Metric system

# Metric system

Overview
The metric system is an international decimal
Decimal
The decimal numeral system has ten as its base. It is the numerical base most widely used by modern civilizations....

ised system of measurement
Systems of measurement
A system of measurement is a set of units which can be used to specify anything which can be measured and were historically important, regulated and defined because of trade and internal commerce...

. France
France
The French Republic , The French Republic , The French Republic , (commonly known as France , is a unitary semi-presidential republic in Western Europe with several overseas territories and islands located on other continents and in the Indian, Pacific, and Atlantic oceans. Metropolitan France...

was first to adopt a metric system, in 1799, and a metric system is now the official system of measurement
Systems of measurement
A system of measurement is a set of units which can be used to specify anything which can be measured and were historically important, regulated and defined because of trade and internal commerce...

, used in almost every country in the world. The United States is the only industrialised country in the world that has not defined a metric system as its official system of measurement, although the use of a metric system has been sanctioned for use there since 1866. Although the United Kingdom committed to officially adopting a metric system for many measurement applications, one is still not in universal use there and the customary imperial system is still in common and widespread use. Although the originators intended to devise a system that was equally accessible to all, it proved necessary to use prototype units under the custody of government or other approved authorities as standards. Until 1875, control of the prototype units of measure was maintained by the French Government when it passed to an inter-governmental organisation – the Conférence générale des poids et mesures (CGPM). It is now hoped that the last of these prototypes can be retired by 2014.
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Encyclopedia
The metric system is an international decimal
Decimal
The decimal numeral system has ten as its base. It is the numerical base most widely used by modern civilizations....

ised system of measurement
Systems of measurement
A system of measurement is a set of units which can be used to specify anything which can be measured and were historically important, regulated and defined because of trade and internal commerce...

. France
France
The French Republic , The French Republic , The French Republic , (commonly known as France , is a unitary semi-presidential republic in Western Europe with several overseas territories and islands located on other continents and in the Indian, Pacific, and Atlantic oceans. Metropolitan France...

was first to adopt a metric system, in 1799, and a metric system is now the official system of measurement
Systems of measurement
A system of measurement is a set of units which can be used to specify anything which can be measured and were historically important, regulated and defined because of trade and internal commerce...

, used in almost every country in the world. The United States is the only industrialised country in the world that has not defined a metric system as its official system of measurement, although the use of a metric system has been sanctioned for use there since 1866. Although the United Kingdom committed to officially adopting a metric system for many measurement applications, one is still not in universal use there and the customary imperial system is still in common and widespread use. Although the originators intended to devise a system that was equally accessible to all, it proved necessary to use prototype units under the custody of government or other approved authorities as standards. Until 1875, control of the prototype units of measure was maintained by the French Government when it passed to an inter-governmental organisation – the Conférence générale des poids et mesures (CGPM). It is now hoped that the last of these prototypes can be retired by 2014.

From its beginning, the main feature of the metric system was the standard set of inter-related base units and a standard set of prefixes in powers of ten. These base units are used to derive larger and smaller units and replaced a huge number of unstandardised units of measure that existed previously. While the system was first developed for commercial use, its coherent set of units made it particularly suitable for scientific and engineering purposes.

The uncoordinated use of the metric system by different scientific and engineering disciplines, particularly in the late 19th century, resulted in different choices of fundamental unit
Fundamental unit
A set of fundamental units is a set of units for physical quantities from which every other unit can be generated.In the language of measurement, quantities are quantifiable aspects of the world, such as time, distance, velocity, mass, momentum, energy, and weight, and units are used to describe...

s, even though all were based on the same definitions of the metre
Metre
The metre , symbol m, is the base unit of length in the International System of Units . Originally intended to be one ten-millionth of the distance from the Earth's equator to the North Pole , its definition has been periodically refined to reflect growing knowledge of metrology...

and the kilogram
Kilogram
The kilogram or kilogramme , also known as the kilo, is the base unit of mass in the International System of Units and is defined as being equal to the mass of the International Prototype Kilogram , which is almost exactly equal to the mass of one liter of water...

. During the 20th century, efforts were made to rationalise these units and in 1960 the CGPM published the International System of Units
International System of Units
The International System of Units is the modern form of the metric system and is generally a system of units of measurement devised around seven base units and the convenience of the number ten. The older metric system included several groups of units...

("Système international d'unités" in French, hence "SI") which, since then, has been the internationally recognised standard
International standard
International standards are standards developed by international standards organizations. International standards are available for consideration and use, worldwide...

metric system.

## Features

Although the metric system has changed and developed since its inception, its basic features have remained constant.

### Universality

The metric system was, in the words of the French philosopher Condorcet
Marquis de Condorcet
Marie Jean Antoine Nicolas de Caritat, marquis de Condorcet , known as Nicolas de Condorcet, was a French philosopher, mathematician, and early political scientist whose Condorcet method in voting tally selects the candidate who would beat each of the other candidates in a run-off election...

to be "for all people for all time". It was designed for ordinary people, for engineers who worked in human-related measurements and for astronomers and physicists who worked with numbers both small and large, hence the huge range of prefixes that have now been defined in SI.

The metric system was designed to be universal, that is, available to all. When the French Government first investigated the idea of overhauling their system of measurement, Talleyrand, in the late 1780s, acting on Concordet's advice, invited Riggs
John Riggs Miller
Sir John Riggs-Miller, 1st Baronet was an Anglo-Irish politician who championed reform of the customary system of weights and measures in favour of a scientifically founded system.-Early life:...

, a British Parliamentarian and Jefferson
Thomas Jefferson
Thomas Jefferson was the principal author of the United States Declaration of Independence and the Statute of Virginia for Religious Freedom , the third President of the United States and founder of the University of Virginia...

, the American Secretary of State to George Washington
George Washington
George Washington was the dominant military and political leader of the new United States of America from 1775 to 1799. He led the American victory over Great Britain in the American Revolutionary War as commander-in-chief of the Continental Army from 1775 to 1783, and presided over the writing of...

, to work with the French in producing an international standard by promoting legislation in their respective legislative bodies. However, these overtures failed and the custody of the metric system remained in the hands of the French Government until 1875.

To help make it universal, common unit symbols that are independent of language were developed. Thus the length unit symbol "km" is used in French and in British English for "kilometre", in German and in American English for "kilometer", in Spanish for "kilómetro", in Portuguese for "quilómetro", in Italian for "chilometro", in Greek for "χιλιόμετρα", in Russian for "Километр" and so on.

### Decimal multiples

The metric system is decimal, except where the non-SI units for time and plane angle measurement are concerned. All multiples and divisions of the decimal units are factors of the power of ten, an idea first proposed by Stevin
Simon Stevin
Simon Stevin was a Flemish mathematician and military engineer. He was active in a great many areas of science and engineering, both theoretical and practical...

in 1586.

Decimal prefixes are a characteristic of the metric system; the use of base 10 arithmetic aids in unit conversion. Differences in expressing units are simply a matter of shifting the decimal point or changing an exponent; for example, the speed of light
Speed of light
The speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...

may be expressed as  km/s or .

The use of decimal multiples results in less convenient non-integer quantities for common divisions such as by 3,4, 6 and 12.

### Non-SI units

The tonne
Tonne
The tonne, known as the metric ton in the US , often put pleonastically as "metric tonne" to avoid confusion with ton, is a metric system unit of mass equal to 1000 kilograms. The tonne is not an International System of Units unit, but is accepted for use with the SI...

(1000 kg), the litre (now defined as exactly 0.001 m3), and the hectare(10000 m2), all of which were initially defined by the CGPM in 1879 and which are classified as non-SI units, have been given CGPM approval to continue to be used alongside the SI units.

### Prefixes

A common set of decimal-based prefixes is applied to some units which are too large or too small for practical use without adjustment. The effect of the prefixes is to multiply or divide the unit by a factor of ten, one hundred or an integer power of one thousand. (This idea was first suggested by Mouton
Gabriel Mouton
Gabriel Mouton was a French abbot and scientist. He was a doctor of theology from Lyon, but was also interested in mathematics and astronomy....

in 1670.) 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 grams and metres respectively, and a milligram and millimetre are one thousandth of a gram and metre respectively. These relations can be written symbolically as:
1 mg = 0.001 g
1 km = 1000 m

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 here:
1 mm2 (square millimetre) = (1 mm)2 = (0.001 m)2 =
1 km2 (square kilometre) = (1 km)2 = (1000 m)2 =
1 mm3 (cubic millimetre) = (1 mm)3 = (0.001 m)3 =
1 km3 (cubic kilometre) = (1 km)3 = (1000 m)3 =

On the other hand, prefixes are used for multiples of the non-SI unit of volume, the litre (l, L), or the stere (cubic metre). Examples:
1 ml = 0.001 l
1 kl = 1000 l

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.

