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International System of Units

January 01, 1970

"SI" redirects here. For other uses, see Si (disambiguation).

The International System of Units, internationally known by the abbreviation SI (from French Système international d'unités), is the modern form of the metric system and the world's most widely used system of measurement. Coordinated by the International Bureau of Weights and Measures (abbreviated BIPM from French: Bureau international des poids et mesures) it is the only system of measurement with an official status in nearly every country in the world, employed in science, technology, industry, and everyday commerce.

SI base units (outer ring) and constants (inner ring)

The SI comprises a coherent system of units of measurement starting with seven base units, which are the second (symbol s, the unit of time), metre (m, length), kilogram (kg, mass), ampere (A, electric current), kelvin (K, thermodynamic temperature), mole (mol, amount of substance), and candela (cd, luminous intensity). The system can accommodate coherent units for an unlimited number of additional quantities. These are called coherent derived units, which can always be represented as products of powers of the base units. Twenty-two coherent derived units have been provided with special names and symbols.

The seven base units and the 22 coherent derived units with special names and symbols may be used in combination to express other coherent derived units. Since the sizes of coherent units will be convenient for only some applications and not for others, the SI provides twenty-four prefixes which, when added to the name and symbol of a coherent unit produce twenty-four additional (non-coherent) SI units for the same quantity; these non-coherent units are always decimal (i.e. power-of-ten) multiples and sub-multiples of the coherent unit.

The current way of defining the SI is a result of a decades-long move towards increasingly abstract and idealised formulation in which the realisations of the units are separated conceptually from the definitions. A consequence is that as science and technologies develop, new and superior realisations may be introduced without the need to redefine the unit. One problem with artefacts is that they can be lost, damaged, or changed; another is that they introduce uncertainties that cannot be reduced by advancements in science and technology.

The original 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 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, and is based on the metre–kilogram–second system of units (MKS) combined with ideas from the development of the CGS system.

Definition edit

The International System of Units consists of a set of defining constants with corresponding base units, derived units, and a set of decimal-based multipliers that are used as prefixes.[1]: 125 

SI defining constants edit

SI defining constants
Symbol Defining constant Exact value
ΔνCs hyperfine transition frequency of Cs 9192631770 Hz
c speed of light 299792458 m/s
h Planck constant 6.62607015×10−34 J⋅s
e elementary charge 1.602176634×10−19 C
k Boltzmann constant 1.380649×10−23 J/K
NA Avogadro constant 6.02214076×1023 mol−1
Kcd luminous efficacy of 540 THz radiation 683 lm/W

The seven defining constants are the most fundamental feature of the definition of the system of units.[1]: 125  The magnitudes of all SI units are defined by declaring that seven constants have certain exact numerical values when expressed in terms of their SI units. These defining constants are the speed of light in vacuum c, the hyperfine transition frequency of caesium ΔνCs, the Planck constant h, the elementary charge e, the Boltzmann constant k, the Avogadro constant NA, and the luminous efficacy Kcd. The nature of the defining constants ranges from fundamental constants of nature such as c to the purely technical constant Kcd. The values assigned to these constants were fixed to ensure continuity with previous definitions of the base units.[1]: 128 

SI base units edit

Main article: SI base unit

The SI selects seven units to serve as base units, corresponding to seven base physical quantities. They are the second, with the symbol s, which is the SI unit of the physical quantity of time; the metre, symbol m, the SI unit of length; kilogram (kg, the unit of mass); ampere (A, electric current); kelvin (K, thermodynamic temperature); mole (mol, amount of substance); and candela (cd, luminous intensity).[1] The base units are defined in terms of the defining constants. For example, the kilogram is defined by taking the Planck constant h to be 6.62607015×10−34 J s, giving the expression in terms of the defining constants[1]: 131 

1 kg = (299792458)2/(6.62607015×10−34)(9192631770)h ΔνCs/c2.

