{{short descriptiona system of units of measurement for base and derived physical quantities}}{{RedirectSI}}{{broaderOutline of the metric system}}{{2019 SI redefinitiondf=y}}{{Use dmy datesdate=May 2014}}File:International System of Units Logo.pngthumbright264pxThe seven
{ ! Symbol !! Name !! Quantity

cd  candelacandelaThe International System of Units (SI, abbreviated from the French ) 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 second, metre, kilogram, ampere, kelvin, mole, candela, 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 defined in terms of invariant constants of nature, such as the speed of light in vacuum and the charge of the electron, which can be observed and measured with great accuracy. Seven constants are used in various combinations to define the seven base units. Prior to 2019, artefacts were used instead of some of these constants, the last being the International Prototype of the Kilogram, a cylinder of platinumiridium. Concern regarding its stability led to a revision of the definition of the base units entirely in terms of constants of nature, which was put into effect on 20 May 2019.NEWS,weblink Historic Vote Ties Kilogram and Other Units to Natural Constants, Materese, Robin, 20181116, NIST, 20181116, 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 recently named 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 centimetreâ€“gramâ€“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: â€“ 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 to 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 metreâ€“kilogramâ€“second system of units (MKS) rather than any variant of the CGS.{{anchorCoherent SI units}} Units and prefixesThe International System of Units consists of a set of base units, derived units, and a set of decimalbased multipliers that are used as prefixes.{{rp103â€“106}} The units, excluding prefixed units,For historical reasons, the kilogram rather than the gram is treated as the coherent unit, making an exception to this characterisation. 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 Ã— 1 m/s2 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: {{math1=F = m Ã— 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.Ohm's law: {{nowrap1=1 Î© = 1 V/A}} from the relationship {{nowrap1=E = I Ã— R}}, where E is electromotive force or voltage (unit: volt), I is current (unit: ampere), and R is resistance (unit: ohm). 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/s2.Base unitsThe SI base units are the building blocks of the system and all the other units are derived from them.{ class="wikitable" style="margin:1em auto 1em auto" 
6}}Quantities Units and Symbols in Physical Chemistry, IUPACHTTPS://BOOKS.GOOGLE.COM/?ID=NOG0SXXEU64C&PG=PA240 >PAGES=238â€“244 DATE=19750520  EDITORFIRST1=CHESTER H.  EDITORFIRST2=PAUL  NATIONAL BUREAU OF STANDARDS >LOCATION=WASHINGTON, D.C., 
!Unitname!Unitsymbol!
Dimensionsymbol!
Quantityname!Definition
!
secondWithin the context of the SI, the second is the coherent base unit of time, and is used in the definitions of derived units. The name "second" historically arose as being the 2ndlevel
sexagesimal division ({{frac160{{sup2}}}}) of some quantity, the
hour in this case, which the
SI classifies as an "accepted" unit along with its firstlevel sexagesimal division the
minute.
!
metre
m  Llength  {{val299792458}}}} second. 
!
kilogramDespite the prefix "kilo", the kilogram is the coherent base unit of mass, and is used in the definitions of derived units. Nonetheless, prefixes for the unit of mass are determined as if the gram were the base unit.

kg  Mmass  Planck constant h exactly to {{val>6.62607015  u=J.s}} ({{nowrap  2}}â‹…s{{supâˆ’2}}}}), given the definitions of the metre and the second. 
!
ampere!
kelvin
K  Î˜  thermodynamic temperature>thermodynamictemperature  Boltzmann constant k to {{val>1.380649  u=Jâ‹…Kâˆ’1}}, (J = kgâ‹…m2â‹…sâˆ’2), given the definition of the kilogram, the metre, and the second. 
!
mole
mol  N  amount of substance>amount ofsubstance  6.02214076e=23}} elementary entities.When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles. This number is the fixed numerical value of the Avogadro constant, NA, when expressed in the unit molâˆ’1 and is called the Avogadro number. 
!
candela
cd  J  luminous intensity>luminousintensity  5.4  1683}} watt per steradian. 

