International System of Units
This article duplicates the scope of other articles, specifically, Metric system. (December 2017)

This article duplicates the scope of other articles, specifically, Introduction to the metric system. (December 2017)

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 countries except the United States, Liberia, and Burma.^{[2]}
Contents
Units and prefixes
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: 1 N = 1 kg × 1 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 kilogram and metre per second squared respectively and F ∝ m × a, the units of force (and hence of newtons) is formed by multiplication to give 1 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 is defined in SI units as m/s^{2}.
Base units
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).
Derived units
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^{note 1}  Symbol  Quantity  In other SI units  In SI base units 

radian^{note 2}  rad  angle  (m⋅m^{−1})  
steradian^{note 2}  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 table is ordered so that derived units are listed after the units that define them. 2. The radian and steradian are defined as dimensionless derived units. 
Prefixes
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} 
NonSI units accepted for use with SI
It has been suggested that NonSI units mentioned in the SI be merged into this article. (Discuss) Proposed since December 2017.

The SI is capable of describing most useful and measurable physical quantities^{[citation needed]}, 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]}
 NonSI units accepted for use with the SI:
 Certain units of time, angle, and legacy nonSI metric 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 have a large degree of consistency 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
 NonSI units whose values in SI units must be obtained experimentally (Table 7).
 Physicists often use units of measure that are based on natural phenomena, particularly when the quantities associated with these phenomena are many orders of magnitude greater than or less than the equivalent SI unit. The most common ones have been catalogued in the SI Brochure together with consistent symbols and accepted values, but with the caveat that their values in SI units need to be measured.
 electronvolt (symbol eV), and dalton/unified atomic mass unit (Da or u)
 Other nonSI units (Table 8):
 A number of nonSI units that had never been formally sanctioned by the CGPM have continued to be used across the globe in many spheres including health care and navigation. As with the units of measure in Tables 6 and 7, these have been catalogued by the CIPM in the SI Brochure to ensure consistent usage, but with the recommendation that authors who use them should define them wherever they are used.
 bar, millimetre of mercury, ångström, nautical mile, barn, knot and neper
 In the interests of standardising healthrelated units of measure used in the nuclear industry, the 12th CGPM (1964) accepted the continued use of the curie (symbol Ci) as a nonSI unit of activity for radionuclides;^{[3]}^{: 152} the becquerel, sievert and gray were adopted in later years. Similarly, the millimetre of mercury (symbol mmHg) was retained for measuring blood pressure.^{[3]}^{:127}
 NonSI units associated with the CGS and the CGSGaussian system of units (Table 9)
 The SI manual also catalogues a number of legacy units of measure that are used in specific fields such as geodesy and geophysics or are found in the literature, particularly in classical and relativistic electrodynamics where they have certain advantages: The units that are catalogued are:
Common notions of the metric units
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]}
 A second is 1/60 of a minute, which is 1/60 of an hour, which is 1/24 of a day, so a second is 1/86400 of a day; a second is the time it takes a dense object to freely fall 4.9 metres from rest.
 The metre is close to the length of a pendulum that has a period of 2 seconds; most dining tabletops are about 0.75 metre high; a very tall human (basketball forward) is about 2 metres tall.
 The kilogram is the weight of a litre of cold water; a cubic centimetre or millilitre of water weighs a gram (we need not be too concerned about the difference between mass and weight); a 1euro coin, 7.5 g; a Sacagawea US 1dollar coin, 8.1 g; a UK 50pence coin, 8.0 g.