All units in the SI can be expressed in terms of the base units, and the base units serve as a preferred set for expressing or analysing the relationships between units. The choice of which and even how many quantities to use as base quantities is not fundamental or even unique – it is a matter of convention.[1]: 126 

SI base units[1]: 136 
Unit name Unit symbol Dimension symbol Quantity name Typical symbols Definition
second s   time   The duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom.
metre m   length  ,  ,  , etc. The distance travelled by light in vacuum in 1/299792458 second.
kilogram
[n 1] 		kg   mass   The kilogram is defined by setting the Planck constant h to 6.62607015×10−34 J⋅s (J = kg⋅m2⋅s−2), given the definitions of the metre and the second.[2]
ampere A   electric current   The flow of 1/1.602176634×10−19 times the elementary charge e per second, which is approximately 6.2415090744×1018 elementary charges per second.
kelvin K   thermodynamic
temperature 		  The kelvin is defined by setting the fixed numerical value of the Boltzmann constant k to 1.380649×10−23 J⋅K−1, (J = kg⋅m2⋅s−2), given the definition of the kilogram, the metre, and the second.
mole mol   amount of substance   The amount of substance of 6.02214076×1023 elementary entities.[n 2] This number is the fixed numerical value of the Avogadro constant, NA, when expressed in the unit mol−1.
candela cd   luminous intensity   The luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 5.4×1014 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian.
Notes
  1. ^ Despite 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.
  2. ^ When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles.

Derived units edit

Main article: SI derived unit

The system allows for an unlimited number of additional units, called derived units, which can always be represented as products of powers of the base units, possibly with a nontrivial numeric multiplier. When that multiplier is one, the unit is called a coherent derived unit. For example, the coherent derived SI unit unit of velocity is the metre per second, with the symbol m/s.[1]: 139  The base and coherent derived units of the SI together form a coherent system of units (the set of coherent SI units). A useful property of a coherent system is that when the numerical values of physical quantities are expressed in terms of the units of the system, then the equations between the numerical values have exactly the same form, including numerical factors, as the corresponding equations between the physical quantities.[3]: 6 

Twenty-two coherent derived units have been provided with special names and symbols as shown in the table below. The radian and steradian have no base units but are treated as derived units for historical reasons.[1]: 137 

The 22 SI derived units with special names and symbols[4]: 15 
Name Symbol Quantity In SI base units In other SI units
radian[N 1] rad plane angle m/m 1
steradian[N 1] sr solid angle m2/m2 1
hertz Hz frequency s−1
newton N force, weight kg⋅m⋅s−2
pascal Pa pressure, stress kg⋅m−1⋅s−2 N/m2 = J/m3
joule J energy, work, heat kg⋅m2⋅s−2 N⋅m = Pa⋅m3
watt W power, radiant flux kg⋅m2⋅s−3 J/s
coulomb C electric charge s⋅A
volt V electric potential, voltage, emf kg⋅m2⋅s−3⋅A−1 W/A = J/C
farad F capacitance kg−1⋅m−2⋅s4⋅A2 C/V = C2/J
ohm Ω resistance, impedance, reactance kg⋅m2⋅s−3⋅A−2 V/A = J⋅s/C2
siemens S electrical conductance kg−1⋅m−2⋅s3⋅A2 Ω−1
weber Wb magnetic flux kg⋅m2⋅s−2⋅A−1 V⋅s
tesla T magnetic flux density kg⋅s−2⋅A−1 Wb/m2
henry H inductance kg⋅m2⋅s−2⋅A−2 Wb/A
degree Celsius °C temperature relative to 273.15 K K
lumen lm luminous flux cd⋅m2/m2 cd⋅sr
lux lx illuminance cd⋅m2/m4 lm/m2 = cd⋅sr⋅m−2
becquerel Bq activity referred to a radionuclide (decays per unit time) s−1
gray Gy absorbed dose (of ionising radiation) m2⋅s−2 J/kg
sievert Sv equivalent dose (of ionising radiation) m2⋅s−2 J/kg
katal kat catalytic activity mol⋅s−1
Notes
  1. ^ a b The radian and steradian are defined as dimensionless 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.[5]: 103 [4]: 14, 16 

