divisible by 2, 3, 4, and 6. The temporal system of hour–minute–second has sexagesimal (base-60) ratios, which is divisible by an extra integer of 5Example application of divisibility by 5: each numeral on the clock face represents 5 minutes. in addition to the divisors of 2,Example application of divisibility by 2: half an hour is widely used as a unit of time. 3,Example application of divisibility by 3: tea/coffee breaks during a conference are often scheduled to be 20 minutes (1/3 of an hour). 4,Example application of divisibility by 4: a quarter of an hour is widely used as a unit of time. and 6Example application of divisibility by 6: doctor's appointments are often billed by increments of 10 minutes (1/6 of an hour). of the duodecimal ratios, which is actually also the half-day–hour ratio. However, these systems of measures rarely stick to one constant ratio. As mentioned above, the ratio of a day to an hour is 24, unequal to the hour-to-minute or the minute-to-second ratio of 60. Similarly, the foot-to-inch ratio is 12, which is fourfold of the yard-to-foot ratio. A stone is 14 pounds but a pound is 16 ounces. There is no system of notation for successive fractions in these units: for example, of of a stone is not an ounce or a multiple of any unit. Even though any system of counting in a constant ratio has the algebraic property of multiplicative closure (a fraction of a fraction, or a multiple of a fraction is a quantity in the system), the decimal ratios as the predominant counting ratios in most human societies. Naturally, a decimal radix became the ratio between unit sizes of the metric system. In the decimal system, of is , which is also within the same decimal system.

Prefixes for multiples and submultiples

In the metric system, multiples and submultiples of units follow a decimal pattern.Non-SI units for time and plane angle measurement, inherited from existing systems, are an exception to the decimal-multiplier rule A common set of decimal-based prefixes that have the effect of multiplication or division by an integer power of ten can be applied to units that are themselves too large or too small for practical use. The concept of using consistent classical (
Latin Latin (, or , ) is a classical language belonging to the Italic branch of the Indo-European languages. Latin was originally a dialect spoken in the lower Tiber area (then known as Latium) around present-day Rome, but through the power of the ...
or
Greek Greek may refer to: Greece Anything of, from, or related to Greece, a country in Southern Europe: *Greeks, an ethnic group. *Greek language, a branch of the Indo-European language family. **Proto-Greek language, the assumed last common ancestor ...
) names for the prefixes was first proposed in a report by the
French Revolution The French Revolution ( ) was a period of radical political and societal change in France that began with the Estates General of 1789 and ended with the formation of the French Consulate in coup of 18 Brumaire, November 1799. Many of its ...
ary Commission on Weights and Measures in May 1793. The prefix ''kilo'', for example, is used to multiply the unit by 1000, and the prefix ''milli'' is to indicate a one-thousandth part of the unit. Thus the '' kilogram'' and '' kilometre'' are a thousand
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 of pure water equal to th ...
s and metres respectively, and a '' milligram'' and '' millimetre'' are one thousandth of a gram and metre respectively. These relations can be written symbolically as: In the early days, multipliers that were positive powers of ten were given Greek-derived prefixes such as ''kilo-'' and ''mega-'', and those that were negative powers of ten were given Latin-derived prefixes such as ''centi-'' and ''milli-''. However, 1935 extensions to the prefix system did not follow this convention: the prefixes ''nano-'' and ''micro-'', for example have Greek roots. During the 19th century the prefix ''myria-'', derived from the Greek word μύριοι (''mýrioi''), was used as a multiplier for . When applying prefixes to derived units of area and volume that are expressed in terms of units of length squared or cubed, the square and cube operators are applied to the unit of length including the prefix, as illustrated below. Prefixes are not usually used to indicate multiples of a second greater than 1; the non-SI units of minute, hour and day are used instead. On the other hand, prefixes are used for multiples of the non-SI unit of volume, the litre (l, L) such as millilitres (ml).

