International System of Units

# International System of Units

Overview

The International System of Units (abbreviated SI from ) is the modern form of the metric system
Metric system
The metric system is an international decimalised system of measurement. France was first to adopt a metric system, in 1799, and a metric system is now the official system of measurement, used in almost every country in the world...

and is generally a system of 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...

devised around seven base units
SI base unit
The International System of Units defines seven units of measure as a basic set from which all other SI units are derived. These SI base units and their physical quantities are:* metre for length...

and the convenience of the number ten. The older metric system included several groups of units. The SI was established in 1960, based on the metre-kilogram-second
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 ....

system, rather than the centimetre-gram-second
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...

system, which, in turn, had a few variants. The SI is declared as an evolving system, thus prefixes and units are created and unit definitions are modified through international agreement as the technology of measurement progresses, and as the precision of measurements improves.

It is the world's most widely used 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...

, which is used both in everyday commerce
Commerce
While business refers to the value-creating activities of an organization for profit, commerce means the whole system of an economy that constitutes an environment for business. The system includes legal, economic, political, social, cultural, and technological systems that are in operation in any...

and in science
Science
Science is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe...

.
Discussion
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Encyclopedia

The International System of Units (abbreviated SI from ) is the modern form of the metric system
Metric system
The metric system is an international decimalised system of measurement. France was first to adopt a metric system, in 1799, and a metric system is now the official system of measurement, used in almost every country in the world...

and is generally a system of 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...

devised around seven base units
SI base unit
The International System of Units defines seven units of measure as a basic set from which all other SI units are derived. These SI base units and their physical quantities are:* metre for length...

and the convenience of the number ten. The older metric system included several groups of units. The SI was established in 1960, based on the metre-kilogram-second
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 ....

system, rather than the centimetre-gram-second
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...

system, which, in turn, had a few variants. The SI is declared as an evolving system, thus prefixes and units are created and unit definitions are modified through international agreement as the technology of measurement progresses, and as the precision of measurements improves.

It is the world's most widely used 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...

, which is used both in everyday commerce
Commerce
While business refers to the value-creating activities of an organization for profit, commerce means the whole system of an economy that constitutes an environment for business. The system includes legal, economic, political, social, cultural, and technological systems that are in operation in any...

and in science
Science
Science is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe...

. The system has been nearly globally adopted
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...

with the United States being the only industrialized nation that does not mainly use the metric system in its commercial and standards activities. The United Kingdom has officially partially adopted metrication
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....

, with no intention of replacing customary measures entirely. Canada
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...

has adopted it for all legal purposes but imperial/US
United States customary units
United States customary units are a system of measurements commonly used in the United States. Many U.S. units are virtually identical to their imperial counterparts, but the U.S. customary system developed from English units used in the British Empire before the system of imperial units was...

units are still in common use, particularly in the buildings trade.

## History

The metric system
Metric system
The metric system is an international decimalised system of measurement. France was first to adopt a metric system, in 1799, and a metric system is now the official system of measurement, used in almost every country in the world...

was conceived by a group of scientists (among them, Antoine-Laurent Lavoisier
Antoine Lavoisier
Antoine-Laurent de Lavoisier , the "father of modern chemistry", was a French nobleman prominent in the histories of chemistry and biology...

, who is known as the "father of modern chemistry") who had been commissioned by the Assemblée nationale and Louis XVI of France to create a unified and rational system of measures. On 1 August 1793, the National Convention adopted the new decimal 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...

with a provisional length as well as the other decimal units with preliminary definitions and terms. On 7 April 1795 (Loi du 18 germinal, an III) the terms gram
Gram
The gram is a metric system unit of mass....

me
and 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...

me
replaced the former terms gravet (correctly milligrave) and grave and on 22 June 1799, after Pierre Méchain
Pierre Méchain
Pierre François André Méchain was a French astronomer and surveyor who, with Charles Messier, was a major contributor to the early study of deep sky objects and comets.-Life:...

and Jean-Baptiste Delambre completed their survey, the definitive standard metre was deposited in the French National Archives. On 10 December 1799 (a month after Napoleon's coup d'état), the metric system was definitively adopted in France.

