The International System of Units (SI, abbreviated from the French Système international (d'unités)) is the modern form of the metric system, and is the most widely used system of measurement. It comprises a coherent system of units of measurement built on seven base units, which are the ampere, kelvin, second, metre, kilogram, candela, mole, and a set of twenty prefixes to the unit names and unit symbols that may be used when specifying multiples and fractions of the units. The system also specifies names for 22 derived units, such as lumen and watt, for other common physical quantities.
The base units are derived from invariant constants of nature, such as the speed of light in vacuum and the triple point of water, which can be observed and measured with great accuracy, and one physical artefact. The artefact is the international prototype kilogram, certified in 1889, and consisting of a cylinder of platinumiridium, which nominally has the same mass as one litre of water at the freezing point. Its stability has been a matter of significant concern, culminating in a revision of the definition of the base units entirely in terms of constants of nature, scheduled to be put into effect on 20 May 2019.^{[1]}
Derived units may be defined in terms of base units or other derived units. They are adopted to facilitate measurement of diverse quantities. The SI is intended to be an evolving system; units and prefixes are created and unit definitions are modified through international agreement as the technology of measurement progresses and the precision of measurements improves. The most recent derived unit, the katal, was defined in 1999.
The reliability of the SI depends not only on the precise measurement of standards for the base units in terms of various physical constants of nature, but also on precise definition of those constants. The set of underlying constants is modified as more stable constants are found, or may be more precisely measured. For example, in 1983 the metre was redefined as the distance that light propagates in vacuum in a given fraction of a second, thus making the value of the speed of light in terms of the defined units exact.
The motivation for the development of the SI was the diversity of units that had sprung up within the centimetre–gram–second (CGS) systems (specifically the inconsistency between the systems of electrostatic units and electromagnetic units) and the lack of coordination between the various disciplines that used them. The General Conference on Weights and Measures (French: Conférence générale des poids et mesures – CGPM), which was established by the Metre Convention of 1875, brought together many international organisations to establish the definitions and standards of a new system and standardise the rules for writing and presenting measurements. The system was published in 1960 as a result of an initiative that began in 1948. It is based on the metre–kilogram–second system of units (MKS) rather than any variant of the CGS. Since then, the SI has been adopted by all countries except the United States, Liberia and Myanmar.^{[2]}
The International System of Units consists of a set of base units, derived units, and a set of decimalbased multipliers that are used as prefixes.^{[3]}^{:103–106} The units, excluding prefixed units,^{[Note 1]} form a coherent system of units, which is based on a system of quantities in such a way that the equations between the numerical values expressed in coherent units have exactly the same form, including numerical factors, as the corresponding equations between the quantities. For example, 1 N = 1 kg × 1 m/s^{2} says that one newton is the force required to accelerate a mass of one kilogram at one metre per second squared, as related through the principle of coherence to the equation relating the corresponding quantities: F = m × a.
Derived units apply to derived quantities, which may by definition be expressed in terms of base quantities, and thus are not independent; for example, electrical conductance is the inverse of electrical resistance, with the consequence that the siemens is the inverse of the ohm, and similarly, the ohm and siemens can be replaced with a ratio of an ampere and a volt, because those quantities bear a defined relationship to each other.^{[Note 2]} Other useful derived quantities can be specified in terms of the SI base and derived units that have no named units in the SI system, such as acceleration, which is defined in SI units as m/s^{2}.
The SI base units are the building blocks of the system and all the other units are derived from them. When Maxwell first introduced the concept of a coherent system, he identified three quantities that could be used as base units: mass, length and time. Giorgi later identified the need for an electrical base unit, for which the unit of electric current was chosen for SI. Another three base units (for temperature, amount of substance and luminous intensity) were added later.
Unit name 
Unit symbol 
Dimension symbol 
Quantity name 
Definition^{[n 1]} 

metre  m  L  length 

kilogram^{[n 2]}  kg  M  mass 

second  s  T  time 

ampere  A  I  electric current 

kelvin  K  Θ  thermodynamic temperature 

mole  mol  N  amount of substance 

candela  cd  J  luminous intensity 

The Prior definitions of the various base units in the above table were made by the following authorities:
All other definitions result from resolutions by either CGPM or the CIPM and are catalogued in the SI Brochure. 
The early metric systems defined a unit of weight as a base unit, while the SI defines an analogous unit of mass. In everyday use, these are mostly interchangeable, but in scientific contexts the difference matters. Mass, strictly the inertial mass, represents a quantity of matter. It relates the acceleration of a body to the applied force via Newton's law, F = m × a: force equals mass times acceleration. A force of 1 N (newton) applied to a mass of 1 kg will accelerate it at 1 m/s^{2}. This is true whether the object is floating in space or in a gravity field e.g. at the Earth's surface. Weight is the force exerted on a body by a gravitational field, and hence its weight depends on the strength of the gravitational field. Weight of a 1 kg mass at the Earth's surface is m × g; mass times the acceleration due to gravity, which is 9.81 newtons at the Earth's surface and is about 3.5 newtons at the surface of Mars. Since the acceleration due to gravity is local and varies by location and altitude on the Earth, weight is unsuitable for precision measurements of a property of a body, and this makes a unit of weight unsuitable as a base unit.