Initially positive powers of ten had Greek-derived prefixes and negative power of ten Latin-derived prefixes. However later SI extensions to the prefix system did not follow the Greek-greater-than-one/Latin-less-than-one convention. The most familiar prefixes in everyday use are kilo-, which is of Greek origin, and centi- and milli- which are of Latin origin. Most other metric measurements also use prefixes rooted in Latin or Greek: deci- has a Latin root, while nano-, micro-, deca-, hecto-, mega-, giga- have Greek roots.

During the 19th century, the factor 10,000 was also used. The corresponding prefixes myria- (104) and myrio- (10-4) were both Greek-derived.

### Replicable prototypes

The initial way to establish a standard was to make prototypes of the base units and distribute copies to approved centres. This made the new standard reliant on the original prototypes, which would be in conflict with the previous goal, since all countries would have to refer to the one holding the prototypes.

Instead, where possible, definitions of the base units were developed so that any laboratory equipped with proper instruments would be able to construct their own copies of the standard. In the original version of the metric system the base units could be derived from a specified length (the metre) and the weight [mass] of a specified volume ( of a cubic metre) of pure water. Initially the Assemblée Constituante considered defining the metre as the length of a pendulum that has a period of one second at 45°N and an altitude equal to sea level. The altitude and latitude were specified to accommodate variations in gravity – the specified latitude was a compromise between the latitude of , and the median parallel of the United States (38°N) to accommodate variations. However Borda persuaded the Assemblée Constituante that a survey having its ends at sea level and based on a meridian that spanned at least 10% of the earth's quadrant would be more appropriate for such a basis.

### Realisability

The base units used in the metric system must be realisable, ideally with reference to natural phenomena rather than unique artifacts. Each of the base units in SI is accompanied by a mise en pratique published by the BIPM that describes in detail at least one way in which the base unit can be measured.

Two of the base units originally depended on artifacts – the metre and the kilogram. The original prototypes of each artifact were adopted in 1799 and replaced in 1889. The 1889 prototypes used the best technology of the day to ensure stability.

In 1889 there was no generally accepted theory regarding the nature of light but by 1960 the wavelength of specific light spectra could give a more accurate and reproducible value than a prototype metre. In that year the prototype metre was replaced by a formal definition which defines the metre in terms of the wavelength of specified light spectra. By 1983 it was accepted that the speed of light was constant
Theory of relativity
The theory of relativity, or simply relativity, encompasses two theories of Albert Einstein: special relativity and general relativity. However, the word relativity is sometimes used in reference to Galilean invariance....

and that this provided a more reproducible procedure for measuring length, the metre was redefined in terms of the speed of light. These definitions give a much better reproducibility and also allow anyone, anywhere to make their own "standard" metre (assuming that they have a good enough laboratory).

Similarly, at the 13th convocation of the GCPM in 1968, the definitive second was redefined in terms of measurements taken from atomic clocks rather than from the earth's rotation; in 2008 the solar day was 0.002 s longer than in 1820 but it was only in the 1960s that this could be measured more accurately using clocks rather than relying on astronomy
Astronomy
Astronomy is a natural science that deals with the study of celestial objects and phenomena that originate outside the atmosphere of Earth...

.

### Coherence

Each variant of the metric system has a degree of coherence – the various derived units being directly related to the base units without the need of intermediate conversion factors. Whereas the cgs system had two units of energy, the erg
Erg
An erg is the unit of energy and mechanical work in the centimetre-gram-second system of units, symbol "erg". Its name is derived from the Greek ergon, meaning "work"....

that was related to mechanics
Mechanics
Mechanics is the branch of physics concerned with the behavior of physical bodies when subjected to forces or displacements, and the subsequent effects of the bodies on their environment....

and the calorie
Calorie
The calorie is a pre-SI metric unit of energy. It was first defined by Nicolas Clément in 1824 as a unit of heat, entering French and English dictionaries between 1841 and 1867. In most fields its use is archaic, having been replaced by the SI unit of energy, the joule...

that was related to thermal energy
Thermal energy
Thermal energy is the part of the total internal energy of a thermodynamic system or sample of matter that results in the system's temperature....

, coherence was a design aim of SI resulting in only one unit of energy – the joule. For example, the units of force, energy and power are chosen so that the equations
force = mass × acceleration
energy = force × distance
energy = power × time

hold without the introduction of constant factors. Many relationships in physics, including Einstein's
Albert Einstein
Albert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history...

mass-energy equation, E = mc2, do not require extraneous constants when expressed in coherent units.

In SI, the unit of power is the "watt" which is defined as "one joule per second".

Other defined units are derived in a similar way building up on the base units.

## History

In 1586, the Flemish mathematician Simon Stevin
Simon Stevin
Simon Stevin was a Flemish mathematician and military engineer. He was active in a great many areas of science and engineering, both theoretical and practical...

published a small pamphlet called De Thiende ("the tenth"). Decimal fractions had been employed for the extraction of square roots some five centuries before his time, but nobody used decimal numbers in daily life. Stevin declared that using decimals was so important that the universal introduction of decimal weights, measures and coinage was only a matter of time.

The idea of a metric system was proposed by John Wilkins
John Wilkins
John Wilkins FRS was an English clergyman, natural philosopher and author, as well as a founder of the Invisible College and one of the founders of the Royal Society, and Bishop of Chester from 1668 until his death....

, first secretary of the Royal Society
Royal Society
The Royal Society of London for Improving Natural Knowledge, known simply as the Royal Society, is a learned society for science, and is possibly the oldest such society in existence. Founded in November 1660, it was granted a Royal Charter by King Charles II as the "Royal Society of London"...

of London in 1668. Two years later, in 1670, Gabriel Mouton
Gabriel Mouton
Gabriel Mouton was a French abbot and scientist. He was a doctor of theology from Lyon, but was also interested in mathematics and astronomy....

, a French abbot and scientist, proposed a decimal system of measurement based on the circumference of the Earth. His suggestion was that a unit, the milliare, be defined as a minute of arc along a meridian. He then suggested a system of sub-units, dividing successively by factors of ten into the centuria, decuria, virga, virgula, decima, centesima, and millesima. His ideas attracted interest at the time, and were supported by both Jean Picard
Jean Picard
Jean-Felix Picard was a French astronomer and priest born in La Flèche, where he studied at the Jesuit Collège Royal Henry-Le-Grand. He was the first person to measure the size of the Earth to a reasonable degree of accuracy in a survey conducted in 1669–70, for which he is honored with a...

and Christiaan Huygens in 1673, and also studied at the Royal Society in London. In the same year, Gottfried Leibniz
Gottfried Leibniz
Gottfried Wilhelm Leibniz was a German philosopher and mathematician. He wrote in different languages, primarily in Latin , French and German ....

independently made proposals similar to those of Mouton.

In pre-revolutionary Europe, each state had its own system of units of measure. Some countries, such as Spain and Russia, saw the advantages of harmonising their units of measure with those of their trading partners. However, vested interests who profited from variations in units of measure opposed this. This was particularly prevalent in France where there was a huge inconsistency in the size of units of measure. During the early years of the French Revolution
French Revolution
The French Revolution , sometimes distinguished as the 'Great French Revolution' , was a period of radical social and political upheaval in France and Europe. The absolute monarchy that had ruled France for centuries collapsed in three years...

, the leaders of the French revolutionary Assemblée Constituante decided that rather than standardising the size of the existing units, they would a introduce a completely new system based on the principles of logic and natural phenomena.

Initially France attempted to work with other countries towards the adoption of a common set of units of measure. Among the supporters of such an international system of units was Thomas Jefferson
Thomas Jefferson
Thomas Jefferson was the principal author of the United States Declaration of Independence and the Statute of Virginia for Religious Freedom , the third President of the United States and founder of the University of Virginia...

who, in 1790, presented a document Plan for Establishing Uniformity in the Coinage, Weights, and Measures of the United States to congress in which he advocated a decimal system that used traditional names for units (such as ten inches per foot). The report was considered but not adopted by Congress. There was little support from other countries.

### Original system

The law of 18 Germinal, Year III (7 April 1795) defined five units of measure:
• The metre
Metre
The metre , symbol m, is the base unit of length in the International System of Units . Originally intended to be one ten-millionth of the distance from the Earth's equator to the North Pole , its definition has been periodically refined to reflect growing knowledge of metrology...

for length
• The are (100 m2) for area [of land]
• The stère
Stère
The stere or stère is a unit of volume in the original metric system equal to one cubic metre. The name was coined from the Greek στερεός stereos 'solid' in 1793 France as a metric equivalent to the cord. The stère is typically used for measuring large quantities of firewood or other cut wood,...

(1 m3) for volume of stacked firewood
• The litre
Litre
pic|200px|right|thumb|One litre is equivalent to this cubeEach side is 10 cm1 litre water = 1 kilogram water The litre is a metric system unit of volume equal to 1 cubic decimetre , to 1,000 cubic centimetres , and to 1/1,000 cubic metre...

(1 dm3) for volumes of liquid
• The gram
Gram
The gram is a metric system unit of mass....

for mass.