 A candela is about the luminous intensity of a moderately bright candle, or 1 candle power; a 60 W tungstenfilament incandescent light bulb has a luminous intensity of about 64 candela.
 A mole of a substance has a mass that is its molecular weight expressed in units of grams; the mass of a mole of table salt is 58.4 g.
 A temperature difference of one kelvin is the same as one degree centigrade: 1/100 of the temperature differential between the freezing and boiling points of water at sea level; the absolute temperature in kelvins is the temperature in degrees Celsius plus about 273; human body temperature is about 37 °C or 310 K.
 A 60 W incandescent light bulb consumes 0.5 amperes at 120 V (US mains voltage) and about 0.26 amperes at 230 V (European mains voltage).
Lexicographic conventions
Unit names
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}
Unit symbols and the values of quantities
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
General rules^{[Note 2]} for writing SI units and quantities apply to text that is either handwritten or produced using an automated process:
 The value of a quantity is written as a number followed by a space (representing a multiplication sign) and a unit symbol; e.g., 2.21 kg, ×10^{2} m^{2}, 22 K. This rule explicitly includes the percent sign (%)^{[3]}^{:134} and the symbol for degrees of temperature (°C).^{[3]}^{: 133} Exceptions are the symbols for plane angular degrees, minutes, and seconds (°, ′, and ″), which are placed immediately after the number with no intervening space. 7.3
 Symbols are mathematical entities, not abbreviations, and as such do not have an appended period/full stop (.), unless the rules of grammar demand one for another reason, such as denoting the end of a sentence.
 A prefix is part of the unit, and its symbol is prepended to the unit symbol without a separator (e.g., k in km, M in MPa, G in GHz). Compound prefixes are not allowed.
 Symbols for derived units formed by multiplication are joined with a centre dot (⋅) or a nonbreaking space; e.g., N⋅m or N m.
 Symbols for derived units formed by division are joined with a solidus (/), or given as a negative exponent. E.g., the "metre per second" can be written m/s, m s^{−1}, m⋅s^{−1}, or m/s. Only one solidus should be used; e.g., kg/(m⋅s^{2}) and kg⋅m^{−1}⋅s^{−2} are acceptable, but kg/m/s^{2} is ambiguous and unacceptable.
 The first letter of symbols for units derived from the name of a person is written in upper case; otherwise, they are written in lower case. E.g., the unit of pressure is named after Blaise Pascal, so its symbol is written "Pa", but the symbol for mole is written "mol". Thus, "T" is the symbol for tesla, a measure of magnetic field strength, and "t" the symbol for tonne, a measure of mass. Since 1979, the litre may exceptionally be written using either an uppercase "L" or a lowercase "l", a decision prompted by the similarity of the lowercase letter "l" to the numeral "1", especially with certain typefaces or Englishstyle handwriting. The American NIST recommends that within the United States "L" be used rather than "l".
 Symbols of units do not have a plural form; e.g., 25 kg, not 25 kgs.
 Uppercase and lowercase prefixes are not interchangeable. E.g., the quantities 1 mW and 1 MW represent two different quantities; the former is the typical power requirement of a hearing aid (1 milliwatt or 0.001 watts), and the latter the typical power requirement of a suburban train (1 megawatt or 000000 watts). 1
 The symbol for the decimal marker is either a point or comma on the line. In practice, the decimal point is used in most Englishspeaking countries and most of Asia, and the comma in most of Latin America and in continental European countries.^{[18]}
 Spaces should be used as a thousands separator (000000) in contrast to commas or periods (1,000,000 or 1.000.000) to reduce confusion resulting from the variation between these forms in different countries. 1
 Any linebreak inside a number, inside a compound unit, or between number and unit should be avoided. Where this is not possible, line breaks should coincide with thousands separators.
 Since the value of "billion" and "trillion" can vary from language to language, the dimensionless terms "ppb" (parts per billion) and "ppt" (parts per trillion) should be avoided. No alternative is suggested in the SI Brochure.
Printing SI symbols
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.
International System of Quantities




