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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) defines seven units of measure as a basic set from which all other SI units are derived

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...

. These SI base units and their physical quantities are:

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
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...

(US English: meter)
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...

for 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:...

(note: not the gram
Gram
The gram is a metric system unit of mass....

)
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....

for 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....
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...

for 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...
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...

for 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...
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...

for 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...
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...

for the 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...

.

The SI base quantities form a set of mutually independent dimensions as required by dimensional analysis

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...

commonly employed in science and technology. However, in a given realization of these units they may well be interdependent, i.e. defined in terms of each other.

The names of all SI units are written in lowercase characters (e.g., the met has the symbol m), except that the symbols of units named after persons are written with an initial capital letter (e.g., the ampere has the uppercase symbol A).

Many other units, such as the lit

The International System of Units

International System of Units

(SI) defines seven units of measure as a basic set from which all other SI units are derived

SI derived unit

. These SI base units and their physical quantities are:

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
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...

(US English: meter)
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...

for 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:...

(note: not the gram
Gram
The gram is a metric system unit of mass....

)
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....

for 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....
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...

for 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...
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...

for 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...
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...

for 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...
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...

for the 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...

.

The SI base quantities form a set of mutually independent dimensions as required by dimensional analysis

Dimensional analysis

commonly employed in science and technology. However, in a given realization of these units they may well be interdependent, i.e. defined in terms of each other.

The names of all SI units are written in lowercase characters (e.g., the met{{#ifeq:|us|er|re}} has the symbol m), except that the symbols of units named after persons are written with an initial capital letter (e.g., the ampere has the uppercase symbol A).

Many other units, such as the lit

The International System of Units

International System of Units

(SI) defines seven units of measure as a basic set from which all other SI units are derived

SI derived unit

. These SI base units and their physical quantities are:

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
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...

(US English: meter)
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...

for 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:...

(note: not the gram
Gram
The gram is a metric system unit of mass....

)
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....

for 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....
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...

for 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...
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...

for 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...
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...

for 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...
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...

for the 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...

.

The SI base quantities form a set of mutually independent dimensions as required by dimensional analysis

Dimensional analysis

commonly employed in science and technology. However, in a given realization of these units they may well be interdependent, i.e. defined in terms of each other.

The names of all SI units are written in lowercase characters (e.g., the met{{#ifeq:|us|er|re}} has the symbol m), except that the symbols of units named after persons are written with an initial capital letter (e.g., the ampere has the uppercase symbol A).

Many other units, such as the lit{{#ifeq:

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...

(US English: liter), are formally not part of the SI, but are accepted for use with SI.

style="font-size:larger;font-weight:bold;"|SI
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...