This system continued the tradition of having separate base units for geometrically related dimensions, e.g., metre
Metre
The metre , symbol m, is the base unit of length in the International System of Units . Originally intended to be one ten-millionth of the distance from the Earth's equator to the North Pole , its definition has been periodically refined to reflect growing knowledge of metrology...

for lengths, are (100 m2) for areas, stère
Stère
The stere or stère is a unit of volume in the original metric system equal to one cubic metre. The name was coined from the Greek στερεός stereos 'solid' in 1793 France as a metric equivalent to the cord. The stère is typically used for measuring large quantities of firewood or other cut wood,...

(1 m3) for dry capacities, and litre
Litre
pic|200px|right|thumb|One litre is equivalent to this cubeEach side is 10 cm1 litre water = 1 kilogram water The litre is a metric system unit of volume equal to 1 cubic decimetre , to 1,000 cubic centimetres , and to 1/1,000 cubic metre...

(1 dm3) for liquid capacities. The hectare
Hectare
The hectare is a metric unit of area defined as 10,000 square metres , and primarily used in the measurement of land. In 1795, when the metric system was introduced, the are was defined as being 100 square metres and the hectare was thus 100 ares or 1/100 km2...

, equal to a hundred ares, is the area of a square 100 metres on a side (about 2.47 acre
Acre
The acre is a unit of area in a number of different systems, including the imperial and U.S. customary systems. The most commonly used acres today are the international acre and, in the United States, the survey acre. The most common use of the acre is to measure tracts of land.The acre is related...

s), and is still in use. The early metric system included only a few prefixes
SI prefix
The International System of Units specifies a set of unit prefixes known as SI prefixes or metric prefixes. An SI prefix is a name that precedes a basic unit of measure to indicate a decadic multiple or fraction of the unit. Each prefix has a unique symbol that is prepended to the unit symbol...

from milli
Milli
Milli is a prefix in the metric system denoting a factor of one thousandth . Adopted in 1795, the prefix comes from the Latin mille, meaning one thousand ....

(one thousandth) to myria (ten thousand), and they were based on powers of 10 unlike later prefixes added in the SI, which are based on powers of 1,000.

Originally the kilogram
Kilogram
The kilogram or kilogramme , also known as the kilo, is the base unit of mass in the International System of Units and is defined as being equal to the mass of the International Prototype Kilogram , which is almost exactly equal to the mass of one liter of water...

was called the "grave"; the "gram" being an alternative name for a thousandth of a grave. However, the word "grave", being a synonym for the title "count
Count
A count or countess is an aristocratic nobleman in European countries. The word count came into English from the French comte, itself from Latin comes—in its accusative comitem—meaning "companion", and later "companion of the emperor, delegate of the emperor". The adjective form of the word is...

" had aristocratic connotations and was renamed the kilogram.

France officially adopted the metric system on 10 December 1799 with conversion being mandatory first in Paris and then across the provinces.

The areas that were annexed by France during the Napoleonic era inherited the metric system. In 1812, Napoleon introduced a system known as mesures usuelles
Mesures usuelles
Mesures usuelles were a system of measurement introduced by Napoleon I in 1812 to act as compromise between the metric system and traditional measurements...

which used the names of pre-metric units of measure, but defined them in terms of metric units – for example, the livre metrique (metric pound) was 500 g and the toise metrique (metric fathom) was 2 metres. After the Congress of Vienna
Congress of Vienna
The Congress of Vienna was a conference of ambassadors of European states chaired by Klemens Wenzel von Metternich, and held in Vienna from September, 1814 to June, 1815. The objective of the Congress was to settle the many issues arising from the French Revolutionary Wars, the Napoleonic Wars,...

in 1815, France lost the territories that she had annexed; some, such as the Papal States
Papal States
The Papal State, State of the Church, or Pontifical States were among the major historical states of Italy from roughly the 6th century until the Italian peninsula was unified in 1861 by the Kingdom of Piedmont-Sardinia .The Papal States comprised territories under...

reverted to their pre-revolutionary units of measure, others such as Baden
Baden is a historical state on the east bank of the Rhine in the southwest of Germany, now the western part of the Baden-Württemberg of Germany....

adopted a modified version of the mesures usuelles, but France kept her system of measurement intact.

In 1817, the Netherlands
Netherlands
The Netherlands is a constituent country of the Kingdom of the Netherlands, located mainly in North-West Europe and with several islands in the Caribbean. Mainland Netherlands borders the North Sea to the north and west, Belgium to the south, and Germany to the east, and shares maritime borders...

reintroduced the metric system, but used pre-revolutionary names
Dutch units of measurement
The Dutch units of measurement used today are those of the metric system. Before the 19th century, a wide variety of different weights and measures were used by the various Dutch towns and provinces. Despite the country's small size, there was a lack of uniformity...

– for example 1 cm became the duim (thumb), the ons (ounce) became 100 g and so on. Certain German states adopted similar systems and in 1852 the German Zollverein
Zollverein
thumb|upright=1.2|The German Zollverein 1834–1919blue = Prussia in 1834 grey= Included region until 1866yellow= Excluded after 1866red = Borders of the German Union of 1828 pink= Relevant others until 1834...

(customs union) adopted the zollpfund (customs pound) of 500 g for intrastate commerce. In 1872 the newly formed German Empire
German Empire
The German Empire refers to Germany during the "Second Reich" period from the unification of Germany and proclamation of Wilhelm I as German Emperor on 18 January 1871, to 1918, when it became a federal republic after defeat in World War I and the abdication of the Emperor, Wilhelm II.The German...

adopted the metric system as its official system of weights and measures and the newly formed Kingdom of Italy
Kingdom of Italy (1861–1946)
The Kingdom of Italy was a state forged in 1861 by the unification of Italy under the influence of the Kingdom of Sardinia, which was its legal predecessor state...

likewise, following the lead given by Piedmont
Piedmont
Piedmont is one of the 20 regions of Italy. It has an area of 25,402 square kilometres and a population of about 4.4 million. The capital of Piedmont is Turin. The main local language is Piedmontese. Occitan is also spoken by a minority in the Occitan Valleys situated in the Provinces of...

, adopted the metric system in 1861.

The Exposition Universelle (1867)
Exposition Universelle (1867)
The Exposition Universelle of 1867 was a World Exposition held in Paris, France, in 1867.-Conception:In 1864, Emperor Napoleon III decreed that an international exposition should be held in Paris in 1867. A commission was appointed with Prince Jerome Napoleon as president, under whose direction...

(Paris exhibition) devoted a stand to the metric system and by 1875 two thirds of the European population and close on half the world's population had adopted the metric system. The principal European countries not to have adopted the metric system were Russia and the United Kingdom.

The first attempt to have the US adopt the metric system was in the late 1920s by The General Federation of Women's Clubs for the US to adopt the metric system sending 100,000 petitions to Congress in 1927 with over seven million signatures. This first effort as with all future efforts failed as the old system had too much tradition behind it.

### International Standards

In 1861, a committee of the British Association for Advancement of Science (BAAS) including William Thomson (later Lord Kelvin
William Thomson, 1st Baron Kelvin
William Thomson, 1st Baron Kelvin OM, GCVO, PC, PRS, PRSE, was a mathematical physicist and engineer. At the University of Glasgow he did important work in the mathematical analysis of electricity and formulation of the first and second laws of thermodynamics, and did much to unify the emerging...

), James Clerk Maxwell
James Clerk Maxwell
James Clerk Maxwell of Glenlair was a Scottish physicist and mathematician. His most prominent achievement was formulating classical electromagnetic theory. This united all previously unrelated observations, experiments and equations of electricity, magnetism and optics into a consistent theory...

and James Prescott Joule
James Prescott Joule
James Prescott Joule FRS was an English physicist and brewer, born in Salford, Lancashire. Joule studied the nature of heat, and discovered its relationship to mechanical work . This led to the theory of conservation of energy, which led to the development of the first law of thermodynamics. The...

introduced the concept of a coherent system of units based on the metre, gram and second which, in 1873, was extended to include electrical units.

On 20 May 1875 an international treaty known as the Convention du Mètre (Metre Convention) was signed by 17 states. This treaty established the following organisations to conduct international activities relating to a uniform system for measurements:
• Conférence générale des poids et mesures (CGPM), an intergovernmental conference of official delegates of member nations and the supreme authority for all actions;
• Comité international des poids et mesures (CIPM), consisting of selected scientists and metrologist
Metrologist
Metrologists perform metrology work involving precision measurement and comparison of physical quantities such as mass, length, time, force, speed, voltage and current. They calibrate precision equipment which measures these physical units. They may also certify that outside standards of such...

s, which prepares and executes the decisions of the CGPM and is responsible for the supervision of the International Bureau of Weights and Measures;
• Bureau international des poids et mesures (BIPM), a permanent laboratory and world centre of scientific metrology, the activities of which include the establishment of the basic standards and scales of the principal physical quantities and maintenance of the international prototype standards.

In 1881, first International Electrical Congress adopted the BAAS recommendations on electrical units, followed by a series of congresses in which further units of measure were defined.