The desire for international cooperation on 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"...

led to the signing in 1875 of the Metre Convention, a treaty that established three international organizations to oversee the keeping of metric standards:
• General Conference on Weights and Measures
General Conference on Weights and Measures
The General Conference on Weights and Measures is the English name of the Conférence générale des poids et mesures . It is one of the three organizations established to maintain the International System of Units under the terms of the Convention du Mètre of 1875...

(Conférence générale des poids et mesures or CGPM) – a meeting every four to six years of delegates from all member states;
• International Bureau of Weights and Measures
International Bureau of Weights and Measures
The International Bureau of Weights and Measures , is an international standards organisation, one of three such organisations established to maintain the International System of Units under the terms of the Metre Convention...

(Bureau international des poids et mesures or BIPM) – an international metrology centre at Sèvres
Sèvres
Sèvres is a commune in the southwestern suburbs of Paris, France. It is located from the centre of Paris.The town is known for its porcelain manufacture, the Manufacture nationale de Sèvres, making the famous Sèvres porcelain, as well as being the location of the International Bureau of Weights...

in France; and
• International Committee for Weights and Measures
International Committee for Weights and Measures
The Interglobal Committee for Weights and Measures is the English name of the Comité international des poids et mesures . It consists of eighteen persons from Member States of the Metre Convention...

(Comité international des poids et mesures or CIPM) – an administrative committee which meets annually at the BIPM.

The history of the metric system has seen a number of variations, whose use has spread around the world, to replace many traditional measurement systems
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...

. At the end of World War II, a number of different systems of measurement were still in use throughout the world. Some of these systems were metric-system variations, whereas others were based on customary systems. It was recognised that additional steps were needed to promote a worldwide measurement system
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...

. As a result, the 9th General Conference on Weights and Measures (CGPM), in 1948, asked the International Committee for Weights and Measures (CIPM) to conduct an international study of the measurement needs of the scientific, technical, and educational communities.

Based on the findings of this study, the 10th CGPM in 1954 decided that an international system should be derived from six base units to provide for the measurement of temperature and optical radiation in addition to mechanical and electromagnetic quantities. The six base units that were recommended are 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...

, 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....

, 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...

, degree Kelvin (later renamed 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 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...

. In 1960, the 11th CGPM named the system the International System of Units, abbreviated SI from the French name, . The seventh base unit, the 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...

, was added in 1971 by the 14th CGPM.

One of the CIPM committees, the CCU, has proposed a number of changes
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....

to the definitions of the base units used in SI. The CIPM meeting of October 2010 found that the proposal was not complete, and it is expected that the CGPM will consider the full proposal in 2015.

## Units and prefixes

The International System of Units consists of a set of units together with a set of 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...

. The units are divided into two classes—base units and derived units. There are seven base units
SI base unit
The International System of Units defines seven units of measure as a basic set from which all other SI units are derived. These SI base units and their physical quantities are:* metre for length...

, each representing, by convention, different kinds of physical quantities
Dimensional analysis
In physics and all science, dimensional analysis is a tool to find or check relations among physical quantities by using their dimensions. The dimension of a physical quantity is the combination of the basic physical dimensions which describe it; for example, speed has the dimension length per...

.
SI base units
Unit name Unit symbol Quantity name Quantity symbol Dimension symbol
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 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...

l (a lowercase L), x, r L
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...

Despite the prefix, the kilogram is the base unit of mass. The kilogram, not the gram, is used in the definitions of derived units.
kg 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:...

m M
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 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....

t T
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 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...

I (an uppercase i) I
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 thermodynamic temperature
Thermodynamic temperature
Thermodynamic temperature is the absolute measure of temperature and is one of the principal parameters of thermodynamics. Thermodynamic temperature is an "absolute" scale because it is the measure of the fundamental property underlying temperature: its null or zero point, absolute zero, is the...