 SI Brochure



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]}
Realisation of units
Metrologists carefully distinguish between the definition of a unit and its realisation. The definition of each base unit of the SI is drawn up so that it is unique and provides a sound theoretical basis 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.^{[citation needed]} In particular:
 At least three separate experiments be carried out yielding values having a relative standard uncertainty in the determination of the kilogram of no more than ×10^{−8} and at least one of these values should be better than 5×10^{−8}. Both the 2Watt balance and the Avogadro project should be included in the experiments and any differences between these be reconciled.^{[26]}^{[27]}
 When the kelvin is being determined, the relative uncertainty of the Boltzmann constant derived from two fundamentally different methods such as acoustic gas thermometry and dielectric constant gas thermometry be better than one part in and that these values be corroborated by other measurements.^{[28]} 10^{−6}
Evolution of the SI
Changes to the SI
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 1/792458 299 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.
Proposed redefinitions
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:
 In addition to the speed of light, four constants of nature – the Planck constant, an elementary charge, the Boltzmann constant and the Avogadro number – be defined to have exact values.
 The International prototype kilogram be retired
 The current definitions of the kilogram, ampere, kelvin and mole be revised.
 The wording of base unit definitions should change emphasis from explicit unit to explicit constant definitions.
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]}
History
The improvisation of units
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 (000 metres) was in widespread use in both France and parts of Germany, while the kilogram ( 10 grams) rather than the myriagram was used for mass.^{[33]} 1000
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.
Metre Convention
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]}
The cgs and MKS systems
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.
This section is missing information about all 22 named derived units of SI.
(December 2017)

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]}
This section is missing information about a period of ~3540 years between early 20th century and end of WW2 covering most of the industrial revolution.
(December 2017)

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.
The Practical system of units
This section is missing information about changeover centigrade>Kelvin and candlepower>candela.
(December 2017)

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}
Birth of the SI
This section needs expansion. You can help by adding to it. (December 2017)