 Notes
{{reflistgroup=n}} 
Derived units
The derived units in the SI are formed by powers, products, or quotients of the base units and are potentially unlimited in number.{{rp103}}{{rp14,16}} 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)â€”and the pascal can be defined as one newton per square metre (N/m2).WEB, Units & Symbols for Electrical & Electronic Engineers,
weblink Institution of Engineering and Technology, 1996, 8â€“11, 20130819,
weblink" title="web.archive.org/web/20130628212624
weblink">weblink 20130628, { class="wikitable floatleft" style="margin:1em auto 1em auto;lineheight:1.4"15}}! Name! Symbol! Quantity! In SI base units! In other SI units

radiannote 1

rad  angle>plane angle  m/m  1 

steradiannote 1

hertz
joule
watt
coulomb
volt
farad
degree Celsius
lux
becquerel
sievert
katal
Notes1. The radian and steradian are defined as dimensionless derived units. 
{ class="wikitable floatleft" style="margin:1em auto 1em auto;lineheight:1.4"17}}! Name! Symbol! Derived quantity! Typical symbol

square metre
cubic metre
metre per second
metre per second squared
vergence (optics)
kilogram per cubic metre
kilogram per square metre
cubic metre per kilogram
ampere per square metre
mole per cubic metre
kilogram per cubic metre
kg/m3  Mass concentration (chemistry)>mass concentration  Ï, Î³ 

candela per square metre{ class="wikitable floatleft" style="margin:1em auto 1em auto;lineheight:1.4"16}}! Name! Symbol! Quantity! In SI base units

newton metre
newton per metre
radian per second
radian per second squared
watt per square metre
W/m2 heat flux density  kgâ‹…sâˆ’3 

joule per kelvin
joule per kilogram kelvin
joule per kilogram
watt per metre kelvin
joule per cubic metre
volt per metre
coulomb per cubic metre
coulomb per square metre
farad per metre
henry per metre
H/m  Permeability (electromagnetism)>permeability  mâ‹…kgâ‹…sâˆ’2â‹…Aâˆ’2 

joule per mole
joule per mole kelvin
coulomb per kilogram
C/kg  Exposure (photography)>exposure  kgâˆ’1â‹…sâ‹…A 

gray per second
watt per steradian
watt per square metre steradian
katal per cubic metre{{clear}}
Prefixes
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.{{rp122}}BOOK, Ambler, Thompson, Barry N., Taylor, 2008,
weblink Guide for the Use of the International System of Units (SI) (Special publication 811), Gaithersburg, MD,
National Institute of Standards and Technology, {{rp14}} When prefixes are used to form multiples and submultiples of SI base and derived units, the resulting units are no longer coherent.{{rp7}}The BIPM specifies 20 prefixes for the International System of Units (SI):
{{SI prefixes (infobox)}}
NonSI units accepted for use with 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:(File:CubeLitre.svgrightthumbupright=1.1While not an SIunit, the litre may be used with SI units. It is equivalent to (10 cm)3 = (1 dm)3 = 10âˆ’3 m3)Some units of time, angle, and legacy nonSI units have a long history of 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 {{sfrac2Ï€}} of a revolution, has mathematical advantages but is rarely used for navigation. Further, the units used in navigation around the world are similar. 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:{ class="wikitable"+ NonSI units accepted for use with SI units!
Quantity! Name!
Symbol! Value in SI units

hour h 1 h = 60 min = 3600 s

day d

length
astronomical unit au

Minute and second of arc>minute â€²  10800}}) rad 

Minute and second of arc>second â€³  648000}}) rad 

area
hectare ha 1 ha = 1 hm2 = 104 m2

volume
litre l, L 1 l = 1 L = 1 dm3 = 103 cm3 = 10âˆ’3 m3

dalton (unit)>dalton Da  1.660539040  e=27u=kg}} 

energy
electronvolt eV

logarithmicratio quantities neper Np  In using these units it is important that thenature of the quantity be specified and thatany reference value used be specified. 
 bel B