T Θ
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 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...

Iv (an uppercase i with lowercase non-italicized v subscript) J
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 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...

n N

Note

Derived units
SI derived unit
The International System of Units specifies a set of seven base units from which all other units of measurement are formed, by products of the powers of base units. These other units are called SI derived units, for example, the SI derived unit of area is square metre , and of density is...

are formed from multiplication and division of the seven base units and other derived units and are unlimited in number; for example, the SI derived unit of speed is metre per second, m/s. Some derived units have special names; for example, the unit of resistance, the ohm, symbol Ω, is uniquely defined by the relation Ω = m2·kg·s−3·A−2, which follows from the definition of the quantity electrical resistance
Electrical resistance
The electrical resistance of an electrical element is the opposition to the passage of an electric current through that element; the inverse quantity is electrical conductance, the ease at which an electric current passes. Electrical resistance shares some conceptual parallels with the mechanical...

Radian is the ratio between the length of an arc and its radius. The radian is the standard unit of angular measure, used in many areas of mathematics. The unit was formerly a SI supplementary unit, but this category was abolished in 1995 and the radian is now considered a SI derived unit...

The steradian is the SI unit of solid angle. It is used to describe two-dimensional angular spans in three-dimensional space, analogous to the way in which the radian describes angles in a plane...

, once given special status, are now considered dimensionless derived units.

A prefix
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...

may be added to a unit to produce a multiple of the original unit. All multiples are integer powers of ten, and beyond a hundred(th) all are integer powers of a thousand. For example, kilo- denotes a multiple of a thousand and milli- denotes a multiple of a thousandth; hence there are one thousand millimetres to the metre and one thousand metres to the kilometre. The prefixes are never combined: a millionth of a metre is a micrometre not a millimillimetre.
In addition to the SI units, there is also a set of non-SI units accepted for use with SI
Non-SI units accepted for use with SI
This is a list of units that are not defined as part of the International System of Units , but are otherwise mentioned in the SI, because either the General Conference on Weights and Measures accepts their use as being multiples or submultiples of SI-units, they have important contemporary...

, which includes some commonly used non-coherent units such as 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...

.

## Writing unit symbols and the values of quantities

• The value of a quantity is written as a number followed by a space (representing a multiplication sign) and a unit symbol; e.g., "2.21 kg", "", "22 K". This rule explicitly includes the percent sign (%). Exceptions are the symbols for plane angular degrees, minutes and seconds (°, ′ and ″), which are placed immediately after the number with no intervening space.
• Symbols for derived units formed by multiplication are joined with a centre dot
Interpunct
An interpunct —also called an interpoint—is a small dot used for interword separation in ancient Latin script, which also appears in some modern languages as a stand-alone sign inside a word. It is present in Unicode as code point ....

(·) or a non-break space, for example, "N·m" or "N m".
• Symbols for derived units formed by division are joined with a solidus
Solidus (punctuation)
The solidus is a punctuation mark used to indicate fractions including fractional currency. It may also be called a shilling mark, an in-line fraction bar, or a fraction slash....

(/), or given as a negative exponent. For example, the "metre per second" can be written "m/s", "m s−1", "m·s−1" or . Only one solidus should be used; e.g., "kg/(m·s2)" and "kg·m−1·s−2" are acceptable, but "kg/m/s2" is ambiguous and unacceptable.
• Symbols are mathematical entities, not abbreviations, and do not have an appended period/full stop (.).
• Symbols are written in upright (Roman
Roman type
In typography, roman is one of the three main kinds of historical type, alongside blackletter and italic. Roman type was modelled from a European scribal manuscript style of the 1400s, based on the pairing of inscriptional capitals used in ancient Rome with Carolingian minuscules developed in the...