## Variants

A number of variants of the metric system evolved, all using the Mètre des Archives and Kilogramme des Archives as their base units, but differing in the definitions of the various derived units.
Variants of the metric system
Quantity CGS MKS MTS
length (l) centimetre (cm)
Centimetre
A centimetre is a unit of length in the metric system, equal to one hundredth of a metre, which is the SI base unit of length. Centi is the SI prefix for a factor of . Hence a centimetre can be written as or — meaning or respectively...

metre (m)
Metre
The metre , symbol m, is the base unit of length in the International System of Units . Originally intended to be one ten-millionth of the distance from the Earth's equator to the North Pole , its definition has been periodically refined to reflect growing knowledge of metrology...

metre
mass(m) gram (g)
Gram
The gram is a metric system unit of mass....

kilogram (kg)
Kilogram
The kilogram or kilogramme , also known as the kilo, is the base unit of mass in the International System of Units and is defined as being equal to the mass of the International Prototype Kilogram , which is almost exactly equal to the mass of one liter of water...

tonne (t)
Tonne
The tonne, known as the metric ton in the US , often put pleonastically as "metric tonne" to avoid confusion with ton, is a metric system unit of mass equal to 1000 kilograms. The tonne is not an International System of Units unit, but is accepted for use with the SI...

time (t) second (s)
Second
The second is a unit of measurement of time, and is the International System of Units base unit of time. It may be measured using a clock....

second second
velocity(v) cm/s m/s m/s
acceleration (a) gal (Gal)
Gal
-Given name:* Gal Costa, Brazilian Bossa Nova singer*Gal Fridman , windsurfer and first Israeli to win an Olympic gold medal-Surname:* Austrian composer and artist Bernhard Gál* Jenny Gal, Dutch-Italian judoka...

m/s² m/s²
force (F) dyne (dyn)
Dyne
In physics, the dyne is a unit of force specified in the centimetre-gram-second system of units, a predecessor of the modern SI. One dyne is equal to exactly 10 µN...

newton (N)
Newton
Newton is a contraction of "New Town", the name of many places in English-speaking countries. It may refer to:-People:* Isaac Newton , English mathematician, philosopher and scientist* Newton , lists of notable people with the surname...

sthene (sn)
Sthène
The sthène is the unit of force in the metre-tonne-second system of units , invented in France and used in the Soviet Union 1933-1955. The symbol is sn. It is also used to measure thrust. It is approximately 224 pounds force.1 sn := 1 t·m/s²...

pressure (p) barye (Ba)
Barye
The barye , or sometimes barad, barrie, bary, baryd, baryed, or barie, is the centimetre-gram-second unit of pressure. It is equal to 1 dyne per square centimetre....

pascal (Pa)
Pascal
Pascal or PASCAL may refer to:-People:* Pascal , a French given name* Pascal , a French and Italian surname* Adam Pascal , American actor and singer, best known for his role of Roger Davis in the Broadway musical Rent* Blaise Pascal , French mathematician and philosopher* Cleo Paskal, environmental...

pieze (pz)
Pièze
The pièze is the unit of pressure in the metre-tonne-second system of units , used, e.g., in the former Soviet Union 1933-1955. It is defined as one sthène per square metre. The symbol is pz....

energy (W) erg (erg)
Erg
An erg is the unit of energy and mechanical work in the centimetre-gram-second system of units, symbol "erg". Its name is derived from the Greek ergon, meaning "work"....

joule (J)
Joule
The joule ; symbol J) is a derived unit of energy or work in the International System of Units. It is equal to the energy expended in applying a force of one newton through a distance of one metre , or in passing an electric current of one ampere through a resistance of one ohm for one second...

kilojoule (kJ)
power (P) erg/s watt (W)
Watt
The watt is a derived unit of power in the International System of Units , named after the Scottish engineer James Watt . The unit, defined as one joule per second, measures the rate of energy conversion.-Definition:...

kilowatt (kW)
viscosity (µ) poise (p)
Poise
The poise is the unit of dynamic viscosity in the centimetre gram second system of units. It is named after Jean Louis Marie Poiseuille ....

Pa·s pz·s

### Centimetre-gram-second systems

The centimetre gram second system of units
Centimetre gram second system of units
The centimetre–gram–second system is a metric system of physical units based on centimetre as the unit of length, gram as a unit of mass, and second as a unit of time...

(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
British Association for the Advancement of Science
frame|right|"The BA" logoThe British Association for the Advancement of Science or the British Science Association, formerly known as the BA, is a learned society with the object of promoting science, directing general attention to scientific matters, and facilitating interaction between...

(BAAS). The system's characteristics are that density is expressed in , force expressed in dyne
Dyne
In physics, the dyne is a unit of force specified in the centimetre-gram-second system of units, a predecessor of the modern SI. One dyne is equal to exactly 10 µN...

s and mechanical energy in erg
Erg
An erg is the unit of energy and mechanical work in the centimetre-gram-second system of units, symbol "erg". Its name is derived from the Greek ergon, meaning "work"....

s. Thermal energy was defined in calorie
Calorie
The calorie is a pre-SI metric unit of energy. It was first defined by Nicolas Clément in 1824 as a unit of heat, entering French and English dictionaries between 1841 and 1867. In most fields its use is archaic, having been replaced by the SI unit of energy, the joule...

s, 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 proposed two sets of units for electrical and magnetic properties
Centimetre gram second system of units
The centimetre–gram–second system is a metric system of physical units based on centimetre as the unit of length, gram as a unit of mass, and second as a unit of time...

- the electrostatic set of units and the electromagnetic set of units.

### Metre-kilogram-second systems

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
Metre
The metre , symbol m, is the base unit of length in the International System of Units . Originally intended to be one ten-millionth of the distance from the Earth's equator to the North Pole , its definition has been periodically refined to reflect growing knowledge of metrology...

, kilogram
Kilogram
The kilogram or kilogramme , also known as the kilo, is the base unit of mass in the International System of Units and is defined as being equal to the mass of the International Prototype Kilogram , which is almost exactly equal to the mass of one liter of water...

and second
Second
The second is a unit of measurement of time, and is the International System of Units base unit of time. It may be measured using a clock....

. In 1901, Giorgi
Giovanni Giorgi
Giovanni Giorgi was an Italian electrical engineer who invented the Giorgi system of measurement, the precursor to the International System ....

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
Ampere
The ampere , often shortened to amp, is the SI unit of electric current and is one of the seven SI base units. It is named after André-Marie Ampère , French mathematician and physicist, considered the father of electrodynamics...

(MKSA) systems are examples of such systems.

The International System of Units
Si
Si, si, or SI may refer to :- Measurement, mathematics and science :* International System of Units , the modern international standard version of the metric system...

(System international units or SI) is the current international standard metric system and 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
Kelvin
The kelvin is a unit of measurement for temperature. It is one of the seven base units in the International System of Units and is assigned the unit symbol K. The Kelvin scale is an absolute, thermodynamic temperature scale using as its null point absolute zero, the temperature at which all...

, candela
Candela
The candela is the SI base unit of luminous intensity; that is, power emitted by a light source in a particular direction, weighted by the luminosity function . A common candle emits light with a luminous intensity of roughly one candela...

and mole
Mole (unit)
The mole is a unit of measurement used in chemistry to express amounts of a chemical substance, defined as an amount of a substance that contains as many elementary entities as there are atoms in 12 grams of pure carbon-12 , the isotope of carbon with atomic weight 12. This corresponds to a value...

. Proposals have been made to change the definitions
New SI definitions
A committee of the International Committee for Weights and Measures has proposed revised formal definitions of the SI base units, which are being examined by the CIPM and which may be considered by the 25th CGPM, in 2014....

of four of the base units at the 24th meeting of the CGPM in October 2011. These changes should not affect the average person.

### Metre-tonne-second systems

The metre-tonne-second system of units
Metre-tonne-second system of units
The metre-tonne-second or mts system of units is a system of physical units. It was invented in France, hence the unit names sthène and pièze, and was adopted only by the Soviet Union in 1933, and abolished there in 1955. It was built on the same principles as the cgs system, but with larger units...

(MTS) was based on the metre, tonne
Tonne
The tonne, known as the metric ton in the US , often put pleonastically as "metric tonne" to avoid confusion with ton, is a metric system unit of mass equal to 1000 kilograms. The tonne is not an International System of Units unit, but is accepted for use with the SI...

and second - the unit of force is the sthène
Sthène
The sthène is the unit of force in the metre-tonne-second system of units , invented in France and used in the Soviet Union 1933-1955. The symbol is sn. It is also used to measure thrust. It is approximately 224 pounds force.1 sn := 1 t·m/s²...

and the unit of pressure is the pièze
Pièze
The pièze is the unit of pressure in the metre-tonne-second system of units , used, e.g., in the former Soviet Union 1933-1955. It is defined as one sthène per square metre. The symbol is pz....

. It was invented in France in industry and was mostly used in the Soviet Union
Soviet Union
The Soviet Union , officially the Union of Soviet Socialist Republics , was a constitutionally socialist state that existed in Eurasia between 1922 and 1991....

from 1933 to 1955.