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]}
See also
 Introduction to the metric system
 Outline of the metric system
 List of international common standards
 Metre–tonne–second system of units
Organisations
Standards and conventions
Notes
 ^ This grouping reflects the 2014 revision of the 8th Edition of the SI Brochure (2006).
 ^ ^{a} ^{b} Except where specifically noted, these rules are common to both the SI Brochure and the NIST brochure.
 ^ This term is a translation of the official [French] text of the SI Brochure.
 ^ The 8th edition of the SI Brochure (2008) notes that [at that time of publication] the term "mise en pratique" had not been fully defined.
 ^ The text "Des comparaisons périodiques des étalons nationaux avec les prototypes internationaux" (English: the periodic comparisons of national standards with the international prototypes) in article 6.3 of the Metre Convention distinguishes between the words "standard" (OED: "The legal magnitude of a unit of measure or weight") and "prototype" (OED: "an original on which something is modelled").
 ^ Pferd is German for "horse" and Stärke is German for "strength" or "power". The Pferdestärke is the power needed to raise 75 kg against gravity at the rate of one metre per second. (1 PS = 0.985 HP).
References
 ^ "Convocation of the General Conference on Weights and Measures (25th meeting)" (PDF). International Bureau of Weights and Measures. p. 32. Retrieved 20140527.
 ^ "The World Factbook Appendix G". CIA. Retrieved 20171026.
 ^ ^{a} ^{b} ^{c} ^{d} ^{e} ^{f} ^{g} ^{h} ^{i} ^{j} ^{k} ^{l} ^{m} ^{n} ^{o} ^{p} ^{q} ^{r} ^{s} ^{t} ^{u} ^{v} ^{w} ^{x} ^{y} ^{z} International Bureau of Weights and Measures (2006), The International System of Units (SI) (PDF) (8th ed.), ISBN 9282222136, archived (PDF) from the original on 20170814
 ^ Ohm's law: 1 Ω = 1 V/A usually represented as E = I × R, where E is electromotive force or voltage (unit: volt), I is current (unit: ampere), and R is resistance (unit: ohm).
 ^ ^{a} ^{b} ^{c} ^{d} ^{e} Taylor, Barry N.; Thompson, Ambler (2008). The International System of Units (SI) (Special publication 330) (PDF). Gaithersburg, MD: National Institute of Standards and Technology. Retrieved 20170804.
 ^ Quantities Units and Symbols in Physical Chemistry, IUPAC
 ^ Page, Chester H.; Vigoureux, Paul, eds. (19750520). The International Bureau of Weights and Measures 1875–1975: NBS Special Publication 420. Washington, D.C.: National Bureau of Standards. pp. 238–244.
 ^ This object is the International Prototype Kilogram or IPK called rather poetically Le Grand K.
 ^ Secula, Erik M. (7 October 2014). "Redefining the Kilogram, The Past". Nist.gov. Retrieved 22 August 2017.
 ^ McKenzie, A. E. E. (1961). Magnetism and Electricity. Cambridge University Press. p. 322.
 ^ "Units & Symbols for Electrical & Electronic Engineers". Institution of Engineering and Technology. 1996. pp. 8–11. Retrieved 20130819.
 ^ ^{a} ^{b} Thompson, Ambler; Taylor, Barry N. (2008). Guide for the Use of the International System of Units (SI) (Special publication 811) (PDF). Gaithersburg, MD: National Institute of Standards and Technology.
 ^ While the second is readily determined from the Earth's rotation period, the metre, originally defined in terms of the Earth's size and shape, is less amenable; however, that the Earth's circumference is very close to 40,000 km may be a useful mnemonic.
 ^ Rowlett, Russ (20040714). "Using Abbreviations or Symbols". University of North Carolina. Retrieved 20131211.
 ^ "SI Conventions". National Physical Laboratory. Retrieved 20131211.
 ^ Thompson, A.; Taylor, B. N. (July 2008). "NIST Guide to SI Units – Rules and Style Conventions". National Institute of Standards and Technology. Retrieved 20091229.
 ^ "Interpretation of the International System of Units (the Metric System of Measurement) for the United States" (PDF). Federal Register. National Archives and Records Administration. 73 (96): 28432–28433. 20080509. FR Doc number E811058. Retrieved 20091028.
 ^ Williamson, Amelia A. (March–April 2008). "Period or Comma? Decimal Styles over Time and Place" (PDF). Science Editor. Council of Science Editors. 31 (2): 42. Archived from the original (PDF) on 20130228. Retrieved 20120519.
 ^ "ISO 800001:2009(en) Quantities and Units—Past 1:General". International Organization for Standardization. 2009. Retrieved 20130822.
 ^ so for example the United States' National Institute of Standards and Technology (NIST) has produced a version of the CGPM document (NIST SP 330) which clarifies local interpretation for Englishlanguage publications that use American English
 ^ "The International Vocabulary of Metrology (VIM)".
 ^ "1.16". International vocabulary of metrology – Basic and general concepts and associated terms (VIM) (PDF) (3rd ed.). International Bureau of Weights and Measures (BIPM): Joint Committee for Guides in Metrology. 2012. Retrieved 20150328.
 ^ S. V. Gupta, Units of Measurement: Past, Present and Future. International System of Units, p. 16, Springer, 2009. ISBN 3642007384.
 ^ "Avogadro Project". National Physical Laboratory. Retrieved 20100819.
 ^ "What is a mise en pratique?". International Bureau of Weights and Measures. Retrieved 20121110.
 ^ "Recommendations of the Consultative Committee for Mass and Related Quantities to the International Committee for Weights and Measures" (PDF). 12th Meeting of the CCM. Sèvres: Bureau International des Poids et Mesures. 20100326. Retrieved 20120627.
 ^ "Recommendations of the Consultative Committee for Amount of Substance – Metrology in Chemistry to the International Committee for Weights and Measures" (PDF). 16th Meeting of the CCQM. Sèvres: Bureau International des Poids et Mesures. 15–16 April 2010. Retrieved 20120627.
 ^ "Recommendations of the Consultative Committee for Thermometry to the International Committee for Weights and Measures" (PDF). 25th Meeting of the CCT. Sèvres: Bureau International des Poids et Mesures. 6–7 May 2010. Retrieved 20120627.
 ^ pg. 221 – McGreevy
 ^ "Redefining the kilogram". UK National Physical Laboratory. Retrieved 20141130.

^ Wood, B. (3–4 November 2014). "Report on the Meeting of the CODATA Task Group on Fundamental Constants" (PDF). BIPM. p. 7.
[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.