) type (m for metres, s for seconds), so as to differentiate from the italic type
Italic type
In typography, italic type is a cursive typeface based on a stylized form of calligraphic handwriting. Owing to the influence from calligraphy, such typefaces often slant slightly to the right. Different glyph shapes from roman type are also usually used—another influence from calligraphy...

used for quantities (m for mass, s for displacement). By consensus of international standards bodies, this rule is applied independent of the font used for surrounding text.
• Symbols for units are written in lower case (e.g., "m", "s", "mol"), except for symbols derived from the name of a person. For example, the unit of 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 :...

is named after Blaise Pascal
Blaise Pascal
Blaise Pascal , was a French mathematician, physicist, inventor, writer and Catholic philosopher. He was a child prodigy who was educated by his father, a tax collector in Rouen...

, so its symbol is written "Pa", whereas the unit
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...

itself is written "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...

".
• The one exception is 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...

, whose original symbol "l" is unsuitably similar to the numeral "1" or the uppercase letter "i" (depending on the typeface used), at least in many English-speaking countries. The American National Institute of Standards and Technology
National Institute of Standards and Technology
The National Institute of Standards and Technology , known between 1901 and 1988 as the National Bureau of Standards , is a measurement standards laboratory, otherwise known as a National Metrological Institute , which is a non-regulatory agency of the United States Department of Commerce...

recommends that "L" be used instead, a usage which is common in the US, Canada and Australia (but not elsewhere). This has been accepted as an alternative by the CGPM
General Conference on Weights and Measures
The General Conference on Weights and Measures is the English name of the Conférence générale des poids et mesures . It is one of the three organizations established to maintain the International System of Units under the terms of the Convention du Mètre of 1875...

since 1979. The cursive ℓ is occasionally seen, especially in Japan and Greece, but this is not currently recommended by any standards body
Standards organization
A standards organization, standards body, standards developing organization , or standards setting organization is any organization whose primary activities are developing, coordinating, promulgating, revising, amending, reissuing, interpreting, or otherwise producing technical standards that are...

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...

.
• A prefix is part of the unit, and its symbol is prepended to the unit symbol without a separator (e.g., "k" in "km", "M" in "MPa", "G" in "GHz"). Compound prefixes are not allowed.
• All symbols of prefixes larger than 103 (kilo) are uppercase.
• Symbols of units are not pluralised; e.g., "25 kg", not "25 kgs".
• The 10th resolution of CGPM in 2003 declared that "the symbol for the decimal marker
Decimal separator
Different symbols have been and are used for the decimal mark. The choice of symbol for the decimal mark affects the choice of symbol for the thousands separator used in digit grouping. Consequently the latter is treated in this article as well....

shall be either the point
Full stop
A full stop is the punctuation mark commonly placed at the end of sentences. In American English, the term used for this punctuation is period. In the 21st century, it is often also called a dot by young people...

on the line or the comma
Comma
A comma is a type of punctuation mark . The word comes from the Greek komma , which means something cut off or a short clause.Comma may also refer to:* Comma , a type of interval in music theory...

on the line." In practice, the decimal point is used in English-speaking countries and most of Asia, and the comma in most continental European languages
Languages of Europe
Most of the languages of Europe belong to Indo-European language family. These are divided into a number of branches, including Romance, Germanic, Balto-Slavic, Greek, and others. The Uralic languages also have a significant presence in Europe, including the national languages Hungarian, Finnish,...

.
• Spaces may be used as a thousands separator () in contrast to commas or periods (1,000,000 or 1.000.000) in order to reduce confusion resulting from the variation between these forms in different countries. In print
Space (punctuation)
In writing, a space is a blank area devoid of content, serving to separate words, letters, numbers, and punctuation. Conventions for interword and intersentence spaces vary among languages, and in some cases the spacing rules are quite complex....

, the space used for this purpose is typically narrower than that between words (commonly a thin space).
• Any line-break inside a number, inside a compound unit, or between number and unit should be avoided, but, if necessary, the last-named option should be used.
• In Chinese
Chinese language
The Chinese language is a language or language family consisting of varieties which are mutually intelligible to varying degrees. Originally the indigenous languages spoken by the Han Chinese in China, it forms one of the branches of Sino-Tibetan family of languages...