### Gravitational systems

Gravitational metric system
Gravitational metric system
In the gravitational metric system the base unit of force is not normalised to one mass unit times one length unit per time unit squared as in the SI, but it depends on a selected or locally measured gravitational constant gn. This constant is usually set to an acceleration of 9.80665 m/s²...

s use the kilogram-force
Kilogram-force
A kilogram-force , or kilopond , is a gravitational metric unit of force. It is equal to the magnitude of the force exerted by one kilogram of mass in a gravitational field...

(kilopond) as a base unit of force, with mass measured in a unit known as the hyl
Hyl
HYL or hyl may refer to:* HYL, National Rail station code for Hayle railway station* Helsingin yhteislyseo, a school in Kontula, Helsinki, Finland...

, TME, mug or metric slug. Note these are not part of the International System of Units
International System of Units
The International System of Units is the modern form of the metric system and is generally a system of units of measurement devised around seven base units and the convenience of the number ten. The older metric system included several groups of units...

(SI).

## International System of Units

The 9th CGPM met in 1948, fifteen years after the 8th CGPM. In response to formal requests made by the International Union of Pure and Applied Physics and by the French Government to establish a practical system of units of measure, the CGPM requested the CIPM to prepare recommendations for a single practical system of units of measurement, suitable for adoption by all countries adhering to the Metre Convention. At the same time the CGPM formally adopted a recommendation for the writing and printing of unit symbols and of numbers. The recommendation also catalogued the recommended symbols for the most important MKS
Mks system of units
The MKS system of units is a physical system of units that expresses any given measurement using fundamental units of the metre, kilogram, and/or second ....

and CGS
Centimetre gram second system of units
The centimetre–gram–second system is a metric system of physical units based on centimetre as the unit of length, gram as a unit of mass, and second as a unit of time...

units of measure and for the first time the CGPM made recommendations concerning derived units.

The CIPM's draft proposal, which was an extensive revision and simplification of the metric unit definitions, symbols and terminology based on the MKS system of units, was put to the 10th CGPM in 1954. In accordance with Giorgi's proposals of 1901, the CIPM also recommended that the ampere be the base unit from which electromechanical would be derived. The definitions for the ohm and volt that had previously been in use were discarded and these units became derived units based on the metre, ampere, second and kilogram. After negotiations with the CIS and IUPAP, two further base units, the degree kelvin and the candela were also proposed as base units. The full system and name "Système International d'Unités" were adopted at the 11th CGPM. During the years that followed the definitions of the base units and particularly the mise en pratique to realise these definitions have been refined.

The formal definition of International System of Units (SI) along with the associated resolutions passed by the CGPM and the CIPM are published by the BIPM on the Internet and in brochure form at regular intervals. The eighth edition of the brochure Le Système International d'Unités - The International System of Units was published in 2006.

### "New SI"

When the metre was redefined in 1960, the kilogram was the only SI base unit that relied on a specific artifact. Moreover, after the 1996-1998 recalibration a clear divergence between the various prototype kilograms was observed.

At its 23rd meeting (2007), the CGPM mandated the CIPM to investigate the use of natural constants as the basis for all units of measure rather than the artifacts that were then in use. At a meeting of the CCU held in Reading, United Kingdom
Reading is a large town and unitary authority area in England. It is located in the Thames Valley at the confluence of the River Thames and River Kennet, and on both the Great Western Main Line railway and the M4 motorway, some west of London....

in September 2010, a resolution and draft changes to the SI brochure that were to be presented to the next meeting of the CIPM in October 2010 were agreed to in principle. The proposals that the CCU put forward were:
• In addition to the speed of light, four constants of nature - Planck's constant, an elementary charge
Elementary charge
The elementary charge, usually denoted as e, is the electric charge carried by a single proton, or equivalently, the absolute value of the electric charge carried by a single electron. This elementary charge is a fundamental physical constant. To avoid confusion over its sign, e is sometimes called...

, Boltzmann constant and Avogadro's number
In chemistry and physics, the Avogadro constant is defined as the ratio of the number of constituent particles N in a sample to the amount of substance n through the relationship NA = N/n. Thus, it is the proportionality factor that relates the molar mass of an entity, i.e...

be defined to have exact values.
• The international prototype kilogram be retired
• The current definitions of the kilogram, ampere
Ampere
The ampere , often shortened to amp, is the SI unit of electric current and is one of the seven SI base units. It is named after André-Marie Ampère , French mathematician and physicist, considered the father of electrodynamics...

, kelvin
Kelvin
The kelvin is a unit of measurement for temperature. It is one of the seven base units in the International System of Units and is assigned the unit symbol K. The Kelvin scale is an absolute, thermodynamic temperature scale using as its null point absolute zero, the temperature at which all...

and mole
Mole (unit)
The mole is a unit of measurement used in chemistry to express amounts of a chemical substance, defined as an amount of a substance that contains as many elementary entities as there are atoms in 12 grams of pure carbon-12 , the isotope of carbon with atomic weight 12. This corresponds to a value...

be revised.
• The wording of the definitions of all the base units be tightened up

The CIPM meeting of October 2010 found that "the conditions set by the General Conference at its 23rd meeting have not yet been fully met. For this reason the CIPM does not propose a revision of the SI at the present time". The CIPM did however sponsor a resolution at the 24th CGPM in which the changes were agreed in principal and which were expected to be finalised at the CGPM's next meeting in 2014.

## Usage around the world

The usage of the metric system varies around the world. According to the American Central Intelligence Agency's Factbook, the International System of Units is the official system of measurement for all nations in the world except for Burma, Liberia
Liberia
Liberia , officially the Republic of Liberia, is a country in West Africa. It is bordered by Sierra Leone on the west, Guinea on the north and Côte d'Ivoire on the east. Liberia's coastline is composed of mostly mangrove forests while the more sparsely populated inland consists of forests that open...

and the United States. Some sources, though, suggest that this information is out of date: an Agence France-Presse
Agence France-Presse
Agence France-Presse is a French news agency, the oldest one in the world, and one of the three largest with Associated Press and Reuters. It is also the largest French news agency. Currently, its CEO is Emmanuel Hoog and its news director Philippe Massonnet...

of 2010 noted that Sierra Leone
Sierra Leone
Sierra Leone , officially the Republic of Sierra Leone, is a country in West Africa. It is bordered by Guinea to the north and east, Liberia to the southeast, and the Atlantic Ocean to the west and southwest. Sierra Leone covers a total area of and has an estimated population between 5.4 and 6.4...

was to adopt the metric system, thereby aligning her system of measurement with her Mano River Union (MRU)
Mano River Union
The Mano River Union is an international association established in 1973 between Liberia and Sierra Leone. In 1980, Guinea joined the union. The goal of the Union was to foster economic cooperation among the countries...

neighbours Guinea
Guinea
Guinea , officially the Republic of Guinea , is a country in West Africa. Formerly known as French Guinea , it is today sometimes called Guinea-Conakry to distinguish it from its neighbour Guinea-Bissau. Guinea is divided into eight administrative regions and subdivided into thirty-three prefectures...

and Liberia. Reports from Burma suggest that that country is planning to adopt the metric system.

In the United States, where the use of metric units was by authorised by Congress
United States Congress
The United States Congress is the bicameral legislature of the federal government of the United States, consisting of the Senate and the House of Representatives. The Congress meets in the United States Capitol in Washington, D.C....

in 1866, such units are widely used in science, military, and partially in industry, but customary units predominate in household use. At retail stores, the litre is a commonly used unit for volume, especially on bottles of beverages, and milligrams are used to denominate the amounts of medications, rather than grains. Also, other standardised measuring systems other than metric are still in universal international use, such as nautical mile
Nautical mile
The nautical mile is a unit of length that is about one minute of arc of latitude along any meridian, but is approximately one minute of arc of longitude only at the equator...

s and knots in international aviation.

In the countries of the Commonwealth of Nations
Commonwealth of Nations
The Commonwealth of Nations, normally referred to as the Commonwealth and formerly known as the British Commonwealth, is an intergovernmental organisation of fifty-four independent member states...

the metric system has replaced the imperial system by varing degrees: Australia
Metrication in Australia
Metrication in Australia took place between 1970 and 1988. Before then, Australia mostly used the imperial system for measurement, which the Australian colonies had inherited from the United Kingdom. Between 1970 and 1988, imperial units were withdrawn from general legal use and replaced with SI...

, New Zealand
Metrication in New Zealand
New Zealand started metrication in 1969 with the establishment of the Metric Advisory Board and completed metrication on 14 December 1976 .-Strategy toward Metrication:...

and Commonwealth countries in Africa are almost totally metric, India is mostly metric
Metrication in India
Metrication or metrification is the process of converting to the metric system based on the International System of Units . India's conversion to the metric system occurred in stages between 1955 and 1962...

Canada has converted to the metric system for many purposes but there is still significant use of non-metric units and standards in many sectors of the Canadian economy...

while in the United Kingdom the metric system
Metrication in the United Kingdom
Metrication in the United Kingdom is the process of introducing the metric system of measurement in place of imperial units in the United Kingdom....