Coherence

Each variant of the metric system has a degree of coherence—the derived units are directly related to the base units without the need for intermediate conversion factors. For example, in a coherent system the units of force, energy and
power Power most often refers to: * Power (physics), meaning "rate of doing work" ** Engine power, the power put out by an engine ** Electric power * Power (social and political), the ability to influence people or events ** Abusive power Power may a ...
are chosen so that the equations hold without the introduction of unit conversion factors. Once a set of coherent units have been defined, other relationships in physics that use those units will automatically be true. Therefore, Einstein's mass–energy equation, , does not require extraneous constants when expressed in coherent units. The CGS system had two units of energy, the erg that was related to mechanics and the calorie that was related to
thermal energy The term "thermal energy" is used loosely in various contexts in physics and engineering. It can refer to several different well-defined physical concepts. These include the internal energy or enthalpy of a body of matter and radiation; heat, de ...
; so only one of them (the erg) could bear a coherent relationship to the base units. Coherence was a design aim of SI, which resulted in only one unit of energy being defined – the joule.

Rationalisation

Maxwell's equations of electromagnetism contained a factor relating to steradians, representative of the fact that electric charges and magnetic fields may be considered to emanate from a point and propagate equally in all directions, i.e. spherically. This factor appeared awkwardly in many equations of physics dealing with the dimensionality of electromagnetism and sometimes other things.

Common metric systems

A number of different metric system have been developed, all using the ''Mètre des Archives'' and ''Kilogramme des Archives'' (or their descendants) as their base units, but differing in the definitions of the various derived units.

Gaussian second and the first mechanical system of units

In 1832, Gauss used the astronomical second as a base unit in defining the gravitation of the earth, and together with the gram and millimetre, became the first system of mechanical units.

Centimetre–gram–second systems

The centimetre–gram–second system of units (CGS) was the first coherent metric system, having been developed in the 1860s and promoted by Maxwell and Thomson. In 1874, this system was formally promoted by the British Association for the Advancement of Science (BAAS). The system's characteristics are that density is expressed in , force expressed in
dyne The dyne (symbol: dyn; ) is a derived unit of force specified in the centimetre–gram–second (CGS) system of units, a predecessor of the modern SI. History The name dyne was first proposed as a CGS unit of force in 1873 by a Committee of ...
s and mechanical energy in ergs. Thermal energy was defined in calories, one calorie being the energy required to raise the temperature of one gram of water from 15.5 °C to 16.5 °C. The meeting also recognised two sets of units for electrical and magnetic properties – the electrostatic set of units and the electromagnetic set of units.

The EMU, ESU and Gaussian systems of electrical units

Several systems of electrical units were defined following discovery of Ohm's law in 1824.

International System of Electrical and Magnetic Units

The CGS units of electricity were cumbersome to work with. This was remedied at the 1893 International Electrical Congress held in Chicago by defining the "international" ampere and ohm using definitions based on the metre, kilogram and second.

Other early electromagnetic systems of units

During the same period in which the CGS system was being extended to include electromagnetism, other systems were developed, distinguished by their choice of coherent base unit, including the Practical System of Electric Units, or QES (quad–eleventhgram–second) system, was being used. Here, the base units are the quad, equal to (approximately a quadrant of the earth's circumference), the eleventhgram, equal to , and the second. These were chosen so that the corresponding electrical units of potential difference, current and resistance had a convenient magnitude.

MKS and MKSA systems

In 1901, Giovanni Giorgi showed that by adding an electrical unit as a fourth base unit, the various anomalies in electromagnetic systems could be resolved. The metre–kilogram–second– coulomb (MKSC) and metre–kilogram–second– ampere (MKSA) systems are examples of such systems. The International System of Units (''Système international d'unités'' or SI) is the current international standard metric system and is also the system most widely used around the world. It is an extension of Giorgi's MKSA system – its base units are the metre, kilogram, second, ampere, kelvin,
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 t ...
and
mole Mole (or Molé) may refer to: Animals * Mole (animal) or "true mole", mammals in the family Talpidae, found in Eurasia and North America * Golden moles, southern African mammals in the family Chrysochloridae, similar to but unrelated to Talpida ...
. The MKS (metre–kilogram–second) system came into existence in 1889, when artefacts for the metre and kilogram were fabricated according to the Metre Convention. Early in the 20th century, an unspecified electrical unit was added, and the system was called MKSX. When it became apparent that the unit would be the ampere, the system was referred to as the MKSA system, and was the direct predecessor of the SI.