 
Arrangement of the principal measurements in physics based on the mathematical manipulation of length, time, and mass

Derived units apply to some 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.[a] Other useful derived quantities can be specified in terms of the SI base and derived units that have no named units in the SI, such as acceleration, which has the SI unit m/s2.[1]: 139 

A combination of base and derived units may be used to express a derived unit. 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/m2).[6]

Prefixes edit

Main article: Metric prefix

Like all metric systems, the SI uses metric prefixes to systematically construct, for the same physical quantity, a set of units that are decimal multiples of each other over a wide range. For example, driving distances are normally given in kilometres (symbol km) rather than in metres. Here the metric prefix 'kilo-' (symbol 'k') stands for a factor of 1000; thus, 1 km = 1000 m.

The current version of the SI provides twenty-four metric prefixes that signify decimal powers ranging from 10−30 to 1030, the most recent being adopted in 2022.[1]: 143–144 [7][8][9] Most prefixes correspond to integer powers of 1000; the only ones that do not are those for 10, 1/10, 100, and 1/100. The conversion between different SI units for one and the same physical quantity is always through a power of ten. This is why the SI (and metric systems more generally) are called decimal systems of measurement units.[10]

The grouping formed by a prefix symbol attached to a unit symbol (e.g. 'km', 'cm') constitutes a new inseparable unit symbol. This new symbol can be raised to a positive or negative power. It can also be combined with other unit symbols to form compound unit symbols.[1]: 143  For example, g/cm3 is an SI unit of density, where cm3 is to be interpreted as (cm)3.

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.[5]: 122 [11]: 14 

The BIPM specifies 24 prefixes for the International System of Units (SI):

SI prefixes
Prefix Base 10 Decimal Adoption
[nb 1]
Name Symbol
quetta Q 1030 1000000000000000000000000000000 2022[12]
ronna R 1027 1000000000000000000000000000
yotta Y 1024 1000000000000000000000000 1991
zetta Z 1021 1000000000000000000000
exa E 1018 1000000000000000000 1975[13]
peta P 1015 1000000000000000
tera T 1012 1000000000000 1960
giga G 109 1000000000
mega M 106 1000000 1873
kilo k 103 1000 1795
hecto h 102 100
deca da 101 10
— — 100 1 —
deci d 10−1 0.1 1795
centi c 10−2 0.01
milli m 10−3 0.001
micro μ 10−6 0.000001 1873
nano n 10−9 0.000000001 1960
pico p 10−12 0.000000000001
femto f 10−15 0.000000000000001 1964
atto a 10−18 0.000000000000000001
zepto z 10−21 0.000000000000000000001 1991
yocto y 10−24 0.000000000000000000000001
ronto r 10−27 0.000000000000000000000000001 2022[12]
quecto q 10−30 0.000000000000000000000000000001
Notes
  1. ^ Prefixes adopted before 1960 already existed before SI. The introduction of the CGS system was in 1873.

Coherent and non-coherent SI units edit

Further information: Coherent unit

The base units and the derived units formed as the product of powers of the base units with a numerical factor of one form a coherent system of units. Every physical quantity has exactly one coherent SI unit. For example, 1 m/s = 1 m / (1 s) is the coherent derived unit for velocity.[1]: 139  With the exception of the kilogram (for which the prefix kilo- is required for a coherent unit), when prefixes are used with the coherent SI units, the resulting units are no longer coherent, because the prefix introduces a numerical factor other than one.[1]: 137  For example, the metre, kilometre, centimetre, nanometre, etc. are all SI units of length, though only the metre is a coherent SI unit. The complete set of SI units consists of both the coherent set and the multiples and sub-multiples of coherent units formed by using the SI prefixes.[1]: 138 