, Japanese
Japanese language
is a language spoken by over 130 million people in Japan and in Japanese emigrant communities. It is a member of the Japonic language family, which has a number of proposed relationships with other languages, none of which has gained wide acceptance among historical linguists .Japanese is an...

, and Korean language
Korean language
Korean is the official language of the country Korea, in both South and North. It is also one of the two official languages in the Yanbian Korean Autonomous Prefecture in People's Republic of China. There are about 78 million Korean speakers worldwide. In the 15th century, a national writing...

computing (CJK), some of the commonly used units, prefix-unit combinations, or unit-exponent combinations have been allocated predefined single characters taking up a full square. Unicode includes these in its CJK Compatibility and Letterlike Symbols subranges for back compatibility, without necessarily recommending future usage.
• When writing dimensionless quantities, the terms 'ppb' (parts per billion) and 'ppt' (parts per trillion
Long and short scales
The long and short scales are two of several different large-number naming systems used throughout the world for integer powers of ten. Many countries, including most in continental Europe, use the long scale whereas most English-speaking countries use the short scale...

) are recognised as language-dependent terms, since the value of billion and trillion can vary from language to language
Long and short scales
The long and short scales are two of several different large-number naming systems used throughout the world for integer powers of ten. Many countries, including most in continental Europe, use the long scale whereas most English-speaking countries use the short scale...

. SI, therefore, recommends avoiding these terms. However, no alternative is suggested by the International Bureau of Weights and Measures
International Bureau of Weights and Measures
The International Bureau of Weights and Measures , is an international standards organisation, one of three such organisations established to maintain the International System of Units under the terms of the Metre Convention...

(BIPM).

## Writing the unit names

• Names of units
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...

follow the grammatical rules associated with common nouns - in English and in French they start with a lowercase letter (e.g., newton, hertz, pascal), even when the symbol for the unit begins with a capital letter. This also applies to 'degrees Celsius', since 'degree' is the unit. In German however, names of units, in common with all nouns, start with a capital letter.
• Names of units are pluralised using the normal English grammar
English grammar
English grammar is the body of rules that describe the structure of expressions in the English language. This includes the structure of words, phrases, clauses and sentences...

rules; e.g., "henries" is the plural of "henry". The units 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...

, 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....

, and 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...

are exceptions from this rule: they remain the same in singular and plural form. Note that this rule applies only to the full names of units, not to their symbols.
• The official US spellings for deca, metre, and litre are deka, meter, and liter, respectively.

## Realisation of units

Metrologists carefully distinguish between the definition of a unit and its realisation. The definition of each base unit of the SI is drawn up so that it is unique and provides a sound theoretical basis upon which the most accurate and reproducible measurements can be made. The realisation of the definition of a unit is the procedure by which the definition may be used to establish the value and associated uncertainty of a quantity of the same kind as the unit. A description of how the definitions of some important units are realised in practice is given on the BIPM website. However, "any method consistent with the laws of physics could be used to realise any SI unit." (p. 111).

## Related systems

The definitions of the terms 'quantity', 'unit', 'dimension' etc. used in measurement, are given in the International Vocabulary of Metrology
International vocabulary of metrology
The International vocabulary of metrology is an attempt to find a common language and terminology in metrology, e.g. the science of measurements, across different fields of science, legislature and commerce...

.

The quantities and equations which define the SI units are now referred to as the International System of Quantities (ISQ), and are set out in the ISO/IEC 80000 Quantities and Units
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...

.

## Conversion factors

The relationship between the units used in different systems is determined by convention or from the basic definition of the units. Conversion of units from one system to another is accomplished by use of a conversion factor
Conversion of units
Conversion of units is the conversion between different units of measurement for the same quantity, typically through multiplicative conversion factors.- Process :...

. There are several compilations of conversion factors; see, for example, Appendix B of NIST SP 811.