base units
Name	Symbol	Measure	Current (2005) Formal Definition	Historical origin / justification
met{{#ifeq: 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...	"The met{{#ifeq:\|us\|er\|re}} is the length of the path travelled by light in vacuum during a time interval of {{nowrap\|1/299 792 458}} of a second." 17th CGPM (1983, Resolution 1, CR, 97)	{{frac\|10,000,000}} of the distance from the Earth Earth Earth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets... 's equator to the North Pole measured on the circumference through Paris Paris Paris is the capital and largest city in France, situated on the river Seine, in northern France, at the heart of the Île-de-France region... .
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	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:...	"The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram." 3rd CGPM (1901, CR, 70)	The mass of one lit{{#ifeq: 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... of water Water Water is a chemical substance with the chemical formula H2O. A water molecule contains one oxygen and two hydrogen atoms connected by covalent bonds. Water is a liquid at ambient conditions, but it often co-exists on Earth with its solid state, ice, and gaseous state . Water also exists in a... . A lit{{#ifeq:\|us\|er\|re}} is one thousandth of a cubic met{{#ifeq:\|us\|er\|re}}.
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....	"The second is the duration of {{nowrap\|9 192 631 770}} periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom." 13th CGPM (1967/68, Resolution 1; CR, 103) "This definition refers to a caesium atom at rest at a temperature of 0 K." (Added by CIPM in 1997)	The day is divided in 24 hours, each hour divided in 60 minutes, each minute divided in 60 seconds. A second is {{frac\|(24 × 60 × 60)}} of the 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...
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...	"The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 met{{#ifeq:\|us\|er\|re}} apart in vacuum, would produce between these conductors a force equal to {{nowrap\|2 × 10⁻⁷}} newton per met{{#ifeq:\|us\|er\|re}} of length." 9th CGPM (1948)	The original "International Ampere" was defined electrochemically as the current required to deposit 1.118 milligrams of silver per second from a solution of silver nitrate Silver nitrate Silver nitrate is an inorganic compound with chemical formula . This compound is a versatile precursor to many other silver compounds, such as those used in photography. It is far less sensitive to light than the halides... . Compared to the SI ampere, the difference is 0.015%.
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...	"The kelvin, unit of thermodynamic temperature, is the fraction 1/273.16 of the thermodynamic temperature of the triple point Triple point In thermodynamics, the triple point of a substance is the temperature and pressure at which the three phases of that substance coexist in thermodynamic equilibrium... of water." 13th CGPM (1967/68, Resolution 4; CR, 104) "This definition refers to water having the isotopic composition defined exactly by the following amount of substance ratios: {{nowrap\|0.000 155 76}} mole of ²H per mole of ¹H, {{nowrap\|0.000 379 9}} mole of ¹⁷O per mole of ¹⁶O, and {{nowrap\|0.002 005 2}} mole of ¹⁸O per mole of ¹⁶O." (Added by CIPM in 2005)	The Celsius scale: the Kelvin scale uses the degree Celsius for its unit increment, but is a thermodynamic scale (0 K is absolute zero Absolute zero Absolute zero is the theoretical temperature at which entropy reaches its minimum value. The laws of thermodynamics state that absolute zero cannot be reached using only thermodynamic means.... ).
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...	"1. The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12; its symbol is 'mol.' 2. When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles." 14th CGPM (1971, Resolution 3; CR, 78) "In this definition, it is understood that unbound atoms of carbon 12, at rest and in their ground state, are referred to." (Added by CIPM in 1980)	Atomic weight Atomic weight Atomic weight is a dimensionless physical quantity, the ratio of the average mass of atoms of an element to 1/12 of the mass of an atom of carbon-12... or molecular weight divided by the molar mass constant Molar mass constant The molar mass constant, symbol Mu, is a physical constant which relates atomic weight and molar mass. Its value is defined to be 1 g/mol in SI units.... , 1 g/mol.
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...	"The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency {{nowrap\|540 × 10¹²}} hertz and that has a radiant intensity in that direction of 1/683 watt per steradian Steradian 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... ." 16th CGPM (1979, Resolution 3; CR, 100)	The candlepower Candlepower Candlepower is a now-obsolete unit which was used to express levels of light intensity in terms of the light emitted by a candle of specific size and constituents... , which is based on the light emitted from a burning candle of standard properties.

Future redefinitions

{{main|New SI definitions}}
There have been several modifications to the definitions of the base units, and additions of base units, since the Metre Convention in 1875. Since the redefinition of the met{{#ifeq:|us|er|re}} in 1960, the kilogram is the only unit which is directly defined in terms of a physical artifact rather than a property of nature. However, the mole, the ampere and the candela are also linked through their definitions to the mass of this platinum

Platinum

Platinum is a chemical element with the chemical symbol Pt and an atomic number of 78. Its name is derived from the Spanish term platina del Pinto, which is literally translated into "little silver of the Pinto River." It is a dense, malleable, ductile, precious, gray-white transition metal...

–iridium

Iridium

Iridium is the chemical element with atomic number 77, and is represented by the symbol Ir. A very hard, brittle, silvery-white transition metal of the platinum family, iridium is the second-densest element and is the most corrosion-resistant metal, even at temperatures as high as 2000 °C...

cylinder stored in a vault near Paris. It has long been an objective of 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"...

to find a way to define the kilogram in terms of a fundamental constant, in the same way that the met{{#ifeq:|us|er|re}} is now defined in terms of 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...

.

The 21st 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...

(CGPM, 1999) placed these efforts on an official footing, and recommended "that national laboratories continue their efforts to refine experiments that link the unit of mass to fundamental or atomic constants with a view to a future redefinition of the kilogram." Two main possibilities have attracted attention: the Planck constant

Planck constant

The Planck constant , also called Planck's constant, is a physical constant reflecting the sizes of energy quanta in quantum mechanics. It is named after Max Planck, one of the founders of quantum theory, who discovered it in 1899...

and the Avogadro constant.

In 2005, the 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...

(CIPM) approved the preparation of new definitions for the kilogram, the ampere, and the kelvin and it noted the possibility of a new definition for the mole based on the Avogadro constant. The 23rd CGPM (2007) decided to postpone any formal change until the next General Conference in 2011.

In a note to the CIPM in October 2009, Ian Mills, the President of the CIPM Consultative Committee - Units (CCU) cataloged the uncertainties of the fundamental constants of physics according to the current definitions and their values under the proposed new definition

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....

. He urged the CIPM to accept the proposed changes in the definition of the kilogram, ampere, kelvin and mole so that they are referenced to the values of the fundamental constants, namely Planck's constant (h), the electron charge (e), Boltzmann's constant (k), and Avogadro's constant (N_A).

SI base unit

Future redefinitions

See also

External links