, the use of which was first permitted for trade in 1864, is used in much government business, in most industries including building, health and engineering and for pricing by measure or weight in most trading situations, both wholesale and retail. However the imperial system continues to be used in many unregulated applications and is in widespread daily use.

A number of other jurisdictions, such as Hong Kong, have laws mandating or permitting other systems of measurement in parallel with the metric system in some or all contexts.

### Variations in spelling

The SI symbols for the metric units are intended to be identical, regardless of the language used. For example, the SI unit symbol for kilometre is "km" everywhere in the world, even though the local language word for the unit name may vary. Language variants for the kilometre unit name include: chilometro (Italian), kilometer (German, Malay), kilomètre (French), χιλιόμετρο (Greek), quilómetro (Portuguese) and Километър (Bulgarian). Variations are also found with the spelling of unit names in countries using the same language, including differences in American English and British spelling. For example meter and liter are used in the United States whereas metre and litre are used in other English-speaking countries. In addition, the official US spelling for the rarely used SI prefix for ten is deka. In American English the term metric ton is the normal usage whereas in other varieties of English tonne is common. Gram is also sometimes spelled gramme in English-speaking countries other than the United States, though this older usage is declining.

The US government has approved this terminology for official use. In scientific contexts, only the symbols are used; since these are universally the same, the differences do not arise in practice in scientific use.

## Conversion and calculation errors

The dual usage of metric and non metric units has resulted in serious errors. These include:
• The degree of overloading of an American International Airways aircraft flying from Miami to Maiquetia, Venezuela on 26 May 1994 was consistent with a cargo weighed in kilograms, not pounds.
• The Institute for Safe Medication Practices has reported that confusion between grains and grams led to a patient receiving phenobarbital
Phenobarbital
Phenobarbital or phenobarbitone is a barbiturate, first marketed as Luminal by Friedr. Bayer et comp. It is the most widely used anticonvulsant worldwide, and the oldest still commonly used. It also has sedative and hypnotic properties but, as with other barbiturates, has been superseded by the...

0.5 grams instead of 0.5 grains (0.03 grams) after the practitioner misread the prescription.
Gimli Glider
The Gimli Glider is the nickname of the Air Canada aircraft that was involved in a notable aviation incident. On 23 July 1983, Air Canada Flight 143, a Boeing 767-200 jet, ran out of fuel at an altitude of ASL, about halfway through its flight from Montreal to Edmonton via Ottawa...

" accident in 1983, when a Boeing 767
Boeing 767
The Boeing 767 is a mid-size, wide-body twin-engine jet airliner built by Boeing Commercial Airplanes. It was the manufacturer's first wide-body twinjet and its first airliner with a two-crew glass cockpit. The aircraft features two turbofan engines, a supercritical wing, and a conventional tail...

jet ran out of fuel in mid-flight because of two mistakes in calculating the fuel supply of Air Canada
Air Canada is the flag carrier and largest airline of Canada. The airline, founded in 1936, provides scheduled and charter air transport for passengers and cargo to 178 destinations worldwide. It is the world's tenth largest passenger airline by number of destinations, and the airline is a...

's first aircraft to use metric measurements.
• The root cause of NASA
NASA
The National Aeronautics and Space Administration is the agency of the United States government that is responsible for the nation's civilian space program and for aeronautics and aerospace research...

's 1999 loss of the \$125 million Mars Climate Orbiter
Mars Climate Orbiter
The Mars Climate Orbiter was a 338 kilogram robotic space probe launched by NASA on December 11, 1998 to study the Martian climate, atmosphere, surface changes and to act as the communications relay in the Mars Surveyor '98 program, for Mars Polar Lander...

which crashed into Mars was a mismatch of units - the spacecraft engineers calculated the thrust forces required for velocity changes using US customary units (lbf·s) whereas the team who built the thrusters were expecting a value in metric units (N·s) as per the agreed specification.

## Conversion between SI and legacy units

During its evolution, the metric system has adopted many units of measure. The introduction of SI rationalised both the way in which units of measure were defined and also the list of units in use. These are now catalogued in the official SI Brochure. The table below lists the units of measure in this catalogue and shows the conversion factors connecting them with the equivalent units that were in use on the eve of the adoption of SI.
Quantity Dimension SI unit and symbol Legacy unit and symbol
Time
Time
Time is a part of the measuring system used to sequence events, to compare the durations of events and the intervals between them, and to quantify rates of change such as the motions of objects....

second
Second
The second is a unit of measurement of time, and is the International System of Units base unit of time. It may be measured using a clock....

(s)
second (s) 1
Length
Length
In geometric measurements, length most commonly refers to the longest dimension of an object.In certain contexts, the term "length" is reserved for a certain dimension of an object along which the length is measured. For example it is possible to cut a length of a wire which is shorter than wire...

metre
Metre
The metre , symbol m, is the base unit of length in the International System of Units . Originally intended to be one ten-millionth of the distance from the Earth's equator to the North Pole , its definition has been periodically refined to reflect growing knowledge of metrology...

(m)
centimetre
Centimetre
A centimetre is a unit of length in the metric system, equal to one hundredth of a metre, which is the SI base unit of length. Centi is the SI prefix for a factor of . Hence a centimetre can be written as or — meaning or respectively...

(cm)
ångström
Ångström
The angstrom or ångström, is a unit of length equal to 1/10,000,000,000 of a meter . Its symbol is the Swedish letter Å....

(Å)
0.01
10−10
Mass
Mass
Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...

kilogram
Kilogram
The kilogram or kilogramme , also known as the kilo, is the base unit of mass in the International System of Units and is defined as being equal to the mass of the International Prototype Kilogram , which is almost exactly equal to the mass of one liter of water...

(kg)
gram
Gram
The gram is a metric system unit of mass....

(g)
0.001
Area
Area
Area is a quantity that expresses the extent of a two-dimensional surface or shape in the plane. Area can be understood as the amount of material with a given thickness that would be necessary to fashion a model of the shape, or the amount of paint necessary to cover the surface with a single coat...

square metre
Square metre
The square metre or square meter is the SI derived unit of area, with symbol m2 . It is defined as the area of a square whose sides measure exactly one metre...

(m2)
are (are) 100
Acceleration
Acceleration
In physics, acceleration is the rate of change of velocity with time. In one dimension, acceleration is the rate at which something speeds up or slows down. However, since velocity is a vector, acceleration describes the rate of change of both the magnitude and the direction of velocity. ...

(ms−2) gal (gal) 10−2
Electric current
Electric current
Electric current is a flow of electric charge through a medium.This charge is typically carried by moving electrons in a conductor such as wire...

ampere
Ampere
The ampere , often shortened to amp, is the SI unit of electric current and is one of the seven SI base units. It is named after André-Marie Ampère , French mathematician and physicist, considered the father of electrodynamics...

(A)
international ampere
Ampere
The ampere , often shortened to amp, is the SI unit of electric current and is one of the seven SI base units. It is named after André-Marie Ampère , French mathematician and physicist, considered the father of electrodynamics...

abampere
Abampere
The abampere , also called the biot after Jean-Baptiste Biot, is the basic electromagnetic unit of electric current in the emu-cgs system of units . One abampere is equal to ten amperes in the SI system of units...

or biot
Biot
Biot or BIOT may refer to:* Biot, Alpes-Maritimes, a commune in France* Biot , a lunar crater* British Indian Ocean Territory* Camille Biot , French physician...

statampere
Centimetre gram second system of units
The centimetre–gram–second system is a metric system of physical units based on centimetre as the unit of length, gram as a unit of mass, and second as a unit of time...

1.000022
10.0
3.335641×10−10
Temperature
Temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...

kelvin
Kelvin
The kelvin is a unit of measurement for temperature. It is one of the seven base units in the International System of Units and is assigned the unit symbol K. The Kelvin scale is an absolute, thermodynamic temperature scale using as its null point absolute zero, the temperature at which all...

(K)
degrees Celsius
Celsius
Celsius is a scale and unit of measurement for temperature. It is named after the Swedish astronomer Anders Celsius , who developed a similar temperature scale two years before his death...

(°C)
Celsius
Celsius is a scale and unit of measurement for temperature. It is named after the Swedish astronomer Anders Celsius , who developed a similar temperature scale two years before his death...

(°C)
K = °C + 273.15
1
Luminous intensity
Luminous intensity
In photometry, luminous intensity is a measure of the wavelength-weighted power emitted by a light source in a particular direction per unit solid angle, based on the luminosity function, a standardized model of the sensitivity of the human eye...

candela
Candela
The candela is the SI base unit of luminous intensity; that is, power emitted by a light source in a particular direction, weighted by the luminosity function . A common candle emits light with a luminous intensity of roughly one candela...

(cd)
international candle
Candela
The candela is the SI base unit of luminous intensity; that is, power emitted by a light source in a particular direction, weighted by the luminosity function . A common candle emits light with a luminous intensity of roughly one candela...