decibel dB
These units are used in combination with SI units in common units such as the kilowatthour (1 kWâ‹…h = 3.6 MJ).
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 â€“ 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.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, the fact that the Earth's circumference is very close to 40,000 km may be a useful mnemonic.
 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 (the use of base 60 dates back to Babylonian times); a second is the time it takes a dense object to freely fall 4.9 metres from rest.
 The length of the equator is close to 40,000,000 metres (more precisely 40,075,014.2 metres).WEB,weblink How Big Is Earth?, Science, Tim Sharp 20170915T15:47:00Z, Astronomy, Space.com, 20191022, In fact, the dimensions of our planet were used by the French Academy in the original definition of the metre.WEB,weblink Metre {{!, measurementwebsite=Encyclopedia Britannicaaccessdate=20191022}}
 The metre is close to the length of a pendulum that has a period of 2 seconds;{{cndate=October 2019}} most dining tabletops are about 0.75 metres high;WEB,weblink Standard Table Sizes, Bassett Furniture, 20191022, a very tall human (basketball forward) is about 2 metres tall.WEB,weblink The Average Height of NBA Players  From Point Guards to Centers, 20181209, The Hoops Geek, 20191022,
 The kilogram is the mass of a litre of cold water; a cubic centimetre or millilitre of water has a mass of one gram; a 1euro coin weighs 7.5 g;WEB,weblink RUBINGHSCIENCE.ORG / Using Euro coins as weights, www.rubinghscience.org, 20191022, a Sacagawea US 1dollar coin weighs 8.1 g;WEB,weblink Coin Specifications {{!, U.S. Mintwebsite=www.usmint.govaccessdate=20191022}} a UK 50pence coin weighs 8.0 g.WEB,weblink Fifty Pence Coin, www.royalmint.com, 20191022,
 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 mass expressed in units of grams; the mass of a mole of carbon is 12.0 g, and the mass of a mole of table salt is 58.4 g.
 Since all gases have the same volume per mole at a given temperature and pressure far from their points of liquefaction and solidification (see Perfect gas), and air is about 1/5 oxygen (molecular mass 32) and 4/5 nitrogen (molecular mass 28), the density of any nearperfect gas relative to air can be obtained to a good approximation by dividing its molecular mass by 29 (because 4/5 Ã— 28 + 1/5 Ã— 32 = 28.8 â‰ˆ 29). For example carbon monoxide (molecular mass 28) has almost the same density as air.
 A temperature difference of one kelvin is the same as one degree Celsius: 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 Â°C or 310 K.
 A 60 W incandescent light bulb rated at 120 V (US mains voltage) consumes 0.5 A at this voltage. A 60 W bulb rated at 240 V (European mains voltage) consumes 0.25 A at this voltage.
Lexicographic conventions
Unit names
The symbols for the SI units are intended to be identical, regardless of the language used,{{rp130â€“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.WEB,
weblink Using Abbreviations or Symbols, 20040714, 20131211, Russ, Rowlett,
University of North Carolina, WEB,
weblink SI Conventions, 20131211, National Physical Laboratory, The English spelling for certain SI units differs:
US English uses the spelling
deka,
meter, and
liter, whilst
International English more commonly uses
deca,
metre, and
litre.
Unit symbols and the values of quantities {{anchorSI_writing_style}}
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.{{rp130â€“135}} The guideline produced by the
National Institute of Standards and Technology (NIST)WEB,
weblink NIST Guide to SI Units â€“ Rules and Style Conventions, 20091229, Thompson, A., July 2008, Taylor, B. N.,
National Institute of Standards and Technology, clarifies languagespecific areas in respect of American English that were left open by the SI Brochure, but is otherwise identical to the SI Brochure.JOURNAL, 20080509,
weblink Interpretation of the International System of Units (the Metric System of Measurement) for the United States, Federal Register, 73, 96, 28432â€“28433, FR Doc number E811058, 20091028,
General rules
General rulesExcept where specifically noted, these rules are common to both the SI Brochure and the NIST brochure. 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, {{val7.3e=2u=m2}}, 22 K. This rule explicitly includes the percent sign (%){{rp 134}} and the symbol for degrees Celsius (Â°C).{{rp133}} Exceptions are the symbols for plane angular degrees, minutes, and seconds (Â°, ′, and ″), which are placed immediately after the number with no intervening space.
 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 a unit symbol without a separator (e.g., k in km, M in MPa, G in GHz, Î¼ in Î¼g). Compound prefixes are not allowed. A prefixed unit is atomic in expressions (e.g., km2 is equivalent to (km)2).
