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 (ampere, kelvin, second, metre, kilogram, candela, mole) and a set of twenty decimal 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 for other common physical quantities like lumen, watt, etc.
The base units, except for one, are derived from invariant constants of nature, such as the speed of light and triple point of water, which can be readily observed and measured with great accuracy. The kilogram standard of mass is a physical artefact certified in 1889, consisting of a cylinder of platinumiridium, which ostensibly has the same mass (weight) as one litre of water at the freezing point. Its stability has been a matter of significant concern, resulting in recent proposals to change the definition to one derived from some invariant constant of nature.^{[1]}
Derived units may be defined in terms of base units or other derived units. They are adopted to facilitate measurement in diverse fields of endeavor. 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 last new derived unit 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 other constants may be more precisely measured. For example, in 1983, the metre was redefined to be the distance of light propagation in vacuum in an exact fraction of a second. Thus, the speed of light is now an exactly defined constant of nature.
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 developed countries except the United States.^{[2]}
The International System of Units consists of a set of base units, a set of coherent derived units, and a set of decimalbased multipliers that are used as prefixes.^{[3]}^{:103–106} Coherent units are derived units that contain no numerical factor other than 1—quantities such as standard gravity and density of water are absent from their definitions. For example: N = kg × m/s^{2} which says that one newton is the force required to accelerate a mass of one kilogram at one metre per second squared. Since the SI units of mass and acceleration are kg and m⋅s^{−2} respectively and F ∝ m × a, the units of force (and hence of newtons) is formed by multiplication to give kg⋅m⋅s^{−2}. Since the newton is part of a coherent set of units, the constant of proportionality is 1.
While the base and specified derived units are coherent, they are not all independent: for example, siemens can be specified in terms of ohms as its inverse. Ohms and siemens can be replaced with a combination of amperes and volts, because those quantities bear a defined relationship to each other.^{[4]} 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 as 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, 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. In SI units, if you apply a force of 1 N (newton) to a mass of 1 kg, it will accelerate 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 at the earth's surface is 9.81 newtons, and at the surface of Mars is about 3.5 newtons. Weight is not an accurate base unit for precision measurement because the acceleration due to gravity is local and varies over the surface of the earth, since the earth does not have uniform density or radius in all directions. It also varies with altitude or depth (distance from earth's centre).
The derived units in the SI are formed by powers, products or quotients of the base units and are unlimited in number.^{[3]}^{:103}^{[5]}^{: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}).^{[11]}
Name  Symbol  Quantity  In other SI units  In SI base units 

radian^{note 1}  rad  angle  (m⋅m^{−1})  
steradian  sr  solid angle  (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  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 ionizing radiation)  J/kg  m^{2}⋅s^{−2} 
sievert  Sv  equivalent dose (of ionizing radiation)  J/kg  m^{2}⋅s^{−2} 
katal  kat  catalytic activity  mol⋅s^{−1}  
Notes 1. The radian and steradian are now considered dimensionless derived units. 2. The table ordering is such that any derived unit is based on base or derived units that precede it. 
Prefixes are added to unit names to produce multiples and submultiples of the original unit, All multiples 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}^{[12]}^{:14}
Multiples  Prefix name  deca  hecto  kilo  mega  giga  tera  peta  exa  zetta  yotta  

Prefix symbol  da  h  k  M  G  T  P  E  Z  Y  
Factor  10^{0}  10^{1}  10^{2}  10^{3}  10^{6}  10^{9}  10^{12}  10^{15}  10^{18}  10^{21}  10^{24}  
Submultiples  Prefix name  deci  centi  milli  micro  nano  pico  femto  atto  zepto  yocto  
Prefix symbol  d  c  m  μ  n  p  f  a  z  y  
Factor  10^{0}  10^{−1}  10^{−2}  10^{−3}  10^{−6}  10^{−9}  10^{−12}  10^{−15}  10^{−18}  10^{−21}  10^{−24} 
The SI is capable of describing most useful and measurable physical quantities, but many nonSI units still appear in the scientific, technical, and commercial literature. Some units are deeply embedded in history and culture. The CIPM recognised and acknowledged such traditions by compiling a list of nonSI units accepted for use with SI, which are grouped as follows:^{[3]}^{:123–129}^{[12]}^{:7–11}^{[Note 1]}
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.^{[13]}
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.^{[14]}^{[15]} 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.^{[5]}^{: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)^{[16]} clarifies languagespecific areas in respect of American English that were left open by the SI Brochure, but is otherwise identical to the SI Brochure.^{[17]}
General rules^{[Note 2]} 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.^{[19]}
Further rules^{[Note 2]} are specified in respect of production of text using printing presses, word processors, typewriters and the like.
The CGPM publishes a brochure which 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.^{[20]}^{[5]}
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,^{[21]}
The quantities and equations that define the SI units 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.^{[22]} The ISQ is defined in the international standard ISO/IEC 80000, and was finalised in 2009 with the publication of ISO 800001.^{[23]}
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 3]} of the base units is given in an electronic appendix to the SI Brochure.^{[25]}^{[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 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 ionizing radiation, the sievert (symbol Sv) as the unit of dose equivalent radiation, and the katal (symbol kat) for catalytic activity.^{[3]}^{:156}^{[29]}^{[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 were also made to alleviate lexicographic ambiguities.
After the metre was redefined in 1960, the kilogram remained the only SI base unit that relied 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.^{[30]} During the 2nd and 3rd Periodic Verification of National Prototypes of the Kilogram, a significant divergence in weight between the IPK and all of its official copies stored around the world had occurred: the copies had all noticeably gained weight 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 undermines the reliability of the entire metric system to precision measurement from small (atomic) to large (astrophysical) scales.
The existing proposals are:
The redefinitions are expected to be adopted at the 26th CGPM in November 2018.^{[31]} The CODATA task group on fundamental constants has announced special submission deadlines for data to compute the values that will be announced at this event.^{[32]}
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.^{[34]} The group, which included preeminent French men of science^{[35]}^{:89} used the same principles for relating length, volume, and mass that had been proposed by the English clergyman John Wilkins in 1668^{[36]}^{[37]} 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.^{[38]}^{[39]}
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.^{[40]}^{: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.^{[46]} ^{[47]} 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.^{[33]}
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.^{[41]} 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.^{[48]}^{[49]}
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 4]} 
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.^{[50]}^{[35]}^{: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.^{[42]}^{[3]}^{:96}
A set of 30 prototypes of the metre and 40 prototypes of the kilogram,^{[Note 5]} 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.^{[51]}
The treaty also established a number of international organisations to oversee the keeping of international standards of measurement:^{[52]} ^{[53]}
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.^{[44]}
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".^{[54]}
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.^{[55]} 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.^{[45]} 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.^{[56]} 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,^{[57]}^{[Note 6]} the darcy for permeability^{[58]} and "millimetres of mercury" for barometric and blood pressure were developed or propagated, some of which incorporated standard gravity in their definitions.^{[59]}
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".^{[60]} 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 Georgi'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.^{[61]} 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 synthesized the results of the 12 year 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}^{[62]}
Organisations
Standards and conventions
[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.
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.
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 ...'.
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