0.982
Amount of substance
Amount of substance
Amount of substance is a standards-defined quantity that measures the size of an ensemble of elementary entities, such as atoms, molecules, electrons, and other particles. It is sometimes referred to as chemical amount. The International System of Units defines the amount of substance to be...

mole
Mole (unit)
The mole is a unit of measurement used in chemistry to express amounts of a chemical substance, defined as an amount of a substance that contains as many elementary entities as there are atoms in 12 grams of pure carbon-12 , the isotope of carbon with atomic weight 12. This corresponds to a value...

(mol)
No legacy unit n/a
Frequency
Frequency
Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...

hertz
Hertz
The hertz is the SI unit of frequency defined as the number of cycles per second of a periodic phenomenon. One of its most common uses is the description of the sine wave, particularly those used in radio and audio applications....

(Hz)
cycles per second 1
Energy
Energy
In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...

joule
Joule
The joule ; symbol J) is a derived unit of energy or work in the International System of Units. It is equal to the energy expended in applying a force of one newton through a distance of one metre , or in passing an electric current of one ampere through a resistance of one ohm for one second...

(J)
erg
Erg
An erg is the unit of energy and mechanical work in the centimetre-gram-second system of units, symbol "erg". Its name is derived from the Greek ergon, meaning "work"....

(erg)
10−7
Power
Power (physics)
In physics, power is the rate at which energy is transferred, used, or transformed. For example, the rate at which a light bulb transforms electrical energy into heat and light is measured in watts—the more wattage, the more power, or equivalently the more electrical energy is used per unit...

watt
Watt
The watt is a derived unit of power in the International System of Units , named after the Scottish engineer James Watt . The unit, defined as one joule per second, measures the rate of energy conversion.-Definition:...

(W)
(erg/s)
horsepower
Horsepower
Horsepower is the name of several units of measurement of power. The most common definitions equal between 735.5 and 750 watts.Horsepower was originally defined to compare the output of steam engines with the power of draft horses in continuous operation. The unit was widely adopted to measure the...

(HP)
Pferdestärke (PS)
10−7
745.7
735.5
Force
Force
In physics, a force is any influence that causes an object to undergo a change in speed, a change in direction, or a change in shape. In other words, a force is that which can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a flexible object to deform...

newton (N) dyne
Dyne
In physics, the dyne is a unit of force specified in the centimetre-gram-second system of units, a predecessor of the modern SI. One dyne is equal to exactly 10 µN...

(dyn)
sthene
Sthène
The sthène is the unit of force in the metre-tonne-second system of units , invented in France and used in the Soviet Union 1933-1955. The symbol is sn. It is also used to measure thrust. It is approximately 224 pounds force.1 sn := 1 t·m/s²...

(sn)
kilopond (kp)
10−5
103
9.80665
Pressure
Pressure
Pressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :...

pascal
Pascal (unit)
The pascal is the SI derived unit of pressure, internal pressure, stress, Young's modulus and tensile strength, named after the French mathematician, physicist, inventor, writer, and philosopher Blaise Pascal. It is a measure of force per unit area, defined as one newton per square metre...

(Pa)
barye
Barye
The barye , or sometimes barad, barrie, bary, baryd, baryed, or barie, is the centimetre-gram-second unit of pressure. It is equal to 1 dyne per square centimetre....

(Ba)
pieze
Pièze
The pièze is the unit of pressure in the metre-tonne-second system of units , used, e.g., in the former Soviet Union 1933-1955. It is defined as one sthène per square metre. The symbol is pz....

(pz)
atmosphere (at)
0.1
103
1.0197×10−5
Electric charge
Electric charge
Electric charge is a physical property of matter that causes it to experience a force when near other electrically charged matter. Electric charge comes in two types, called positive and negative. Two positively charged substances, or objects, experience a mutual repulsive force, as do two...

coulomb (C) abcoulomb
Abcoulomb
The abcoulomb or electromagnetic unit of charge is the basic physical unit of electric charge in the cgs-emu system of units...

statcoulomb
Statcoulomb
The statcoulomb or franklin or electrostatic unit of charge is the physical unit for electrical charge used in the centimetre-gram-second system of units and Gaussian units. It is a derived unit given by...

or franklin
10
3.335641×10−10
Potential difference
Voltage
Voltage, otherwise known as electrical potential difference or electric tension is the difference in electric potential between two points — or the difference in electric potential energy per unit charge between two points...

volt
Volt
The volt is the SI derived unit for electric potential, electric potential difference, and electromotive force. The volt is named in honor of the Italian physicist Alessandro Volta , who invented the voltaic pile, possibly the first chemical battery.- Definition :A single volt is defined as the...

(V)
international volt
Volt
The volt is the SI derived unit for electric potential, electric potential difference, and electromotive force. The volt is named in honor of the Italian physicist Alessandro Volta , who invented the voltaic pile, possibly the first chemical battery.- Definition :A single volt is defined as the...

abvolt
Abvolt
The abvolt is one option for the unit of potential difference in the CGS system of units, and is equal to 10−8 volts in the SI system.A potential difference of 1 abV will drive a current of one abampere through a resistance of one abohm....

statvolt
Statvolt
The statvolt is a unit of voltage and electrical potential used in the cgs system of units. The conversion to the SI system isIt is a useful unit for electromagnetism because one statvolt per centimetre is equal in magnitude to one gauss. Thus, for example, an electric field of one statvolt/cm has...

1.00034
10−8
2.997925×102
Capacitance
Capacitance
In electromagnetism and electronics, capacitance is the ability of a capacitor to store energy in an electric field. Capacitance is also a measure of the amount of electric potential energy stored for a given electric potential. A common form of energy storage device is a parallel-plate capacitor...

The farad is the SI unit of capacitance. The unit is named after the English physicist Michael Faraday.- Definition :A farad is the charge in coulombs which a capacitor will accept for the potential across it to change 1 volt. A coulomb is 1 ampere second...

(F)
109
1.112650×10−12
Inductance
Inductance
In electromagnetism and electronics, inductance is the ability of an inductor to store energy in a magnetic field. Inductors generate an opposing voltage proportional to the rate of change in current in a circuit...

henry (H) abhenry
Abhenry
Abhenry is the centimeter-gram-second electromagnetic unit of inductance, equal to one billionth of a henry....

stathenry
10−9
8.987552×1011
Electric resistance ohm
Ohm
The ohm is the SI unit of electrical resistance, named after German physicist Georg Simon Ohm.- Definition :The ohm is defined as a resistance between two points of a conductor when a constant potential difference of 1 volt, applied to these points, produces in the conductor a current of 1 ampere,...

(Ω)
international ohm
abohm
Abohm
The abohm is the basic unit of electrical resistance in the emu-cgs system of units . One abohm is equal to 10-9 ohms in the SI system of units; one abohm is a nanoohm....

statohm
Centimetre gram second system of units
The centimetre–gram–second system is a metric system of physical units based on centimetre as the unit of length, gram as a unit of mass, and second as a unit of time...

1.00049
10−9
8.987552×1011
Electric conductance siemens
Siemens (unit)
The siemens is the SI derived unit of electric conductance and electric admittance. Conductance and admittance are the reciprocals of resistance and impedance respectively, hence one siemens is equal to the reciprocal of one ohm, and is sometimes referred to as the mho. In English, the term...

(S)
mho (℧)
abmho
Abmho
Abmho is a unit of electrical conductance in the emu-cgs system of units . It's equal to gigasiemens...

statmho
0.99951
109
1.112650×10−12
Magnetic flux
Magnetic flux
Magnetic flux , is a measure of the amount of magnetic B field passing through a given surface . The SI unit of magnetic flux is the weber...

weber
Weber (unit)
In physics, the weber is the SI unit of magnetic flux. A flux density of one Wb/m2 is one tesla.The weber is named for the German physicist Wilhelm Eduard Weber .- Definition :...

(Wb)
maxwell
Maxwell (unit)
The maxwell, abbreviated as Mx, is the compound derived CGS unit of magnetic flux. The unit was previously called a line. The unit name honours James Clerk Maxwell, who presented the unified theory of electromagnetism, and was established by the IEC in 1930.In a magnetic field of strength one...

(Mx)
10−8
Magnetic flux density
Magnetic field
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...

tesla
Tesla (unit)
The tesla is the SI derived unit of magnetic field B . One tesla is equal to one weber per square meter, and it was defined in 1960 in honour of the inventor, physicist, and electrical engineer Nikola Tesla...

(T)
gauss
Gauss (unit)
The gauss, abbreviated as G, is the cgs unit of measurement of a magnetic field B , named after the German mathematician and physicist Carl Friedrich Gauss. One gauss is defined as one maxwell per square centimeter; it equals 1 tesla...

(G)
1×10−4
Magnetic field strength
Magnetic field
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...

(A/m) oersted
Oersted
Oersted is the unit of magnetizing field in the CGS system of units.-Difference between cgs and SI systems:...

(Oe)
103/4π = 79.57747
Dynamic viscosity
Viscosity
Viscosity is a measure of the resistance of a fluid which is being deformed by either shear or tensile stress. In everyday terms , viscosity is "thickness" or "internal friction". Thus, water is "thin", having a lower viscosity, while honey is "thick", having a higher viscosity...