The derived units in the SI are formed by powers, products or quotients of the base units and are unlimited in number.^{[3]}^{:103}^{[4]}^{:3} Derived units are associated with derived quantities; for example, velocity is a quantity that is derived from the base quantities of time and length, and thus the SI derived unit is metre per second (symbol m/s). The dimensions of derived units can be expressed in terms of the dimensions of the base units.
Combinations of base and derived units may be used to express other derived units. For example, the SI unit of force is the newton (N), the SI unit of pressure is the pascal (Pa)—and the pascal can be defined as one newton per square metre (N/m^{2}).^{[9]}
SI derived unit  Symbol  Quantity  Symbol 

square metre  m^{2}  area  A 
cubic metre  m^{3}  volume  V 
metre per second  m⋅s^{−1}  speed, velocity  v 
metre per second squared  m⋅s^{−2}  acceleration  a 
reciprocal metre  m^{−1}  wavenumber  σ, ṽ 
kilogram per cubic metre  kg⋅m^{−3}  density  ρ 
kilogram per square metre  kg⋅m^{−2}  surface density  ρ_{A} 
cubic metre per kilogram  m^{3}⋅kg^{−1}  specific volume  v 
ampere per square metre  A⋅m^{−2}  current density  j 
ampere per metre  A⋅m^{−1}  magnetic field strength  H 
mole per cubic metre  mol⋅m^{−3}  concentration  c 
kilogram per cubic metre  kg⋅m^{−3}  mass concentration  ρ, γ 
candela per square metre  cd⋅m^{−2}⋅  luminance  L_{v} 
one  1  refractive index  n 
one  1  relative permeability  μ_{r} 
Name^{note 1}  Symbol  Quantity  In other SI units  In SI base units 

radian^{note 2}  rad  plane angle  1  (m⋅m^{−1}) 
steradian^{note 2}  sr  solid angle  1  (m^{2}⋅m^{−2}) 
hertz  Hz  frequency  s^{−1}  
newton  N  force, weight  kg⋅m⋅s^{−2}  
pascal  Pa  pressure, stress  N/m^{2}  kg⋅m^{−1}⋅s^{−2} 
joule  J  energy, work, heat  N⋅m = Pa⋅m^{3}  kg⋅m^{2}⋅s^{−2} 
watt  W  power, radiant flux  J/s  kg⋅m^{2}⋅s^{−3} 
coulomb  C  electric charge or quantity of electricity  s⋅A  
volt  V  voltage (electrical potential), emf  W/A  kg⋅m^{2}⋅s^{−3}⋅A^{−1} 
farad  F  capacitance  C/V  kg^{−1}⋅m^{−2}⋅s^{4}⋅A^{2} 
ohm  Ω  resistance, impedance, reactance  V/A  kg⋅m^{2}⋅s^{−3}⋅A^{−2} 
siemens  S  electrical conductance  Ω^{−1}  kg^{−1}⋅m^{−2}⋅s^{3}⋅A^{2} 
weber  Wb  magnetic flux  V⋅s  kg⋅m^{2}⋅s^{−2}⋅A^{−1} 
tesla  T  magnetic flux density  Wb/m^{2}  kg⋅s^{−2}⋅A^{−1} 
henry  H  inductance  Wb/A  kg⋅m^{2}⋅s^{−2}⋅A^{−2} 
degree Celsius  °C  temperature relative to 273.15 K  K  
lumen  lm  luminous flux  cd⋅sr  cd 
lux  lx  illuminance  lm/m^{2}  m^{−2}⋅cd 
becquerel  Bq  radioactivity (decays per unit time)  s^{−1}  
gray  Gy  absorbed dose (of ionising radiation)  J/kg  m^{2}⋅s^{−2} 
sievert  Sv  equivalent dose (of ionising radiation)  J/kg  m^{2}⋅s^{−2} 
katal  kat  catalytic activity  mol⋅s^{−1}  
Notes 1. The table is ordered so that a derived unit is listed after the units upon which its definition depends. 2. The radian and steradian are defined as dimensionless derived units. 
Name^{note 1}  Symbol  Quantity  In other SI units  In SI base units 

pascal second  Pa⋅s  dynamic viscosity  
newton metre  N⋅m  moment of force  
newton per metre  N/m  surface tension  
radian per second  rad/s  angular velocity  
radian per second squared  angular acceleration  
watt per square metre  heat flux density  
joule per kelvin  heat capacity, entropy  
joule per kilogram kelvin  specific heat capacity, specific entropy  
joule per kilogram  specific energy  
watt per metre kelvin  thermal conductivity  
joule per cubic metre  energy density  
volt per metre  electric field strength  
coulomb per cubic metre  electric charge density  
coulomb per square metre  surface charge density, electric flux density  
farad per metre  permittivity  
henry per metre  permeability  
joule per mole  molar energy  
joule per mole kelvin  molar heat capacity, molar entropy  
coulomb per kilogram  exposure  
gray per second  absorbed dose rate  
watt per steradian  radiant intensity  
watt per square metre steradian  radiance  
katal per cubic metre  catalytic activity concentration  
Notes 1. The table is ordered so that a derived unit is listed after the units upon which its definition depends. 