The kilogram is the only coherent SI unit whose name and symbol include a prefix. For historical reasons, the names and symbols for multiples and sub-multiples of the unit of mass are formed as if the gram were the base unit. Prefix names and symbols are attached to the unit name gram and the unit symbol g respectively. For example, 10−6 kg is written milligram and mg, not microkilogram and μkg.[1]: 144 

Several different quantities may share the same coherent SI unit. For example, the joule per kelvin (symbol J/K) is the coherent SI unit for two distinct quantities: heat capacity and entropy; another example is the ampere, which is the coherent SI unit for both electric current and magnetomotive force. This illustrates why it is important not to use the unit alone to specify the quantity. As the SI Brochure states,[1]: 140  "this applies not only to technical texts, but also, for example, to measuring instruments (i.e. the instrument read-out needs to indicate both the unit and the quantity measured)".

Furthermore, the same coherent SI unit may be a base unit in one context, but a coherent derived unit in another. For example, the ampere is a base unit when it is a unit of electric current, but a coherent derived unit when it is a unit of magnetomotive force.[1]: 140 

Examples of coherent derived units in terms of base units[4]: 17 
Name Symbol Derived quantity Typical symbol
square metre m2 area A
cubic metre m3 volume V
metre per second m/s speed, velocity v
metre per second squared m/s2 acceleration a
reciprocal metre m−1 wavenumber σ, ṽ
vergence (optics) V, 1/f
kilogram per cubic metre kg/m3 density ρ
kilogram per square metre kg/m2 surface density ρA
cubic metre per kilogram m3/kg specific volume v
ampere per square metre A/m2 current density j
ampere per metre A/m magnetic field strength H
mole per cubic metre mol/m3 concentration c
kilogram per cubic metre kg/m3 mass concentration ρ, γ
candela per square metre cd/m2 luminance Lv
Examples of derived units that include units with special names[4]: 18 
Name Symbol Quantity In SI base units
pascal-second Pa⋅s dynamic viscosity m−1⋅kg⋅s−1
newton-metre N⋅m moment of force m2⋅kg⋅s−2
newton per metre N/m surface tension kg⋅s−2
radian per second rad/s angular velocity, angular frequency s−1
radian per second squared rad/s2 angular acceleration s−2
watt per square metre W/m2 heat flux density, irradiance kg⋅s−3
joule per kelvin J/K entropy, heat capacity m2⋅kg⋅s−2⋅K−1
joule per kilogram-kelvin J/(kg⋅K) specific heat capacity, specific entropy m2⋅s−2⋅K−1
joule per kilogram J/kg specific energy m2⋅s−2
watt per metre-kelvin W/(m⋅K) thermal conductivity m⋅kg⋅s−3⋅K−1
joule per cubic metre J/m3 energy density m−1⋅kg⋅s−2
volt per metre V/m electric field strength m⋅kg⋅s−3⋅A−1
coulomb per cubic metre C/m3 electric charge density m−3⋅s⋅A
coulomb per square metre C/m2 surface charge density, electric flux density, electric displacement m−2⋅s⋅A
farad per metre F/m permittivity m−3⋅kg−1⋅s4⋅A2
henry per metre H/m permeability m⋅kg⋅s−2⋅A−2
joule per mole J/mol molar energy m2⋅kg⋅s−2⋅mol−1
joule per mole-kelvin J/(mol⋅K) molar entropy, molar heat capacity m2⋅kg⋅s−2⋅K−1⋅mol−1
coulomb per kilogram C/kg exposure (x- and γ-rays) kg−1⋅s⋅A
gray per second Gy/s absorbed dose rate m2⋅s−3
watt per steradian W/sr radiant intensity m2⋅kg⋅s−3
watt per square metre-steradian W/(m2⋅sr) radiance kg⋅s−3
katal per cubic metre kat/m3 catalytic activity concentration m−3⋅s−1⋅mol

Lexicographic conventions edit

See also: ISO 31-0 § Typographic conventions, and Space (punctuation) § Unit symbols and numbers
 
Example of lexical conventions. In the expression of acceleration due to gravity, a space separates the value and the units, both the 'm' and the 's' are lowercase because neither the metre nor the second are named after people, and exponentiation is represented with a superscript '2'.