 Unit symbols are written using roman (upright) type, regardless of the type used in the surrounding text.
 Symbols for derived units formed by multiplication are joined with a centre dot (â‹…) or a nonbreaking space; e.g., Nâ‹…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 sâˆ’1, mâ‹…sâˆ’1, or {{sfracms}}. A solidus must not be used more than once in a given expression without parentheses to remove ambiguities; e.g., kg/(mâ‹…s2) and kgâ‹…mâˆ’1â‹…sâˆ’2 are acceptable, but kg/m/s2 is ambiguous and unacceptable.
(File:981ms2.pngthumbAcceleration due to gravity.Note the lowercase letters (neither "metres" nor "seconds" were named after people), the space between the value and the units, and the superscript "2" to denote "squared".)
 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 do not have a plural form, e.g., 25 kg, but not 25 {{Not a typokgs}}.
 Uppercase and lowercase prefixes are not interchangeable. E.g., the quantities 1 mW and 1 MW represent two different quantities (milliwatt and megawatt).
 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.JOURNAL, Marchâ€“April 2008, Period or Comma? Decimal Styles over Time and Place,weblink Science Editor, 31, 2, 42,weblink" title="web.archive.org/web/20130228062258weblink">weblink 20130228, Amelia A., Williamson, 20120519,
 Spaces should be used as a thousands separator ({{val1000000}}) 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.
 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.
 Because the value of "billion" and "trillion" varies between languages, the dimensionless terms "ppb" (parts per billion) and "ppt" (parts per trillion) should be avoided. The SI Brochure does not suggest alternatives.
Printing SI symbols
The rules covering printing of quantities and units are part of ISO 800001:2009.WEB,
weblink ISO 800001:2009(en) Quantities and Unitsâ€”Past 1:General,
International Organization for Standardization, 2009, 20130822, Further rules are specified in respect of production of text using
printing presses,
word processors,
typewriters, and the like.
International System of Quantities
{{anchorSI Brochure}}
(File:SI Brochure Cover.jpgthumbrightCover of brochure
The International System of Units)The CGPM publishes a brochure that defines and presents the SI.{{SIbrochure8th}} Its official version is in French, in line with the
Metre Convention.{{rp102}} It leaves some scope for local interpretation, particularly regarding names and terms in different languages.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 EnglishBOOK, David B. Newell, Eite Tiesinga, The International System of Units (SI) (NIST Special publication 330, 2019 edition),
weblink 20191130,
National Institute of Standards and Technology, NIST, Gaithersburg, MD, 2019, 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.WEB,
weblink The International Vocabulary of Metrology (VIM), 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.BOOK, International vocabulary of metrology â€“ Basic and general concepts and associated terms (VIM), 2012, International Bureau of Weights and Measures (BIPM): Joint Committee for Guides in Metrology, 3rd,
weblink 20150328, 1.16, The ISQ is defined in the international standard
ISO/IEC 80000, and was finalised in 2009 with the publication of
ISO 800001.S. V. Gupta,
Units of Measurement: Past, Present and Future. International System of Units, p. 16, Springer, 2009. {{ISBN3642007384}}.{{clear}}
Realisation of units
File:Silicon sphere for Avogadro project.jpgthumbuprightSilicon sphere for the
Avogadro project used for measuring the Avogadro constant to a relative
standard uncertainty of {{val2e=âˆ’8}} or less, held by
Achim LeistnerAchim LeistnerMetrologists 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 pratiqueThis term is a
translation of the official [French] text of the SI Brochure. of the base units is given in an electronic appendix to the SI Brochure.WEB,
weblink What is a mise en pratique?,
International Bureau of Weights and Measures, 20121110, {{rp168â€“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."{{rp111}} 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 neededdate=November 2012}} 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 {{val5e=8}} and at least one of these values should be better than {{val2e=8}}. Both the Kibble balance and the Avogadro project should be included in the experiments and any differences between these be reconciled.WEB,weblink Recommendations of the Consultative Committee for Mass and Related Quantities to the International Committee for Weights and Measures, 12th Meeting of the CCM, 20100326, Bureau International des Poids et Mesures, SÃ¨vres, 20120627,weblink" title="web.archive.org/web/20130514081750weblink">weblink 14 May 2013, dead, WEB,weblink Recommendations of the Consultative Committee for Amount of Substance â€“ Metrology in Chemistry to the International Committee for Weights and Measures, 16th Meeting of the CCQM, 15â€“16 April 2010, Bureau International des Poids et Mesures, SÃ¨vres, 20120627,weblink" title="web.archive.org/web/20130514072057weblink">weblink 14 May 2013, dead,