(Pa·s) poise
Poise
The poise is the unit of dynamic viscosity in the centimetre gram second system of units. It is named after Jean Louis Marie Poiseuille ....

(P)
0.1
Kinematic viscosity
Viscosity
Viscosity is a measure of the resistance of a fluid which is being deformed by either shear or tensile stress. In everyday terms , viscosity is "thickness" or "internal friction". Thus, water is "thin", having a lower viscosity, while honey is "thick", having a higher viscosity...

(m2s−1) stokes  (St) 10−4
Luminous flux
Luminous flux
In photometry, luminous flux or luminous power is the measure of the perceived power of light. It differs from radiant flux, the measure of the total power of light emitted, in that luminous flux is adjusted to reflect the varying sensitivity of the human eye to different wavelengths of...

lumen
Lumen (unit)
The lumen is the SI derived unit of luminous flux, a measure of the total "amount" of visible light emitted by a source. Luminous flux differs from power in that luminous flux measurements reflect the varying sensitivity of the human eye to different wavelengths of light, while radiant flux...

(lm)
stilb
Stilb (unit)
The stilb is the CGS unit of luminance for objects that are not self-luminous. It is equal to one candela per square centimeter or 104 nits . The name was coined by the French physicist André Blondel around 1920. It comes from the Greek word stilbein meaning "to glitter".It was in common use in...

(sb)
104
Illuminance
Illuminance
In photometry, illuminance is the total luminous flux incident on a surface, per unit area. It is a measure of the intensity of the incident light, wavelength-weighted by the luminosity function to correlate with human brightness perception. Similarly, luminous emittance is the luminous flux per...

lux
Lux
The lux is the SI unit of illuminance and luminous emittance, measuring luminous flux per unit area. It is used in photometry as a measure of the intensity, as perceived by the human eye, of light that hits or passes through a surface...

(lx)
phot
Phot
A phot is a photometric unit of illuminance, or luminous flux through an area. It is not an SI unit, but rather is associated with the older centimetre gram second system of units...

(ph)
104
Radioactive decay is the process by which an atomic nucleus of an unstable atom loses energy by emitting ionizing particles . The emission is spontaneous, in that the atom decays without any physical interaction with another particle from outside the atom...

becquerel
Becquerel
The becquerel is the SI-derived unit of radioactivity. One Bq is defined as the activity of a quantity of radioactive material in which one nucleus decays per second. The Bq unit is therefore equivalent to an inverse second, s−1...

(Bq)
curie
Curie
The curie is a unit of radioactivity, defined asThis is roughly the activity of 1 gram of the radium isotope 226Ra, a substance studied by the pioneers of radiology, Marie and Pierre Curie, for whom the unit was named. In addition to the curie, activity can be measured using an SI derived unit,...

(Ci)
3.70×1010
Absorbed dose
Absorbed dose is a measure of the energy deposited in a medium by ionizing radiation per unit mass...

gray
Gray (unit)
The gray is the SI unit of absorbed radiation dose of ionizing radiation , and is defined as the absorption of one joule of ionizing radiation by one kilogram of matter ....

(Gy)
roentgen (R)
Rad may mean:* Rad , a villainous character in AC Comics's "Femforce"* Rad , a 1986 release about a young BMX rider* Rad , several fictional characters in the Transformers toy line...

2.58
0.01
Equivalent dose
The equivalent absorbed radiation dose, usually shortened to equivalent dose, is a computed average measure of the radiation absorbed by a fixed mass of biological tissue, that attempts to account for the different biological damage potential of different types of ionizing radiation...

sievert
Sievert
The sievert is the International System of Units SI derived unit of dose equivalent radiation. It attempts to quantitatively evaluate the biological effects of ionizing radiation as opposed to just the absorbed dose of radiation energy, which is measured in gray...

roentgen equivalent man (rem) 0.01
Catalytic activity katal
Katal
The katal is the SI unit of catalytic activity. It is a derived SI unit for expressing quantity values of catalytic activity of enzymes and other catalysts. Its use is recommended by the General Conference on Weights and Measures and other international organizations. It replaces the non-SI enzyme...

(kat)
No legacy unit n/a

The SI brouchure also catalogues certain non-SI units that are widely used with the SI in matters of everyday life or units that are exactly defined values in terms of SI units and are used in particular circumstances to satisfy the needs of commercial, legal, or specialised scientific interests. These units include:
Quantity Dimension Unit and symbol Equivalence
Mass
Mass
Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...

tonne
Tonne
The tonne, known as the metric ton in the US , often put pleonastically as "metric tonne" to avoid confusion with ton, is a metric system unit of mass equal to 1000 kilograms. The tonne is not an International System of Units unit, but is accepted for use with the SI...

(t)
1000 kg
Area
Area
Area is a quantity that expresses the extent of a two-dimensional surface or shape in the plane. Area can be understood as the amount of material with a given thickness that would be necessary to fashion a model of the shape, or the amount of paint necessary to cover the surface with a single coat...

hectare
Hectare
The hectare is a metric unit of area defined as 10,000 square metres , and primarily used in the measurement of land. In 1795, when the metric system was introduced, the are was defined as being 100 square metres and the hectare was thus 100 ares or 1/100 km2...

(ha)
0.01 km2
104 m2
Volume
Volume
Volume is the quantity of three-dimensional space enclosed by some closed boundary, for example, the space that a substance or shape occupies or contains....

litre
Litre
pic|200px|right|thumb|One litre is equivalent to this cubeEach side is 10 cm1 litre water = 1 kilogram water The litre is a metric system unit of volume equal to 1 cubic decimetre , to 1,000 cubic centimetres , and to 1/1,000 cubic metre...

(L or l)
0.001 m3
Time
Time
Time is a part of the measuring system used to sequence events, to compare the durations of events and the intervals between them, and to quantify rates of change such as the motions of objects....

minute
Minute
A minute is a unit of measurement of time or of angle. The minute is a unit of time equal to 1/60th of an hour or 60 seconds. In the UTC time scale, a minute on rare occasions has 59 or 61 seconds; see leap second. The minute is not an SI unit; however, it is accepted for use with SI units...

(min)
hour
Hour
The hour is a unit of measurement of time. In modern usage, an hour comprises 60 minutes, or 3,600 seconds...

(h)
day
Day
A day is a unit of time, commonly defined as an interval equal to 24 hours. It also can mean that portion of the full day during which a location is illuminated by the light of the sun...

(d)
60 s
3600 s
86400 s
Pressure
Pressure
Pressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :...

bar
Bar (unit)
The bar is a unit of pressure equal to 100 kilopascals, and roughly equal to the atmospheric pressure on Earth at sea level. Other units derived from the bar are the megabar , kilobar , decibar , centibar , and millibar...

100 kPa
Plane angle degree
Degree (angle)
A degree , usually denoted by ° , is a measurement of plane angle, representing 1⁄360 of a full rotation; one degree is equivalent to π/180 radians...

(°)
minute
Minute of arc
A minute of arc, arcminute, or minute of angle , is a unit of angular measurement equal to one sixtieth of one degree. In turn, a second of arc or arcsecond is one sixtieth of one minute of arc....

(ʹ)
second (″)

• Conversion of units
Conversion of units
Conversion of units is the conversion between different units of measurement for the same quantity, typically through multiplicative conversion factors.- Process :...

• History of measurement
History of measurement
Units of measurement were among the earliest tools invented by humans. Primitive societies needed rudimentary measures for numerous tasks such as: constructing dwellings of an appropriate size and shape, fashioning clothing, or bartering food or raw materials....

• ISO/IEC 80000
ISO/IEC 80000
International standard ISO 80000 or IEC 80000—depending on which of the two international standards bodies International Organization for Standardization and International Electrotechnical Commission is in charge of each respective part—is a style guide for the use of physical quantities and units...

, style manual for measurements metric and non metric, superseding ISO 31
ISO 31
International Standard ISO 31 was the most widely respected style guide for the use of physical quantities and units of measurement, and formulas involving them, in scientific and educational documents worldwide...

• Metrication
Metrication
Metrication refers to the introduction and use of the SI metric system, the international standard for physical measurements. This has involved a long process of independent and systematic conversions of countries from various local systems of weights and measures. Metrication began in France in...

, the process of introducing the SI metric system as the worldwide standard for physical measurements
• Metrology
Metrology
Metrology is the science of measurement. Metrology includes all theoretical and practical aspects of measurement. The word comes from Greek μέτρον , "measure" + "λόγος" , amongst others meaning "speech, oration, discourse, quote, study, calculation, reason"...

• IEC Binary Prefixes
Binary prefix
In computing, a binary prefix is a specifier or mnemonic that is prepended to the units of digital information, the bit and the byte, to indicate multiplication by a power of 2...

, used in computer science
• Units of measurement
Units of measurement
A unit of measurement is a definite magnitude of a physical quantity, defined and adopted by convention and/or by law, that is used as a standard for measurement of the same physical quantity. Any other value of the physical quantity can be expressed as a simple multiple of the unit of...