Unit names edit

According to the SI Brochure,[1]: 148  unit names should be treated as common nouns of the context language. This means that they should be typeset in the same character set as other common nouns (e.g. Latin alphabet in English, Cyrillic script in Russian, etc.), following the usual grammatical and orthographical rules of the context language. For example, in English and French, even when the unit is named after a person and its symbol begins with a capital letter, the unit name in running text should start with a lowercase letter (e.g., newton, hertz, pascal) and is capitalised only at the beginning of a sentence and in headings and publication titles. As a nontrivial application of this rule, the SI Brochure notes[1]: 148  that the name of the unit with the symbol °C is correctly spelled as 'degree Celsius': the first letter of the name of the unit, 'd', is in lowercase, while the modifier 'Celsius' is capitalised because it is a proper name.[1]: 148 

The English spelling and even names for certain SI units and metric prefixes depend on the variety of English used. US English uses the spelling deka-, meter, and liter, and International English uses deca-, metre, and litre. The name of the unit whose symbol is t and which is defined according to 1 t = 103 kg is 'metric ton' in US English and 'tonne' in International English.[4]: iii 

Unit symbols and the values of quantities edit

Symbols of SI units are intended to be unique and universal, independent of the context language.[5]: 130–35  The SI Brochure has specific rules for writing them.[5]: 130–35 

In addition, the SI Brochure provides style conventions for among other aspects of displaying quantities units: the quantity symbols, formatting of numbers and the decimal marker, expressing measurement uncertainty, multiplication and division of quantity symbols, and the use of pure numbers and various angles.[1]: 147 

In the United States, the guideline produced by the National Institute of Standards and Technology (NIST)[11]: 37  clarifies language-specific details for American English that were left unclear by the SI Brochure, but is otherwise identical to the SI Brochure.[14] For example, 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 English-style handwriting. The American NIST recommends that within the United States "L" be used rather than "l".[11]

Realisation of units edit

Main article: Realisation (metrology)
 
Silicon sphere for the Avogadro project used for measuring the Avogadro constant to a relative standard uncertainty of 2×10−8 or less, held by Achim Leistner[15]

Metrologists carefully distinguish between the definition of a unit and its realisation. The SI units are defined by declaring that seven defining constants[1]: 125–129  have certain exact numerical values when expressed in terms of their SI units. 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.[1]: 135 

For each base unit the BIPM publishes a mises en pratique, (French for 'putting into practice; implementation',[16]) describing the current best practical realisations of the unit.[17] The separation of the defining constants from the definitions of units means that improved measurements can be developed leading to changes in the mises en pratique as science and technology develop, without having to revise the definitions.

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".[5]: 111  Various consultative committees of the CIPM decided in 2016 that more than one mise en pratique would be developed for determining the value of each unit.[18] These methods include the following:

  • 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 5×10−8 and at least one of these values should be better than 2×10−8. Both the Kibble balance and the Avogadro project should be included in the experiments and any differences between these be reconciled.[19][20]
  • The definition of the kelvin measured with a 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 10−6 and that these values be corroborated by other measurements.[21]

Organizational status edit

 
Countries using the metric (SI), imperial, and US customary systems as of 2019

The International System of Units, or SI,[1]: 123  is a decimal and metric system of units established in 1960 and periodically updated since then. The SI has an official status in most countries, including the United States, Canada, and the United Kingdom, although these three countries are among the handful of nations that, to various degrees, also continue to use their customary systems. Nevertheless, with this nearly universal level of acceptance, the SI "has been used around the world as the preferred system of units, the basic language for science, technology, industry, and trade."[1]: 123, 126 

The only other types of measurement system that still have widespread use across the world are the imperial and US customary measurement systems. The international yard and pound are defined in terms of the SI.[22]