 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 {{vale=6}} and that these values be corroborated by other measurements.WEB,weblink Recommendations of the Consultative Committee for Thermometry to the International Committee for Weights and Measures, 25th Meeting of the CCT, 6â€“7 May 2010, Bureau International des Poids et Mesures, SÃ¨vres, 20120627,weblink" title="web.archive.org/web/20130514064646weblink">weblink 14 May 2013, dead,
Evolution of the SI
Changes to the SI
The
International Bureau of Weights and Measures (BIPM) has described SI as "the modern metric system".{{rp95}} Changing technology has led to an evolution of the definitions and standards that has followed two principal strands â€“ 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.{{rp156}}p. 221 â€“ McGreevy{{rp156}}{{rp158}}{{rp159}}{{rp165}}Acknowledging the advancement of precision science at both large and small scales, the range of defined prefixes pico (10âˆ’12) to tera (1012) was extended to 10âˆ’24 to 1024.{{rp152}}{{rp158}}{{rp164}}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 {{sfrac{{val299792458}}}} 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.{{Citation last=Foster first=Marcus P. year=2009 title=Disambiguating the SI notation would guarantee its correct parsing journal=
Proceedings of the Royal Society A volume=465 issue= 2104pages=1227â€“1229 doi=10.1098/rspa.2008.0343 postscript=.}}
2019 redefinitions
File:Unit relations in the new SI.svg thumb right Dependencies of the SI base units on seven
physical constantphysical constantAfter 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.WEB, Redefining the kilogram,
weblink UK National Physical Laboratory, 20141130, 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 addition to the speed of light, four constants of nature â€“ the Planck constant, an elementary charge, the Boltzmann constant, and the Avogadro number â€“ 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.
In 2015, the
CODATA task group on fundamental constants announced special submission deadlines for data to compute the final values for the new definitions.JOURNAL, Mohr, Peter J., Newell, David B., Taylor, Barry N., 2015, CODATA recommended values of the fundamental physical constants: 2014 â€“ Summary,
weblink Zenodo, 10.5281/zenodo.22827, 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 {{mvar, h, , {{mvare}}, {{mvark}}, and {{math
NA}} 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 {{mvarh}}, {{mvare}}, {{mvark}}, and {{math
NA}} 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. }}The new definitions were adopted at the 26th CGPM on 16 November 2018, and came into effect on 20 May 2019.WEB,
weblink Report on the Meeting of the CODATA Task Group on Fundamental Constants, 3â€“4 November 2014,
BIPM, B., Wood, 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., The change was adopted by the European Union through Directive (EU) 2019/1258.WEB,
weblink Commission Directive (EU) 2019/1258 of 23 July 2019 amending, for the purpose of its adaptation to technical progress, the Annex to Council Directive 80/181/EEC as regards the definitions of SI base units, 23 July 2019,
EurLex, 28 August 2019,
History
File:Alter Grenzstein Pontebba 01.jpgthumbuprightStone marking the
AustroHungarian/Italian border at
Pontebba displaying
myriametres, a unit of 10 km used in
Central Europe in the 19th century (but since (Deprecationdeprecated]])WEB,
weblink Amtliche MaÃŸeinheiten in Europa 1842, German, Official units of measure in Europe 1842, Text version of MalaisÃ©'s book: , 20110326, BOOK,
weblink Theoretischpractischer Unterricht im Rechnen, German, Theoretical and practical instruction in arithmetic, Ferdinand von, MalaisÃ©, MÃ¼nchen, 1842, 307â€“322, 20130107, )
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.WEB,
weblink The name 'kilogram',
International Bureau of Weights and Measures, 20060725, dead,
weblink" title="web.archive.org/web/20110514110300
weblink">weblink 14 May 2011, dmyall, The group, which included preeminent French men of science,BOOK, The Measure of all Thingsâ€”The SevenYearOdyssey that Transformed the World, Alder, Ken, 2002, Abacus, London, 9780349115078, {{rp89}} used the same principles for relating length, volume, and mass that had been proposed by the English clergyman
John Wilkins in 1668BOOK, From artefacts to atoms: the BIPM and the search for ultimate measurement standards,