## Cultural issues

The near-worldwide adoption of the metric system as a tool of economy and everyday commerce was based to some extent on the lack of customary systems in many countries to adequately describe some concepts, or as a result of an attempt to standardise the many regional variations in the customary system. International factors also affected the adoption of the metric system, as many countries increased their trade. For use in science, the SI prefixes simplify dealing with very large and small quantities.

Many units in everyday and scientific use are not SI units. In some cases these units have been designated by the BIPM as "non-SI units accepted for use with the SI".

Some examples include:
• The many units of time (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) in use besides the SI second, and are specifically accepted for use according to table 6.
• The year is specifically not included but has a recommended conversion factor.
• The 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...

temperature scale; kelvins are rarely employed in everyday use.
• Electric energy is often billed in kilowatt-hours
Watt-hour
The kilowatt hour, or kilowatt-hour, is a unit of energy equal to 1000 watt hours or 3.6 megajoules.For constant power, energy in watt hours is the product of power in watts and time in hours...

, instead of megajoules. Similarly, battery charge is often measured as milliampere-hours (mA·h), instead of coulombs.
• The 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...

and knot (nautical mile per hour) used to measure travel distance and speed of ships and aircraft (1 International nautical mile =  m or approximately 1 minute of latitude). In addition to these, Annex 5 of the Convention on International Civil Aviation
Convention on International Civil Aviation
The Convention on International Civil Aviation, also known as the Chicago Convention, established the International Civil Aviation Organization , a specialized agency of the United Nations charged with coordinating and regulating international air travel...

permits the "temporary use" of the foot for altitude
Altitude
Altitude or height is defined based on the context in which it is used . As a general definition, altitude is a distance measurement, usually in the vertical or "up" direction, between a reference datum and a point or object. The reference datum also often varies according to the context...

.
• Astronomical distances measured in astronomical unit
Astronomical unit
An astronomical unit is a unit of length equal to about or approximately the mean Earth–Sun distance....

s, parsec
Parsec
The parsec is a unit of length used in astronomy. It is about 3.26 light-years, or just under 31 trillion kilometres ....

s, and light-year
Light-year
A light-year, also light year or lightyear is a unit of length, equal to just under 10 trillion kilometres...

• Atomic scale units used in physics and chemistry, such as the 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....

, electron volt, atomic mass unit
Atomic mass unit
The unified atomic mass unit or dalton is a unit that is used for indicating mass on an atomic or molecular scale. It is defined as one twelfth of the rest mass of an unbound neutral atom of carbon-12 in its nuclear and electronic ground state, and has a value of...

and barn
Barn (unit)
A barn is a unit of area. Originally used in nuclear physics for expressing the cross sectional area of nuclei and nuclear reactions, today it is used in all fields of high energy physics to express the cross sections of any scattering process, and is best understood as a measure of the...

.
• Some physicist
Physicist
A physicist is a scientist who studies or practices physics. Physicists study a wide range of physical phenomena in many branches of physics spanning all length scales: from sub-atomic particles of which all ordinary matter is made to the behavior of the material Universe as a whole...

s prefer the centimetre-gram-second
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) units, or systems based on physical constant
Physical constant
A physical constant is a physical quantity that is generally believed to be both universal in nature and constant in time. It can be contrasted with a mathematical constant, which is a fixed numerical value but does not directly involve any physical measurement.There are many physical constants in...

s, such as Planck units
Planck units
In physics, Planck units are physical units of measurement defined exclusively in terms of five universal physical constants listed below, in such a manner that these five physical constants take on the numerical value of 1 when expressed in terms of these units. Planck units elegantly simplify...

, atomic units
Atomic units
Atomic units form a system of natural units which is especially convenient for atomic physics calculations. There are two different kinds of atomic units, which one might name Hartree atomic units and Rydberg atomic units, which differ in the choice of the unit of mass and charge. This article...

, or geometric units
Geometrized unit system
A geometrized unit system or geometric unit system is a system of natural units in which the base physical units are chosen so that the speed of light in a vacuum, c, and the gravitational constant, G, are set equal to unity. c = 1 \ G = 1 \...