Prefixes are added to unit names to produce multiples and submultiples of the original unit. All of these are integer powers of ten, and above a hundred or below a hundredth all are integer powers of a thousand. For example, kilo denotes a multiple of a thousand and milli denotes a multiple of a thousandth, so there are one thousand millimetres to the metre and one thousand metres to the kilometre. The prefixes are never combined, so for example a millionth of a metre is a micrometre, not a millimillimetre. Multiples of the kilogram are named as if the gram were the base unit, so a millionth of a kilogram is a milligram, not a microkilogram.^{[3]}^{:122}^{[10]}^{:14} When prefixes are used to form multiples and submultiples of SI base and derived units, the resulting units are no longer coherent.^{[3]}^{:7}
The BIPM specifies twenty prefixes for the International System of Units (SI):

Many nonSI units continue to be used in the scientific, technical, and commercial literature. Some units are deeply embedded in history and culture, and their use has not been entirely replaced by their SI alternatives. The CIPM recognised and acknowledged such traditions by compiling a list of nonSI units accepted for use with SI:^{[3]}
Certain units of time, angle, and legacy nonSI units have a long history of consistent use. Most societies have used the solar day and its nondecimal subdivisions as a basis of time and, unlike the foot or the pound, these were the same regardless of where they were being measured. The radian, being 1/2π of a revolution, has mathematical advantages but it is cumbersome for navigation, and, as with time, the units used in navigation are largely consistent around the world. The tonne, litre, and hectare were adopted by the CGPM in 1879 and have been retained as units that may be used alongside SI units, having been given unique symbols. The catalogued units are given below:
Quantity  Name  Symbol  Value in SI units 

time  minute  min  1 min = 60 s 
hour  h  1 h = 60 min = 3600 s  
day  d  1 d = 24 h = 86400 s  
length  astronomical unit  au  1 au = 149597870700 m 
plane and phase angle  degree  °  1° = (π/180) rad 
minute  ′  1′ = (1/60)° = (π/10800) rad  
second  ″  1″ = (1/60)′ = (π/648000) rad  
area  hectare  ha  1 ha = 1 hm^{2} = 10^{4} m^{2} 
volume  litre  l, L  1 l = 1 L = 1 dm^{3} = 10^{3} cm^{3} = 10^{−3} m^{3} 
mass  tonne (metric ton)  t  1 t = 1000 kg 
dalton  Da  1 Da = 1.660539040(20)×10^{−27} kg  
energy  electronvolt  eV  1 eV = 1.602176634×10^{−19} J 
logarithmic ratio quantities  neper  Np  In using these units it is important that the nature of the quantity be specified and that any reference value used be specified. 
bel  B  
decibel  dB 
The basic units of the metric system, as originally defined, represented common quantities or relationships in nature. They still do – the modern precisely defined quantities are refinements of definition and methodology, but still with the same magnitudes. In cases where laboratory precision may not be required or available, or where approximations are good enough, the original definitions may suffice.^{[Note 4]}
The symbols for the SI units are intended to be identical, regardless of the language used,^{[3]}^{:130–135} but unit names are ordinary nouns and use the character set and follow the grammatical rules of the language concerned. Names of units 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.^{[11]}^{[12]} The official British and American spellings for certain SI units differ – British English, as well as Australian, Canadian and New Zealand English, uses the spelling deca, metre, and litre whereas American English uses the spelling deka, meter, and liter, respectively.^{[4]}^{:3}
Although the writing of unit names is languagespecific, the writing of unit symbols and the values of quantities is consistent across all languages and therefore the SI Brochure has specific rules in respect of writing them.^{[3]}^{:130–135} The guideline produced by the National Institute of Standards and Technology (NIST)^{[13]} clarifies languagespecific areas in respect of American English that were left open by the SI Brochure, but is otherwise identical to the SI Brochure.^{[14]}
General rules^{[Note 5]} for writing SI units and quantities apply to text that is either handwritten or produced using an automated process:
The rules covering printing of quantities and units are part of ISO 800001:2009.^{[16]}
Further rules^{[Note 5]} are specified in respect of production of text using printing presses, word processors, typewriters and the like.
The denominator "hour" (h) is often translated to the country language:
Countries with historical ties to the United States often mix up the international "km/h" with the American "MPH":
The CGPM publishes a brochure that defines and presents the SI.^{[3]} Its official version is in French, in line with the Metre Convention.^{[3]}^{:102} It leaves some scope for local interpretation, particularly regarding names and terms in different languages.^{[Note 6]}^{[4]}
The writing and maintenance of the CGPM brochure is carried out by one of the committees of the International Committee for Weights and Measures (CIPM). The definitions of the terms "quantity", "unit", "dimension" etc. that are used in the SI Brochure are those given in the International vocabulary of metrology.^{[17]}
The quantities and equations that provide the context in which the SI units are defined are now referred to as the International System of Quantities (ISQ). The system is based on the quantities underlying each of the seven base units of the SI. Other quantities, such as area, pressure, and electrical resistance, are derived from these base quantities by clear noncontradictory equations. The ISQ defines the quantities that are measured with the SI units.^{[18]} The ISQ is defined in the international standard ISO/IEC 80000, and was finalised in 2009 with the publication of ISO 800001.^{[19]}
Metrologists carefully distinguish between the definition of a unit and its realisation. The definition of each base unit of the SI is drawn up so that it is unique and provides a sound theoretical basis on which the most accurate and reproducible measurements can be made. The realisation of the definition of a unit is the procedure by which the definition may be used to establish the value and associated uncertainty of a quantity of the same kind as the unit. A description of the mise en pratique^{[Note 7]} of the base units is given in an electronic appendix to the SI Brochure.^{[21]}^{[3]}^{:168–169}
The published mise en pratique is not the only way in which a base unit can be determined: the SI Brochure states that "any method consistent with the laws of physics could be used to realise any SI unit."^{[3]}^{:111} In the current (2016) exercise to overhaul the definitions of the base units, various consultative committees of the CIPM have required that more than one mise en pratique shall be developed for determining the value of each unit. In particular:
The International Bureau of Weights and Measures (BIPM) has described SI as "the modern metric system".^{[3]}^{:95} Changing technology has led to an evolution of the definitions and standards that has followed two principal strands – changes to SI itself, and clarification of how to use units of measure that are not part of SI but are still nevertheless used on a worldwide basis.