Oxford University Press, 2012, xxvii, Terry, Quinn, he [Wilkins] proposed essentially what became ... the French decimal metric system, 9780195307863, 705716998, BOOK, John Wilkins, John, Wilkins, 1668, An Essay towards a Real Character and a Philosophical Language, VII, 190â€“194, The Royal Society, WEB,
weblink Reproduction (33 MB), 20110306, ; WEB,
weblink 20110306, Transcription, 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.WEB,
weblink Mouton, Gabriel, Complete Dictionary of Scientific Biography, 2008,
encyclopedia.com, 20121230, {{MacTutor title=Gabriel Mouton id=Mouton date=January 2004}}File:Carl Friedrich Gauss.jpgthumbuprightleft
Carl Friedrich GaussCarl Friedrich GaussIn March 1791, the Assembly adopted the committee's proposed principles for the new decimal system of measure including the metre defined to be 1/10,000,000 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.BOOK, Smoot's Ear: The Measure of Humanity, Robert, Tavernor, 2007,
Yale University Press, 9780300124927, registration,
weblink {{rp82}}{{multiple image
 width1 = 140
 image1 = William Thomson 1st Baron Kelvin.jpg
 alt1 = William Thomson, (Lord Kelvin)
 caption1 =
Thomson  width2 = 153
 image2 = PSM V78 D529 James Clerk Maxwell.png
 alt2 = James Clerk Maxwell
 caption2 =
Maxwell  footer = William Thomson (Lord Kelvin) and James Clerk Maxwell played a prominent role in the development of the principle of coherence and in the naming of many units of measure.JOURNAL, Report on the Fortythird Meeting of the British Association for the Advancement of Science Held at Bradford in September 1873, 1874, First Report of the Committee for the Selection and Nomenclature of Dynamical and Electrical Units, Everett, 222â€“225, Special names, if short and suitable, would ... be better than the provisional designation 'C.G.S. unit of ...'.,
weblink 20130828,
}}
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
mÃ¨tre 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.BOOK, Bigourdan, Guillaume, Guillaume Bigourdan, Le SystÃ¨me MÃ©trique Des Poids Et Mesures: Son Ã‰tablissement Et Sa Propagation Graduelle, Avec L'histoire Des OpÃ©rations Qui Ont Servi Ã€ DÃ©terminer Le MÃ¨tre Et Le Kilogramme (facsimile edition), French, 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, 1901, 2012, Ulan Press, B009JT8UZU, co.uk, 176, JOURNAL,
weblink 20130618, The Foundation of the Metric System in France in the 1790s: The importance of Etienne Lenoir's platinum measuring instruments, William A., Smeaton, Platinum Metals Rev., 2000, 44, 125â€“134, 3, 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 ({{val10000}} metres) was in widespread use in both France and parts of Germany, while the kilogram ({{val1000}} grams) rather than the myriagram was used for mass.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.WEB,
weblink Brief history of the SI, International Bureau of Weights and Measures, 20121112, 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.The strength of the earth's magnetic field was designated 1 G (gauss) at the surface ({{nowrap1== 1 cmâˆ’1/2â‹…g1/2â‹…sâˆ’1}}).JOURNAL,
weblink The intensity of the Earth's magnetic force reduced to absolute measurement, 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 {{frac16}} 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
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.Argentina, AustriaHungary, Belgium, Brazil, Denmark, France, German Empire, Italy, Peru, Portugal, Russia, Spain, Sweden and Norway, Switzerland, Ottoman Empire, United States, and Venezuela.{{rp353â€“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.BOOK, Lord Kelvin, His Influence on Electrical Measurements and Units, Paul, Tunbridge,
weblink 42â€“46, 9780863412370, Peter Pereginus Ltd, 1992, {{rp96}}A set of 30 prototypes of the metre and 40 prototypes of the kilogram,The text "
Des comparaisons pÃ©riodiques des Ã©talons nationaux avec les prototypes internationaux" () 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"). 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
mÃ¨tre 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.JOURNAL, Robert A., Nelson, Foundations of the international system of units (SI), Physics Teacher, 1981, 597,
weblink's%20LECDEM/A101/GetPDFServlet.pdf, {{inconsistent citations}}The treaty also established a number of international organisations to oversee the keeping of international standards of measurement:WEB,
weblink The Metre Convention, Bureau International des Poids et Mesures, 20121001,
The CGS and MKS systems
{{See alsoCGS system of unitsMKS system of units}}(File:US National Length Meter.JPGthumbrightCloseup of the National Prototype Metre, serial number 27, allocated to the United States){{missing infosectionall 22 named derived units of SIdate=December 2017}}{{missing infosectiona period of ~3540 years between early 20th century and end of WW2 covering most of the industrial revolutiondate=December 2017}}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's work and formalised the concept of a coherent system of units with base units and derived units christened the