.
• In some countries, the informal cup
Cup (unit)
The cup is a customary unit of measurement for volume, used in cooking to measure liquids and bulk foods such as granulated sugar...

measurement has become 250 mL. Likewise, a 500 g metric pound is used in many countries. Liquids, especially alcoholic ones, are often sold in units whose origins are historical (for example, pint
Pint
The pint is a unit of volume or capacity that was once used across much of Europe with values varying from state to state from less than half a litre to over one litre. Within continental Europe, the pint was replaced with the metric system during the nineteenth century...

s for beer and cider in glasses in the UK —although pint means 568 mL; Jeroboams for champagne in France).
• A metric mile of 10 km is used in Norway and Sweden. The term metric mile is also used in some countries for the 1500 m foot race.
• In the US, blood glucose
Blood sugar
The blood sugar concentration or blood glucose level is the amount of glucose present in the blood of a human or animal. Normally in mammals, the body maintains the blood glucose level at a reference range between about 3.6 and 5.8 mM , or 64.8 and 104.4 mg/dL...

measurements are recorded in milligrams per decilitre (mg/dL), which would normalise to cg/L; in Canada, Australia, New Zealand, Oceania, and Europe, the standard is millimole per litre (mmol/L) or mM (millimolar).
• Blood pressure
Blood pressure
Blood pressure is the pressure exerted by circulating blood upon the walls of blood vessels, and is one of the principal vital signs. When used without further specification, "blood pressure" usually refers to the arterial pressure of the systemic circulation. During each heartbeat, BP varies...

is usually measured in mmHg(≈Torr
Torr
The torr is a non-SI unit of pressure with the ratio of 760 to 1 standard atmosphere, chosen to be roughly equal to the fluid pressure exerted by a millimetre of mercury, i.e., a pressure of 1 torr is approximately equal to 1 mmHg...

).
• Atmospheric pressure
Atmospheric pressure
Atmospheric pressure is the force per unit area exerted into a surface by the weight of air above that surface in the atmosphere of Earth . In most circumstances atmospheric pressure is closely approximated by the hydrostatic pressure caused by the weight of air above the measurement point...

in government weather reports is measured in inHg in the USA, and in the SI unit hPa in Australia, UK and most other countries.

The fine-tuning that has happened to the metric base-unit definitions over the past 200 years, as experts have tried periodically to find more precise and reproducible methods, does not affect the everyday use of metric units. Since most non-SI units in common use, such as the US customary units, are defined in SI units, any change in the definition of the SI units results in a change of the definition of the older units, as well.

One of the European Union's (EU) objectives is the creation of a single market for trade. In order to achieve this objective, the EU standardised on using SI as the legal units of measure. As of 2009, it has issued two units of measurement directives which catalogued the units of measure that might be used for, amongst other things, trade: the first was Directive 71/354/EEC issued in 1971 which required member states to standardise on SI rather than use the variety of 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...

and 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 ....

units then in use. The second was Directive 80/181/EEC issued in 1979 which replaced the first and which gave the United Kingdom and the Republic of Ireland a number of derogation
Derogation
Derogation is the partial revocation of a law, as opposed to abrogation or the total abolition of a law. The term is used in both civil law and common law. It is sometimes used, loosely, to mean abrogation, as in the legal maxim: Lex posterior derogat priori, i.e...

s from the original directive.

The directives gave a derogation from using SI units in areas where other units of measure had either been agreed by international treaty or which were in universal use in worldwide trade. They also permitted the use of supplementary indicators alongside, but not in place of the units catalogued in the directive. In its original form, Directive 80/181/EEC had a cut-off date for the use of such indicators, but with each amendment this date was moved until, in 2009, supplementary indicators have been allowed indefinitely.