Since 1960 the CGPM has made a number of changes to the SI to meet the needs of specific fields, notably chemistry and radiometry. These are mostly additions to the list of named derived units, and include the mole (symbol mol) for an amount of substance, the pascal (symbol Pa) for pressure, the siemens (symbol S) for electrical conductance, the becquerel (symbol Bq) for "activity referred to a radionuclide", the gray (symbol Gy) for ionising radiation, the sievert (symbol Sv) as the unit of dose equivalent radiation, and the katal (symbol kat) for catalytic activity.^{[3]}^{:156}^{[25]}^{[3]}^{:156}^{[3]}^{:158}^{[3]}^{:159}^{[3]}^{:165}
Acknowledging the advancement of precision science at both large and small scales, the range of defined prefixes pico (10^{−12}) to tera (10^{12}) was extended to 10^{−24} to 10^{24}.^{[3]}^{:152}^{[3]}^{:158}^{[3]}^{:164}
The 1960 definition of the standard metre in terms of wavelengths of a specific emission of the krypton 86 atom was replaced with the distance that light travels in a vacuum in exactly 1/299792458 second, so that the speed of light is now an exactly specified constant of nature.
A few changes to notation conventions have also been made to alleviate lexicographic ambiguities. An analysis under the aegis of CSIRO, published in 2009 by the Royal Society, has pointed out the opportunities to finish the realisation of that goal, to the point of universal zeroambiguity machine readability.^{[26]}
After the metre was redefined in 1960, the kilogram remained the only SI base unit directly based on a specific physical artefact, the international prototype of the kilogram (IPK), for its definition and thus the only unit that was still subject to periodic comparisons of national standard kilograms with the IPK.^{[27]} During the 2nd and 3rd Periodic Verification of National Prototypes of the Kilogram, a significant divergence had occurred between the mass of the IPK and all of its official copies stored around the world: the copies had all noticeably increased in mass with respect to the IPK. During extraordinary verifications carried out in 2014 preparatory to redefinition of metric standards, continuing divergence was not confirmed. Nonetheless, the residual and irreducible instability of a physical IPK undermined the reliability of the entire metric system to precision measurement from small (atomic) to large (astrophysical) scales.
A proposal was made that:
In 2015, the CODATA task group on fundamental constants announced special submission deadlines for data to compute the final values for the new definitions.^{[28]}
The new definitions were adopted at the 26th CGPM in November 2018, and will come into effect in May 2019.^{[29]}
The units and unit magnitudes of the metric system which became the SI were improvised piecemeal from everyday physical quantities starting in the mid18th century. Only later were they moulded into an orthogonal coherent decimal system of measurement.
The degree centigrade as a unit of temperature resulted from the scale devised by Swedish astronomer Anders Celsius in 1742. His scale counterintuitively designated 100 as the freezing point of water and 0 as the boiling point. Independently, in 1743, the French physicist JeanPierre Christin described a scale with 0 as the freezing point of water and 100 the boiling point. The scale became known as the centigrade, or 100 gradations of temperature, scale.
The metric system was developed from 1791 onwards by a committee of the French Academy of Sciences, commissioned to create a unified and rational system of measures.^{[31]} The group, which included preeminent French men of science,^{[32]}^{:89} used the same principles for relating length, volume, and mass that had been proposed by the English clergyman John Wilkins in 1668^{[33]}^{[34]} and the concept of using the Earth's meridian as the basis of the definition of length, originally proposed in 1670 by the French abbot Mouton.^{[35]}^{[36]}
In March 1791, the Assembly adopted the committee's proposed principles for the new decimal system of measure including the metre defined to be 1/10,000,000th of the length of the quadrant of earth's meridian passing through Paris, and authorised a survey to precisely establish the length of the meridian. In July 1792, the committee proposed the names metre, are, litre and grave for the units of length, area, capacity, and mass, respectively. The committee also proposed that multiples and submultiples of these units were to be denoted by decimalbased prefixes such as centi for a hundredth and kilo for a thousand.^{[37]}^{:82}
Later, during the process of adoption of the metric system, the Latin gramme and kilogramme, replaced the former provincial terms gravet (1/1000 grave) and grave. In June 1799, based on the results of the meridian survey, the standard mètre des Archives and kilogramme des Archives were deposited in the French National Archives. Subsequently, that year, the metric system was adopted by law in France.^{[43]} ^{[44]} The French system was shortlived due to its unpopularity. Napoleon ridiculed it, and in 1812, introduced a replacement system, the mesures usuelles or "customary measures" which restored many of the old units, but redefined in terms of the metric system.