centimetreâ€“gramâ€“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.BOOK,
weblink 12, The International Bureau of Weights and Measures 1875â€“1975: NBS Special Publication 420, 19750520, Pageeditorlast2=Vigoureux publisher=
National Bureau of Standards, Washington, D.C., 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 "Î¼" (mu) for "micrometre" or "micron", "Î»" (lambda) for "microlitre", and "Î³" (gamma) for "microgram" started to use the symbols "Î¼m", "Î¼L" and "Î¼g".BOOK, Thomas, McGreevy, Peter, Cunningham, The Basis of Measurement: Volume 2 â€“ Metrication and Current Practice, 222â€“224, 9780948251849, 1997, Pitcon Publishing (Chippenham) Ltd, 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.BOOK, Weights, Measures and Units,
weblink registration, Donald, Fenna, International unit, 9780198605225,
Oxford University Press, 2002, for electrical distribution systems. Attempts to resolve the electrical units in terms of length, mass, and time using
dimensional analysis was beset with difficultiesâ€”the dimensions depended on whether one used the ESU or EMU systems.BOOK, A treatise on electricity and magnetism, 2, J. C., Maxwell, 1873, Clarendon Press, Oxford,
weblink 242â€“245, 20110512, 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.WEB,
weblink Historical figures: Giovanni Giorgi, 2011,
International Electrotechnical Commission, 20110405, 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
PferdestÃ¤rke (metric horsepower) for
power,WEB,
weblink Die gesetzlichen Einheiten in Deutschland, German, 6, List of units of measure in Germany,
PhysikalischTechnische Bundesanstalt (PTB), 20121113,
Pferd is
German for "horse" and
StÃ¤rke is German for "strength" or "power". The PferdestÃ¤rke is the power needed to raise 75 kg against gravity at the rate of one metre per second. ({{nowrap1=1 PS = 0.985 HP}}). the
darcy for
permeabilityWEB,
weblink Materials Science and Engineering, Division of Engineering, The
University of Edinburgh, Porous materials: Permeability, 3, Module Descriptor, Material Science, Materials 3, 2001, 20121113, dead,
weblink" title="web.archive.org/web/20130602124630
weblink">weblink 2 June 2013, dmyall, and "
millimetres of mercury" for
barometric and
blood pressure were developed or propagated, some of which incorporated
standard gravity in their definitions.This constant is unreliable, because it varies over the surface of the earth.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
{{missing infosectionchangeover centigradeâ†’Kelvin and candlepowerâ†’candeladate=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".WEB,
weblink BIPM  Resolution 6 of the 9th CGPM, Bipm.org, 22 August 2017, 1948, 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.WEB,
weblink Resolution 7 of the 9th meeting of the CGPM (1948): Writing and printing of unit symbols and of numbers, 20121106,
International Bureau of Weights and Measures, 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.{{rp104,130}}
Birth of the SI
(File:Metric system adoption map.svgthumbupright=1.5Countries where the metric system is mandatory in trade and commerce (green))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, .{{rp110}}WEB,
weblink BIPM  Resolution 12 of the 11th CGPM, Bipm.org, 22 August 2017,
Historical definitions
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.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, {{nowrap1=
F =
m Ã—
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/s2. 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 {{nowrap
m Ã—
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.{ class="wikitable" style="margin:1em auto 1em auto"6}}HTTPS://BOOKS.GOOGLE.COM/?ID=NOG0SXXEU64C&PG=PA240 >PAGES=238â€“244 DATE=19750520 EDITORFIRST1=CHESTER H. EDITORFIRST2=PAUL NATIONAL BUREAU OF STANDARDS >LOCATION=
WASHINGTON, D.C., !Unitname!DefinitionInterim definitions are given here only when there has been a
significant difference in the definition.
!
second
 Prior: {{sfrac1{{val86400}}}} of a day of 24 hours of 60 minutes of 60 seconds
 Interim (1956): {{sfrac{{val31556925.9747}}}} of the tropical year for 1900 January 0 at 12 hours ephemeris time.
 Current (1967): The duration of {{val9192631770}} periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium133 atom.
!
metre
 Prior (1793): {{sfrac{{val10000000}}}} of the meridian through Paris between the North Pole and the Equator.FG
 Interim (1889): The Prototype of the metre chosen by the CIPM, at the temperature of melting ice, represents the metric unit of length.
 Interim (1960): {{val1650763.73}} wavelengths in a vacuum of the radiation corresponding to the transition between the 2p{{sup10}} and 5d{{sup5}} quantum levels of the krypton86 atom.