^ Mohr, Peter J.; Newell, David B.; Taylor, Barry N. (2015). "CODATA recommended values of the fundamental physical constants: 2014 – Summary". Zenodo. doi:10.5281/zenodo.22827 (inactive 20170608).
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.
 ^ ^{a} ^{b} "Amtliche Maßeinheiten in Europa 1842" [Official units of measure in Europe 1842] (in German). Retrieved 20110326Text version of Malaisé's book</rref>Malaisé, Ferdinand (1842). Theoretischpractischer Unterricht im Rechnen [Theoretical and practical instruction in arithmetic] (in German). München. pp. 307–322. Retrieved 20130107.
 ^ "The name "kilogram"". International Bureau of Weights and Measures. Archived from the original on 14 May 2011. Retrieved 25 July 2006.
 ^ ^{a} ^{b} Alder, Ken (2002). The Measure of all Things—The SevenYearOdyssey that Transformed the World. London: Abacus. ISBN 0349115079.

^ Quinn, Terry (2012). From artefacts to atoms: the BIPM and the search for ultimate measurement standards. Oxford University Press. p. xxvii. ISBN 9780195307863.
he [Wilkins] proposed essentially what became ... the French decimal metric system

^ Wilkins, John (1668). "VII". An Essay towards a Real Character and a Philosophical Language. The Royal Society. pp. 190–194.
"Reproduction (33 MB)" (PDF). Retrieved 20110306.; "Transcription" (PDF). Retrieved 20110306.  ^ "Mouton, Gabriel". Complete Dictionary of Scientific Biography. encyclopedia.com. 2008. Retrieved 20121230.
 ^ O'Connor, John J.; Robertson, Edmund F. (January 2004), "Gabriel Mouton", MacTutor History of Mathematics archive, University of St Andrews.
 ^ Tavernor, Robert (2007). Smoot's Ear: The Measure of Humanity. Yale University Press. ISBN 9780300124927.
 ^ ^{a} ^{b} "Brief history of the SI". International Bureau of Weights and Measures. Retrieved 20121112.
 ^ ^{a} ^{b} Tunbridge, Paul (1992). Lord Kelvin, His Influence on Electrical Measurements and Units. Peter Pereginus Ltd. pp. 42–46. ISBN 0863412378.

^ Everett, ed. (1874). "First Report of the Committee for the Selection and Nomenclature of Dynamical and Electrical Units". Report on the Fortythird Meeting of the British Association for the Advancement of Science held at Bradford in September 1873. British Association for the Advancement of Science: 222–225. Retrieved 20130828.
Special names, if short and suitable, would ... be better than the provisional designation 'C.G.S. unit of ...'.
 ^ ^{a} ^{b} Page, Chester H.; Vigoureux, Paul, eds. (19750520). The International Bureau of Weights and Measures 1875–1975: NBS Special Publication 420. Washington, D.C.: National Bureau of Standards. p. 12.
 ^ ^{a} ^{b} Maxwell, J. C. (1873). A treatise on electricity and magnetism. 2. Oxford: Clarendon Press. pp. 242–245. Retrieved 20110512.
 ^ Bigourdan, Guillaume (2012) [1901]. Le Système Métrique Des Poids Et Mesures: Son Établissement Et Sa Propagation Graduelle, Avec L'histoire Des Opérations Qui Ont Servi À Déterminer Le Mètre Et Le Kilogramme (facsimile edition) [The Metric System of Weights and Measures: Its Establishment and its Successive Introduction, with the History of the Operations Used to Determine the Metre and the Kilogram] (in French). Ulan Press. p. 176. ASIN B009JT8UZU.
 ^ Smeaton, William A. (2000). "The Foundation of the Metric System in France in the 1790s: The importance of Etienne Lenoir's platinum measuring instruments". Platinum Metals Rev. Ely. 44 (3): 125–134. Retrieved 20130618.
 ^ The strength of the earth's magnetic field was designated 1G (gauss) at the surface = cm^{−1/2}g^{1/2}s^{−1}.
 ^ "The intensity of the Earth's magnetic force reduced to absolute measurement" (PDF).
 ^ Argentina, AustriaHungary, Belgium, Brazil, Denmark, France, German Empire, Italy, Peru, Portugal, Russia, Spain, Sweden and Norway, Switzerland, Ottoman Empire, United States and Venezuela.
 ^ Nelson, Robert A. (1981). "Foundations of the international system of units (SI)" (PDF). Physics Teacher: 597.
 ^ "The Metre Convention". Bureau International des Poids et Mesures. Retrieved 20121001.