During the first half of the 19th century there was little consistency in the choice of preferred multiples of the base units: typically the myriametre (10000 metres) was in widespread use in both France and parts of Germany, while the kilogram (1000 grams) rather than the myriagram was used for mass.^{[30]}
In 1832, the German mathematician Carl Friedrich Gauss, assisted by Wilhelm Weber, implicitly defined the second as a base unit when he quoted the Earth's magnetic field in terms of millimetres, grams, and seconds.^{[38]} Prior to this, the strength of the Earth's magnetic field had only been described in relative terms. The technique used by Gauss was to equate the torque induced on a suspended magnet of known mass by the Earth's magnetic field with the torque induced on an equivalent system under gravity. The resultant calculations enabled him to assign dimensions based on mass, length and time to the magnetic field.^{[Note 8]}^{[45]}
A candlepower as a unit of illuminance was originally defined by an 1860 English law as the light produced by a pure spermaceti candle weighing ^{1}⁄_{6} pound (76 grams) and burning at a specified rate. Spermaceti, a waxy substance found in the heads of sperm whales, was once used to make highquality candles. At this time the French standard of light was based upon the illumination from a Carcel oil lamp. The unit was defined as that illumination emanating from a lamp burning pure rapeseed oil at a defined rate. It was accepted that ten standard candles were about equal to one Carcel lamp.
French  English  Pages^{[3]} 

étalons  [Technical] standard  5, 95 
prototype  prototype [kilogram/metre]  5,95 
noms spéciaux  [Some derived units have] special names 
16,106 
mise en pratique  mise en pratique [Practical realisation]^{[Note 9]} 
82, 171 
A Frenchinspired initiative for international cooperation in metrology led to the signing in 1875 of the Metre Convention, also called Treaty of the Metre, by 17 nations.^{[Note 10]}^{[32]}^{:353–354} Initially the convention only covered standards for the metre and the kilogram. In 1921, the Metre Convention was extended to include all physical units, including the ampere and others thereby enabling the CGPM to address inconsistencies in the way that the metric system had been used.^{[39]}^{[3]}^{:96}
A set of 30 prototypes of the metre and 40 prototypes of the kilogram,^{[Note 11]} in each case made of a 90% platinum10% iridium alloy, were manufactured by British metallurgy specialty firm and accepted by the CGPM in 1889. One of each was selected at random to become the International prototype metre and International prototype kilogram that replaced the mètre des Archives and kilogramme des Archives respectively. Each member state was entitled to one of each of the remaining prototypes to serve as the national prototype for that country.^{[46]}
The treaty also established a number of international organisations to oversee the keeping of international standards of measurement:^{[47]} ^{[48]}
In the 1860s, James Clerk Maxwell, William Thomson (later Lord Kelvin) and others working under the auspices of the British Association for the Advancement of Science, built on Gauss' work and formalised the concept of a coherent system of units with base units and derived units christened the centimetre–gram–second system of units in 1874. The principle of coherence was successfully used to define a number of units of measure based on the CGS, including the erg for energy, the dyne for force, the barye for pressure, the poise for dynamic viscosity and the stokes for kinematic viscosity.^{[41]}
In 1879, the CIPM published recommendations for writing the symbols for length, area, volume and mass, but it was outside its domain to publish recommendations for other quantities. Beginning in about 1900, physicists who had been using the symbol "μ" (mu) for "micrometre" or "micron", "λ" (lambda) for "microlitre", and "γ" (gamma) for "microgram" started to use the symbols "μm", "μL" and "μg".^{[49]}
At the close of the 19th century three different systems of units of measure existed for electrical measurements: a CGSbased system for electrostatic units, also known as the Gaussian or ESU system, a CGSbased system for electromechanical units (EMU) and an International system based on units defined by the Metre Convention.^{[50]} for electrical distribution systems. Attempts to resolve the electrical units in terms of length, mass, and time using dimensional analysis was beset with difficulties—the dimensions depended on whether one used the ESU or EMU systems.^{[42]} This anomaly was resolved in 1901 when Giovanni Giorgi published a paper in which he advocated using a fourth base unit alongside the existing three base units. The fourth unit could be chosen to be electric current, voltage, or electrical resistance.^{[51]} Electric current with named unit 'ampere' was chosen as the base unit, and the other electrical quantities derived from it according to the laws of physics. This became the foundation of the MKS system of units.
In the late 19th and early 20th centuries, a number of noncoherent units of measure based on the gram/kilogram, centimetre/metre and second, such as the Pferdestärke (metric horsepower) for power,^{[52]}^{[Note 12]} the darcy for permeability^{[53]} and "millimetres of mercury" for barometric and blood pressure were developed or propagated, some of which incorporated standard gravity in their definitions.^{[Note 13]}
At the end of the Second World War, a number of different systems of measurement were in use throughout the world. Some of these systems were metric system variations; others were based on customary systems of measure, like the U.S customary system and Imperial system of the UK and British Empire.