 Current (1983): The distance travelled by light in vacuum in {{sfrac{{val299792458}}}} second.
!
kilogram
 Prior (1793): The grave was defined as being the mass (then called weight) of one litre of pure water at its freezing point.FG
 Interim (1889): The mass of a small squat cylinder of ~47 cubic centimetres of platinumiridium alloy kept in the Pavillon de Breteuil{{citation neededreason=Though this is the location of the BIPM in SaintCloud,weblink indicates that [...] the IPK, which is kept by the [BIPM] in SÃ¨vres, France. (This borders onto, but is distinct from SaintCloud.)date=July 2018}}, France. Also, in practice, any of numerous official replicas of it.This object is the International Prototype Kilogram or IPK called rather poetically Le Grand K.WEB,weblink Redefining the Kilogram, The Past, Erik M., Secula, 7 October 2014, Nist.gov, 22 August 2017,weblink 20170109,
 Current (2019): The kilogram is defined by setting the Planck constant h exactly to {{val6.62607015e=34u=J.s}} ({{nowrap1=J = kgâ‹…m{{sup2}}â‹…s{{supâˆ’2}}}}), given the definitions of the metre and the second. Then the formula would be {{nowrap1=kg = {{sfrach{{val6.62607015e=34}}â‹…m{{sup2}}â‹…s{{supâˆ’1}}}}}}
!
ampere
 Prior (1881): A tenth of the electromagnetic CGS unit of current. The [CGS] electromagnetic unit of current is that current, flowing in an arc 1 cm long of a circle 1 cm in radius, that creates a field of one oersted at the centre.BOOK,weblink 322, Magnetism and Electricity, McKenzie, A. E. E., Cambridge University Press, 1961, IEC
 Interim (1946): The constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular crosssection, and placed 1 m apart in vacuum, would produce between these conductors a force equal to {{val2e=7}} newtons per metre of length.
 Current (2019): The flow of {{sfrac1{{val1.602176634e=19}}}} times the elementary charge e per second.
!
kelvin
 Prior (1743): The centigrade scale is obtained by assigning 0 Â°C to the freezing point of water and 100 Â°C to the boiling point of water.
 Interim (1954): The triple point of water (0.01 Â°C) defined to be exactly 273.16 K.In 1954 the unit of thermodynamic temperature was known as the "degree Kelvin" (symbol Â°K; "Kelvin" spelt with an uppercase "K"). It was renamed the "kelvin" (symbol "K"; "kelvin" spelt with a lower case "k") in 1967.
 Previous (1967): {{sfrac273.16}} of the thermodynamic temperature of the triple point of water
 Current (2019): The kelvin is defined by setting the fixed numerical value of the Boltzmann constant k to {{val1.380649e=23u=Jâ‹…Kâˆ’1}}, (J = kgâ‹…m2â‹…sâˆ’2), given the definition of the kilogram, the metre, and the second.
!
mole
 Prior (1900): A stoichiometric quantity which is the equivalent mass in grams of Avogadro's number of molecules of a substance.ICAW
 Interim (1967): The amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon12.
 Current (2019): The amount of substance of exactly {{val6.02214076e=23}} elementary entities. This number is the fixed numerical value of the Avogadro constant, NA, when expressed in the unit molâˆ’1 and is called the Avogadro number.
!
candela
 Prior (1946): The value of the new candle (early name for the candela) is such that the brightness of the full radiator at the temperature of solidification of platinum is 60 new candles per square centimetre.
 Current (1979): The luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency {{val5.4e=14}} hertz and that has a radiant intensity in that direction of {{sfrac1683}} watt per steradian.
Note: both old and new definitions are approximately the luminous intensity of a
spermaceti candle burning modestly bright, in the late 19th century called a "candlepower" or a "candle".

 Notes
{{reflistgroup=n}}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. 
See also
{hide}cmncolwidth=30em
 {{annotated linkIntroduction to the metric system{edih}
 {{annotated linkOutline of the metric system}}
 {{annotated linkList of international common standards}}
 {{annotated linkMetreâ€“tonneâ€“second system of units}}
Organisations
 {{annotated linkInstitute for Reference Materials and Measurements}}
Standards and conventions
 {{annotated linkConventional electrical unit}}
 {{annotated linkCoordinated Universal Timeabbreviation=UTC}}
 {{annotated linkUnified Code for Units of Measure}}
}}
Notes
{{Reflistgroup="Note"}}
References
{{Reflist}}
Further reading
 {{GreenBookRef}}
 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. 797â€“807, Novâ€“Dec 2011.
 B. N. Taylor, Ambler Thompson, International System of Units (SI), National Institute of Standards and Technology 2008 edition, {{ISBN1437915582}}.
External links
{{Commons categoryInternational System of Units}}
 Official
 History
 Research
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