International System of Quantities edit

Main article: International System of Quantities

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 ISQ 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, non-contradictory equations. The ISQ defines the quantities that are measured with the SI units.[23] The ISQ is formalised, in part, in the international standard ISO/IEC 80000, which was completed in 2009 with the publication of ISO 80000-1,[24] and has largely been revised in 2019–2020.[25]

Controlling authority edit

Main articles: General Conference on Weights and Measures and International Bureau of Weights and Measures

The SI is regulated and continually developed by three international organisations that were established in 1875 under the terms of the Metre Convention. They are the General Conference on Weights and Measures (CGPM[b]),[26] the International Committee for Weights and Measures (CIPM[c]), and the International Bureau of Weights and Measures (BIPM[d]). All the decisions and recommendations concerning units are collected in a brochure called The International System of Units (SI),[1] which is published in French and English by the BIPM and periodically updated. The writing and maintenance of the brochure is carried out by one of the committees of the 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.[27] The brochure leaves some scope for local variations, particularly regarding unit 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 usage for English-language publications that use American English.[4]

History edit

 
Stone marking the Austro-Hungarian/Italian border at Pontebba displaying myriametres, a unit of 10 km used in Central Europe in the 19th century (but since deprecated)[28]
For broader coverage of this topic, see History of the metric system.

CGS and MKS systems edit

See also: CGS system of units
 
Closeup of the National Prototype Metre, serial number 27, allocated to the United States

The concept of a system of units emerged a hundred years before the SI. 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, building on previous work of Carl Gauss, developed the centimetre–gram–second system of units or cgs system in 1874. The systems formalised the concept of a collection of related units called a coherent system of units. In a coherent system, base units combine to define derived units without extra factors.[4]: 2  For example, using meters per second is coherent in a system that uses meter for length and seconds for time, but kilometre per hour is not coherent. 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.[29]

Metre Convention edit

Main articles: Metre Convention and MKS system of units

A French-inspired 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.[e][30]: 353–354  The General Conference on Weights and Measures (French: Conférence générale des poids et mesures – CGPM), which was established by the Metre Convention,[29] 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.[31]: 37 [32] Initially the convention only covered standards for the metre and the kilogram. This became the foundation of the MKS system of units.[4]: 2 

Giovanni Giorgi and the problem of electrical units edit

At the close of the 19th century three different systems of units of measure existed for electrical measurements: a CGS-based system for electrostatic units, also known as the Gaussian or ESU system, a CGS-based system for electromechanical units (EMU), and an International system based on units defined by the Metre Convention[33] 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.[34] 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.[35]

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. When combined with the MKS the new system, known as MKSA was approved in 1946.[4]

9th CGPM, the precursor to SI edit

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".[36] This working document was Practical system of units of measurement. Based on this study, the 10th CGPM in 1954 defined an international system derived six base units: 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.[37] 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.[5]: 104, 130 

Birth of the SI edit

The 10th CGPM in 1954 resolved to create an international system of units[31]: 41  and in 1960, the 11th CGPM published a long detailed report, including the decision to name system the International System of Units, abbreviated SI from the French name, Le Système international d'unités.[5]: 110 

The International Bureau of Weights and Measures (BIPM) has described SI as "the modern form of metric system".[5]: 95  In 1971 the mole became the seventh base unit of the SI.[4]: 2 

2019 redefinition edit

 
Reverse dependencies of the SI base units on seven physical constants, which are assigned exact numerical values in the 2019 redefinition. Unlike in the previous definitions, the base units are all derived exclusively from constants of nature. Here,   means that   is used to define  .
Main article: 2019 redefinition of the SI base units

After the metre was redefined in 1960, the International Prototype of the Kilogram (IPK) was the only physical artefact upon which base units (directly the kilogram and indirectly the ampere, mole and candela) depended for their definition, making these units subject to periodic comparisons of national standard kilograms with the IPK.[38] 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.[39] By avoiding the use of an artifact to define units, all issues with the loss, damage, and change of the artifact are avoided.[1]: 125 

A proposal was made that:[40]