In 1948, the 9th CGPM commissioned a study to assess the measurement needs of the scientific, technical, and educational communities and "to make recommendations for a single practical system of units of measurement, suitable for adoption by all countries adhering to the Metre Convention".^{[54]} This working document was Practical system of units of measurement. Based on this study, the 10th CGPM in 1954 defined an international system derived from six base units including units of temperature and optical radiation in addition to those for the MKS system mass, length, and time units and Giorgi's current unit. Six base units were recommended: the metre, kilogram, second, ampere, degree Kelvin, and candela.
The 9th CGPM also approved the first formal recommendation for the writing of symbols in the metric system when the basis of the rules as they are now known was laid down.^{[55]} These rules were subsequently extended and now cover unit symbols and names, prefix symbols and names, how quantity symbols should be written and used and how the values of quantities should be expressed.^{[3]}^{:104,130}
In 1960, the 11th CGPM synthesised the results of the 12year study into a set of 16 resolutions. The system was named the International System of Units, abbreviated SI from the French name, Le Système International d'Unités.^{[3]}^{:110}^{[56]}
Organisations
Standards and conventions
Because of the good progress made in both experiment and theory since the 31 December 2010 closing date of the 2010 CODATA adjustment, the uncertainties of the 2014 recommended values of h, e, k and N_{A} are already at the level required for the adoption of the revised SI by the 26th CGPM in the fall of 2018. The formal road map to redefinition includes a special CODATA adjustment of the fundamental constants with a closing date for new data of 1 July 2017 in order to determine the exact numerical values of h, e, k and N_{A} that will be used to define the New SI. A second CODATA adjustment with a closing date of 1 July 2018 will be carried out so that a complete set of recommended values consistent with the New SI will be available when it is formally adopted by the 26th CGPM.
[BIPM director Martin] Milton responded to a question about what would happen if ... the CIPM or the CGPM voted not to move forward with the redefinition of the SI. He responded that he felt that by that time the decision to move forward should be seen as a foregone conclusion.
he [Wilkins] proposed essentially what became ... the French decimal metric system
Special names, if short and suitable, would ... be better than the provisional designation 'C.G.S. unit of ...'.
The ampere (; symbol: A), often shortened to "amp", is the base unit of electric current in the International System of Units (SI). It is named after AndréMarie Ampère (1775–1836), French mathematician and physicist, considered the father of electrodynamics.
The International System of Units defines the ampere in terms of other base units by measuring the electromagnetic force between electrical conductors carrying electric current. The earlier CGS measurement system had two different definitions of current, one essentially the same as the SI's and the other using electric charge as the base unit, with the unit of charge defined by measuring the force between two charged metal plates. The ampere was then defined as one coulomb of charge per second. In SI, the unit of charge, the coulomb, is defined as the charge carried by one ampere during one second.
New definitions, in terms of invariant constants of nature, specifically the elementary charge, will take effect on 20 May 2019.
Bar (unit)The bar is a metric unit of pressure, but is not approved as part of the International System of Units (SI). It is defined as exactly equal to 100,000 Pa, which is slightly less than the current average atmospheric pressure on Earth at sea level.The bar and the millibar were introduced by the Norwegian meteorologist Vilhelm Bjerknes, who was a founder of the modern practice of weather forecasting.The International Bureau of Weights and Measures (BIPM) lists the bar as one of the "nonSI units [that authors] should have the freedom to use", but has declined to include it among the "NonSI units accepted for use with the SI". The bar has been legally recognised in countries of the European Union since 2004. The US National Institute of Standards and Technology (NIST) deprecates its use except for "limited use in meteorology" and lists it as one of several units that "must not be introduced in fields where they are not presently used". The International Astronomical Union (IAU) also lists it under "NonSI units and symbols whose continued use is deprecated".Units derived from the bar include the megabar (symbol: Mbar), kilobar (symbol: kbar), decibar (symbol: dbar), centibar (symbol: cbar), and millibar (symbol: mbar or mb). The notation bar(g), though deprecated by various bodies, represents gauge pressure, i.e., pressure in bars above ambient or atmospheric pressure.
CoulombThe coulomb (symbol: C) is the International System of Units (SI) unit of electric charge. It is the charge (symbol: Q or q) transported by a constant current of one ampere in one second:
Thus, it is also the amount of excess charge on a capacitor of one farad charged to a potential difference of one volt:
The coulomb is equivalent to the charge of approximately ×10^{18} ( 6.242×10^{−5} mol) protons, and −1 C is equivalent to the charge of approximately 1.036×10^{18} electrons. 6.242
A new definition, in terms of the elementary charge, will take effect on 20 May 2019. The new definition defines the elementary charge (the charge of the proton) as exactly 176634×10^{−19} coulombs. 1.602
Gray (unit)The gray (symbol: Gy) is a derived unit of ionizing radiation dose in the International System of Units (SI). It is defined as the absorption of one joule of radiation energy per kilogram of matter.It is used as a unit of the radiation quantity absorbed dose which measures the energy deposited by ionizing radiation in a unit mass of matter being irradiated, and is used for measuring the delivered dose of ionising radiation in applications such as radiotherapy, food irradiation and radiation sterilization. As a measure of low levels of absorbed dose, it also forms the basis for the calculation of the radiation protection unit the sievert, which is a measure of the health effect of low levels of ionizing radiation on the human body.