Metre–tonne–second systems

The metre–tonne–second system of units (MTS) was based on the metre, tonne and second – the unit of force was the
sthène The sthène (; symbol sn), sometimes spelled (or misspelled) sthéne or sthene (from grc, σθένος, sthénos, force), is an obsolete unit of force (physics), force or thrust in the metre–tonne–second system of units (mts) introduced in Fra ...
and the unit of pressure was the pièze. It was invented in France for industrial use and from 1933 to 1955 was used both in France and in the
Soviet Union The Soviet Union,. officially the Union of Soviet Socialist Republics. (USSR),. was a List of former transcontinental countries#Since 1700, transcontinental country that spanned much of Eurasia from 1922 to 1991. A flagship communist state, ...
.

Gravitational systems

Gravitational metric systems use the kilogram-force (kilopond) as a base unit of force, with mass measured in a unit known as the hyl, ''Technische Masseneinheit'' (TME), mug or metric slug. Although the CGPM passed a resolution in 1901 defining the standard value of acceleration due to gravity to be 980.665 cm/s2, gravitational units are not part of the International System of Units (SI).

International System of Units

The International System of Units is the modern metric system. It is based on the metre–kilogram–second–ampere (MKSA) system of units from early in the 20th century. It also includes numerous coherent derived units for common quantities like power (watt) and irradience (lumen). Electrical units were taken from the International system then in use. Other units like those for energy (joule) were modelled on those from the older CGS system, but scaled to be coherent with MKSA units. Two additional base units – the ''kelvin'', which is equivalent to degree Celsius for change in thermodynamic temperature but set so that 0 K is absolute zero, and the ''candela'', which is roughly equivalent to the international candle unit of illumination – were introduced. Later, another base unit, the ''mole'', a unit of amount of substance equivalent to the
Avogadro number The Avogadro constant, commonly denoted or , is the proportionality factor that relates the number of constituent particles (usually molecules, atoms or ions) in a sample with the amount of substance in that sample. It is an SI defining co ...
number of specified molecules, was added along with several other derived units. The system was promulgated by the General Conference on Weights and Measures (French: ''Conférence générale des poids et mesures'' – CGPM) in 1960. At that time, the metre was redefined in terms of the wavelength of a spectral line of the
krypton-86 There are 34 known isotopes of krypton (36Kr) with atomic mass numbers from 69 through 102. Naturally occurring krypton is made of five stable isotopes and one () which is slightly radioactive with an extremely long half-life, plus traces of radi ...
A stable isotope of an inert gas that occurs in undetectable or trace amounts naturally atom, and the standard metre artefact from 1889 was retired. Today, the International system of units consists of 7 base units and innumerable coherent derived units including 22 with special names. The last new derived unit, the ''katal'' for catalytic activity, was added in 1999. All the base units except the second are now defined in terms of exact and invariant constants of physics or mathematics, barring those parts of their definitions which are dependent on the second itself. As a consequence, the speed of light has now become an exactly defined constant, and defines the metre as of the distance light travels in a second. The kilogram was defined by a cylinder of platinum-iridium alloy until a new definition in terms of natural physical constants was adopted in 2019. As of 2022, the range of decimal prefixes has been extended to those for 1030 (''quetta–'') and 10−30 (''quecto–''). The International System of Units has been adopted as the official system of weights and measures by all nations in the world except for Myanmar, Liberia, and the United States. In the United States, the Metric Conversion Act of 1975 declared the metric system to be the "preferred system of weights and measures" but did not suspend use of customary units, and the United States is the only industrialised country where commercial and standards activities do not predominantly use the metric system.

* Binary prefix, used in computer science * Electrostatic units * History of measurement * ISO/IEC 80000, international standard of quantities and their units, superseding
ISO 31 ISO 31 ( Quantities and units, International Organization for Standardization, 1992) is a superseded international standard concerning physical quantities, units of measurement, their interrrelationships and their presentation. It was revised and ...
* List of metric units * Metrology *
Unified Code for Units of Measure The Unified Code for Units of Measure (UCUM) is a system of codes for unambiguously representing measurement units. Its primary purpose is machine-to-machine communication rather than communication between humans. The code set includes all units de ...
* International System of Units