^ * General Conference on Weights and Measures (Conférence générale des poids et mesures or CGPM)
 International Committee for Weights and Measures (Comité international des poids et mesures or CIPM)
 International Bureau of Weights and Measures (Bureau international des poids et mesures or BIPM) – an international metrology centre at Sèvres in France that has custody of the International prototype kilogram, provides metrology services for the CGPM and CIPM,
 ^ McGreevy, Thomas (1997). Cunningham, Peter, ed. The Basis of Measurement: Volume 2 – Metrication and Current Practice. Pitcon Publishing (Chippenham) Ltd. pp. 222–224. ISBN 0948251840.
 ^ Fenna, Donald (2002). Weights, Measures and Units. Oxford University Press. International unit. ISBN 0198605226.
 ^ "In the beginning... Giovanni Giorgi". International Electrotechnical Commission. 2011. Retrieved 20110405.
 ^ "Die gesetzlichen Einheiten in Deutschland" [List of units of measure in Germany] (PDF) (in German). PhysikalischTechnische Bundesanstalt (PTB). p. 6. Retrieved 20121113.
 ^ "Porous materials: Permeability" (PDF). Module Descriptor, Material Science, Materials 3. Materials Science and Engineering, Division of Engineering, The University of Edinburgh. 2001. p. 3. Archived from the original (PDF) on 2 June 2013. Retrieved 13 November 2012.
 ^ This constant is unreliable, because it varies over the surface of the earth.
 ^ "BIPM  Resolution 6 of the 9th CGPM". Bipm.org. Retrieved 22 August 2017.
 ^ "Resolution 7 of the 9th meeting of the CGPM (1948): Writing and printing of unit symbols and of numbers". International Bureau of Weights and Measures. Retrieved 20121106.
 ^ "BIPM  Resolution 12 of the 11th CGPM". Bipm.org. Retrieved 22 August 2017.
Further reading
 International Union of Pure and Applied Chemistry (1993). Quantities, Units and Symbols in Physical Chemistry, 2nd edition, Oxford: Blackwell Science. ISBN 0632035838. Electronic version.
 Unit Systems in Electromagnetism
 MW Keller et al. Metrology Triangle Using a Watt Balance, a Calculable Capacitor, and a SingleElectron Tunneling Device
 "The Current SI Seen From the Perspective of the Proposed New SI". Barry N. Taylor. Journal of Research of the National Institute of Standards and Technology, Vol. 116, No. 6, Pgs. 797–807, Nov–Dec 2011.
 B. N. Taylor, Ambler Thompson, International System of Units (SI), National Institute of Standards and Technology 2008 edition, ISBN 1437915582.
External links
Wikimedia Commons has media related to International System of Units. 
 Official

BIPM Bureau International des Poids et Mesures (SI maintenance agency) (home page)
 BIPM brochure (SI reference)
 ISO 800001:2009 Quantities and units – Part 1: General

NIST Official Publications
 NIST Special Publication 330, 2008 Edition: The International System of Units (SI)
 NIST Special Publication 811, 2008 Edition: Guide for the Use of the International System of Units
 NIST Special Pub 814: Interpretation of the SI for the United States and Federal Government Metric Conversion Policy
 Rules for SAE Use of SI (Metric) Units
 International System of Units at Curlie (based on DMOZ)
 EngNet Metric Conversion Chart Online Categorised Metric Conversion Calculator
 U.S. Metric Association. 2008. A Practical Guide to the International System of Units
 History
 LaTeX SIunits package manual gives a historical background to the SI system.
 Research
 The metrological triangle
 Recommendation of ICWM 1 (CI2005)