The gray is also used in radiation metrology as a unit of the radiation quantity kerma; defined as the sum of the initial kinetic energies of all the charged particles liberated by uncharged ionizing radiation in a sample of matter per unit mass. The gray is an important unit in ionising radiation measurement and was named after British physicist Louis Harold Gray, a pioneer in the measurement of Xray and radium radiation and their effects on living tissue.The gray was adopted as part of the International System of Units in 1975. The corresponding cgs unit to the gray is the rad (equivalent to 0.01 Gy), which remains common largely in the United States, though "strongly discouraged" in the style guide for U.S. National Institute of Standards and Technology authors.
HectareThe hectare (; SI symbol: ha) is an SI accepted metric system unit of area equal to a square with 100metre sides, or 10,000 m2, and is primarily used in the measurement of land. There are 100 hectares in one square kilometre. An acre is about 0.405 hectare and one hectare contains about 2.47 acres.
In 1795, when the metric system was introduced, the "are" was defined as 100 square metres and the hectare ("hecto" + "are") was thus 100 "ares" or 1⁄100 km2 (10,000 square metres). When the metric system was further rationalised in 1960, resulting in the International System of Units (SI), the are was not included as a recognised unit. The hectare, however, remains as a nonSI unit accepted for use with the SI units, mentioned in Section 4.1 of the SI Brochure as a unit whose use is "expected to continue indefinitely".The name was coined in French, from the Latin ārea.
HertzThe hertz (symbol: Hz) is the derived unit of frequency in the International System of Units (SI) and is defined as one cycle per second. It is named for Heinrich Rudolf Hertz, the first person to provide conclusive proof of the existence of electromagnetic waves. Hertz are commonly expressed in multiples: kilohertz (103 Hz, kHz), megahertz (106 Hz, MHz), gigahertz (109 Hz, GHz), terahertz (1012 Hz, THz), petahertz (1015 Hz, PHz), and exahertz (1018 Hz, EHz).
Some of the unit's most common uses are in the description of sine waves and musical tones, particularly those used in radio and audiorelated applications. It is also used to describe the speeds at which computers and other electronics are driven.
ISO 1000International standard ISO 1000 (SI units and recommendations for the use of their multiples and of certain other units, International Organization for Standardization, 1992) is the ISO standard describing the International System of Units (SI).
The ISO 1000:1992 standard was withdrawn in 2009, following the publication of ISO/IEC 800001.
KelvinThe Kelvin scale is an absolute thermodynamic temperature scale using as its null point absolute zero, the temperature at which all thermal motion ceases in the classical description of thermodynamics. The kelvin (symbol: K) is the base unit of temperature in the International System of Units (SI).
Until 2018, the kelvin was defined as the fraction 1/273.16 of the thermodynamic temperature of the triple point of water (exactly 0.01 °C or 32.018 °F). In other words, it was defined such that the triple point of water is exactly 273.16 K.
On 16 November 2018, a new definition was adopted, in terms of a fixed value of the Boltzmann constant. For legal metrology purposes, the new definition will officially come into force on 20 May 2019 (the 130th anniversary of the Metre Convention).The Kelvin scale is named after the Belfastborn, Glasgow University engineer and physicist William Thomson, 1st Baron Kelvin (1824–1907), who wrote of the need for an "absolute thermometric scale". Unlike the degree Fahrenheit and degree Celsius, the kelvin is not referred to or written as a degree. The kelvin is the primary unit of temperature measurement in the physical sciences, but is often used in conjunction with the degree Celsius, which has the same magnitude. The definition implies that absolute zero (0 K) is equivalent to −273.15 °C (−459.67 °F).
MeasurementMeasurement is the assignment of a number to a characteristic of an object or event, which can be compared with other objects or events. The scope and application of measurement are dependent on the context and discipline. In the natural sciences and engineering, measurements do not apply to nominal properties of objects or events, which is consistent with the guidelines of the International vocabulary of metrology published by the International Bureau of Weights and Measures. However, in other fields such as statistics as well as the social and behavioral sciences, measurements can have multiple levels, which would include nominal, ordinal, interval and ratio scales.Measurement is a cornerstone of trade, science, technology, and quantitative research in many disciplines. Historically, many measurement systems existed for the varied fields of human existence to facilitate comparisons in these fields. Often these were achieved by local agreements between trading partners or collaborators. Since the 18th century, developments progressed towards unifying, widely accepted standards that resulted in the modern International System of Units (SI). This system reduces all physical measurements to a mathematical combination of seven base units. The science of measurement is pursued in the field of metrology.
MebibyteThe mebibyte is a multiple of the unit byte for digital information. The binary prefix mebi means 220; therefore one mebibyte is equal to 1048576bytes = 1024 kibibytes. The unit symbol for the mebibyte is MiB.
The unit was established by the International Electrotechnical Commission (IEC) in 1998. It was designed to replace the megabyte when used in the binary sense to mean 220 bytes, which conflicts with the definition of the prefix mega in the International System of Units (SI) as a multiplier of 106.
The binary prefixes have been accepted by all major standards organizations and are part of the International System of Quantities. Many Linux distributions use the unit, but it is not widely acknowledged within the industry or media.