### Chinese characters

In Japanese:
Individual Chinese character
Chinese character
Chinese characters are logograms used in the writing of Chinese and Japanese , less frequently Korean , formerly Vietnamese , or other languages...

s exist for some SI units, namely metre, litre, and gram, with the prefixes from kilo- (1000) to milli- (1/1000), yielding 21 (3×7) characters. These were created in Japan in the late 19th century (Meiji period
Meiji period
The , also known as the Meiji era, is a Japanese era which extended from September 1868 through July 1912. This period represents the first half of the Empire of Japan.- Meiji Restoration and the emperor :...

) by choosing characters for the basic units – 米 "metre", 立 "litre", and 瓦 "gram" – and for the prefixes – 千 "kilo-, 1000", 百 "hecto-, 100", 十 "deca-, 10", 分 "deci-, 1/10", 厘 "centi-, 1/100", and 毛 "milli-, 1/1000" – and then combining them to form a single character, such as 粁 (米+千) for kilometre (in the case of no prefix, the base character alone is used). The entire metre series, for example, is 粁, 粨, 籵, 米, 粉, 糎, 粍. The symbol
Symbol
A symbol is something which represents an idea, a physical entity or a process but is distinct from it. The purpose of a symbol is to communicate meaning. For example, a red octagon may be a symbol for "STOP". On a map, a picture of a tent might represent a campsite. Numerals are symbols for...

s for the metric units are internationally-recognised Latin characters.

In Chinese:
The basic units are 米 mǐ "meter", 升 shēng "liter", 克 kè "gram", and 秒 mǐao "second".
Some sample prefixes are 分 fēn "deci", 厘 lí "centi", 毫 háo "milli", and 微 wēi "micro".
These are not combined into a single character,
so for example centimeters are simply 厘米 límǐ.

 Dimensional analysisDimensional analysisIn physics and all science, dimensional analysis is a tool to find or check relations among physical quantities by using their dimensions. The dimension of a physical quantity is the combination of the basic physical dimensions which describe it; for example, speed has the dimension length per... History of measurementHistory of measurementUnits 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.... International Vocabulary of MetrologyInternational vocabulary of metrologyThe International vocabulary of metrology is an attempt to find a common language and terminology in metrology, e.g. the science of measurements, across different fields of science, legislature and commerce... International System of Quantities List of international common standards Long and short scalesLong and short scalesThe long and short scales are two of several different large-number naming systems used throughout the world for integer powers of ten. Many countries, including most in continental Europe, use the long scale whereas most English-speaking countries use the short scale... Names of large numbersNames of large numbersThis article lists and discusses the usage and derivation of names of large numbers, together with their possible extensions.The following table lists those names of large numbers which are found in many English dictionaries and thus have a special claim to being "real words"... Names of small numbersNames of small numbersThis article lists and discusses the usage and derivation of names of small numbers.-Table of names:The following table lists English language names of small numbers used in the long and short scales, along with the power of ten, engineering notation, and International System of Units symbols and... Non-SI units accepted for use with the SINon-SI units accepted for use with SIThis is a list of units that are not defined as part of the International System of Units , but are otherwise mentioned in the SI, because either the General Conference on Weights and Measures accepts their use as being multiples or submultiples of SI-units, they have important contemporary... Orders of magnitude SI base units SI derived units SI prefixSI prefixThe 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...es Organisations Institute for Reference Materials and MeasurementsInstitute for Reference Materials and MeasurementsThe Institute for Reference Materials and Measurements , located in Geel, Belgium, is one of the seven institutes of the Joint Research Centre , a Directorate-General of the European Commission .... (IRMM) CODATACommittee on Data for Science and TechnologyThe Committee on Data for Science and Technology was established in 1966 as an interdisciplinary committee of the International Council for Science. It seeks to improve the compilation, critical evaluation, storage, and retrieval of data of importance to science and technology.The CODATA Task... Standards and conventions Coordinated Universal TimeCoordinated Universal TimeCoordinated Universal Time is the primary time standard by which the world regulates clocks and time. It is one of several closely related successors to Greenwich Mean Time. Computer servers, online services and other entities that rely on having a universally accepted time use UTC for that purpose... (UTC) ISO 80000