MegabyteThe megabyte is a multiple of the unit byte for digital information. Its recommended unit symbol is MB. The unit prefix mega is a multiplier of 1000000 (106) in the International System of Units (SI). Therefore, one megabyte is one million bytes of information. This definition has been incorporated into the International System of Quantities.
However, in the computer and information technology fields, several other definitions are used that arose for historical reasons of convenience. A common usage has been to designate one megabyte as 1048576bytes (220 B), a measurement that conveniently expresses the binary multiples inherent in digital computer memory architectures. However, most standards bodies have deprecated this usage in favor of a set of binary prefixes, in which this quantity is designated by the unit mebibyte (MiB). Less common is a convention that used the megabyte to mean 1000×1024 (1024000) bytes.
MetreThe metre (British spelling and BIPM spelling) or meter (American spelling) (from the French unit mètre, from the Greek noun μέτρον, "measure") is the base unit of length in the International System of Units (SI). The SI unit symbol is m. The metre is defined as the length of the path travelled by light in vacuum in 1/299 792 458 of a second.The metre was originally defined in 1793 as one tenmillionth of the distance from the equator to the North Pole – as a result the Earth's circumference is approximately 40,000 km today. In 1799, it was redefined in terms of a prototype metre bar (the actual bar used was changed in 1889). In 1960, the metre was redefined in terms of a certain number of wavelengths of a certain emission line of krypton86. In 1983, the current definition was adopted.
The imperial inch is defined as 0.0254 metres (2.54 centimetres or 25.4 millimetres). One metre is about 3 3⁄8 inches longer than a yard, i.e. about 39 3⁄8 inches.
Metric systemThe metric system is an internationally recognised decimalised system of measurement. It is in widespread use, and where it is adopted, it is the only or most common system of weights and measures (see metrication). It is now known as the International System of Units (SI). It is used to measure everyday things such as the mass of a sack of flour, the height of a person, the speed of a car, and the volume of fuel in its tank. It is also used in science, industry and trade.
In its modern form, it consists of a set of base units including metre for length, kilogram for mass, second for time and ampere for electrical current, and a few others, which together with their derived units, can measure any physical quantity. Metric system may also refer to other systems of related base and derived units defined before the middle of the 20th century, some of which are still in limited use today.
The metric system was designed to have properties that make it easy to use and widely applicable, including units based on the natural world, decimal ratios, prefixes for multiples and submultiples, and a structure of base and derived units. It is also a coherent system, which means that its units do not introduce conversion factors not already present in equations relating quantities. It has a property called rationalisation that eliminates certain constants of proportionality in equations of physics.
The units of the metric system, originally taken from observable features of nature, are now defined by phenomena such as the microwave frequency of a caesium atomic clock which accurately measures seconds. One unit, the kilogram, remains defined in terms of a manmade artefact, but scientists recently voted to change the definition to one based on Planck's constant via a Kibble balance. The new definition is expected to be formally propagated on 20 May 2019.
While there are numerous named derived units of the metric system, such as watt and lumen, other common quantities such as velocity and acceleration do not have their own unit, but are defined in terms of existing base and derived units such as metres per second for velocity.
Though other currently or formerly widespread systems of weights and measures continue to exist, such as the British imperial system and the US customary system of weights and measures, in those systems most or all of the units are now defined in terms of the metric system, such as the US foot which is now a defined decimal fraction of a metre.
The metric system is also extensible, and new base and derived units are defined as needed in fields such as radiology and chemistry. The most recent derived unit, the katal, for catalytic activity, was added in 1999. Recent changes are directed toward defining base units in terms of invariant constants of physics to provide more precise realisations of units for advances in science and industry.
MicrogramIn the metric system, a microgram or microgramme (μg; the recommended symbol in the United States when communicating medical information is mcg) is a unit of mass equal to one millionth (1×10−6) of a gram. The unit symbol is μg according to the International System of Units. In μg the prefix symbol for micro is the Greek letter μ (Mu).
Newton (unit)The newton (symbol: N) is the International System of Units (SI) derived unit of force. It is named after Isaac Newton in recognition of his work on classical mechanics, specifically Newton's second law of motion.
See below for the conversion factors.
Revolutions per minuteRevolutions per minute (abbreviated rpm, RPM, rev/min, r/min, or with the notation min−1) is the number of turns in one minute. It is a unit of rotational speed or the frequency of rotation around a fixed axis.
Siemens (unit)The siemens (symbol: S) is the derived unit of electric conductance, electric susceptance, and electric admittance in the International System of Units (SI). Conductance, susceptance, and admittance are the reciprocals of resistance, reactance, and impedance respectively; hence one siemens is redundantly equal to the reciprocal of one ohm, and is also referred to as the mho. The 14th General Conference on Weights and Measures approved the addition of the siemens as a derived unit in 1971.
The unit is named after Ernst Werner von Siemens. In English, the same form siemens is used both for the singular and plural.
TerabyteThe terabyte is a multiple of the unit byte for digital information. The prefix tera represents the fourth power of 1000, and means 1012 in the International System of Units (SI), and therefore one terabyte is one trillion (short scale) bytes. The unit symbol for the terabyte is TB.
WattThe watt (symbol: W) is a unit of power. In the International System of Units (SI) it is defined as a derived unit of 1 joule per second, and is used to quantify the rate of energy transfer. In dimensional analysis, power is described by .
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