The new definitions were adopted at the 26th CGPM on 16 November 2018, and came into effect on 20 May 2019.[41] The change was adopted by the European Union through Directive (EU) 2019/1258.[42]

Prior to its redefinition in 2019, the SI was defined through the seven base units from which the derived units were constructed as products of powers of the base units. After the redefinition, the SI is defined by fixing the numerical values of seven defining constants. This has the effect that the distinction between the base units and derived units is, in principle, not needed, since all units, base as well as derived, may be constructed directly from the defining constants. Nevertheless, the distinction is retained because "it is useful and historically well established", and also because the ISO/IEC 80000 series of standards, which define the International System of Quantities (ISQ), specifies base and derived quantities that necessarily have the corresponding SI units.[1]: 129 

Related units edit

Non-SI units accepted for use with SI edit

Main article: Non-SI units mentioned in the SI
 
While not an SI-unit, the litre may be used with SI units. It is equivalent to (10 cm)3 = (1 dm)3 = 10−3 m3.

Many non-SI 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 non-SI units accepted for use with SI,[5] including the hour, minute, degree of angle, litre, and decibel.

Metric units not recognised by SI edit

Main article: List of metric units

Although the term metric system is often used as an informal alternative name for the International System of Units,[43] other metric systems exist, some of which were in widespread use in the past or are even still used in particular areas. There are also individual metric units such as the sverdrup and the darcy that exist outside of any system of units. Most of the units of the other metric systems are not recognised by the SI.

Unacceptable uses edit

Sometimes, SI unit name variations are introduced, mixing information about the corresponding physical quantity or the conditions of its measurement; however, this practice is unacceptable with the SI. "Unacceptability of mixing information with units: When one gives the value of a quantity, any information concerning the quantity or its conditions of measurement must be presented in such a way as not to be associated with the unit."[5] Instances include: "watt-peak" and "watt RMS"; "geopotential metre" and "vertical metre"; "standard cubic metre"; "atomic second", "ephemeris second", and "sidereal second".

See also edit


Organisations

Standards and conventions

Notes edit

  1. ^ Ohm's law: 1 Ω = 1 V/A from the relationship E = I × R, where E is electromotive force or voltage (unit: volt), I is current (unit: ampere), and R is resistance (unit: ohm).
  2. ^ From French: Conférence générale des poids et mesures.
  3. ^ from French: Comité international des poids et mesures
  4. ^ from French: Bureau international des poids et mesures
  5. ^ Argentina, Austria-Hungary, Belgium, Brazil, Denmark, France, German Empire, Italy, Peru, Portugal, Russia, Spain, Sweden and Norway, Switzerland, Ottoman Empire, United States, and Venezuela.
Attribution

[1]  This article incorporates text from this source, which is available under the CC BY 3.0 license.

References edit

  1. ^ 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 aa ab ac ad International Bureau of Weights and Measures (December 2022), The International System of Units (SI) (PDF), vol. 2 (9th ed.), ISBN 978-92-822-2272-0, from the original on 18 October 2021
  2. ^ Materese, Robin (16 November 2018). "Historic Vote Ties Kilogram and Other Units to Natural Constants". NIST. Retrieved 16 November 2018.
  3. ^ ISO 80000-1:2009 Quantities and units – Part 1: General.
  4. ^ a b c d e f g h i j David B. Newell; Eite Tiesinga, eds. (2019). The International System of Units (SI) (PDF) (NIST Special publication 330, 2019 ed.). Gaithersburg, MD: NIST. Retrieved 30 November 2019.
  5. ^ a b c d e f g h i j International Bureau of Weights and Measures (2006), The International System of Units (SI) (PDF) (8th ed.), ISBN 92-822-2213-6, (PDF) from the original on 4 June 2021, retrieved 16 December 2021
  6. ^ . Institution of Engineering and Technology. 1996. pp. 8–11. Archived from the original on 28 June 2013. Retrieved 19 August 2013.
  7. ^ "Earth now weighs six ronnagrams: New metric prefixes voted in". phys.org. 18 November 2022.
  8. ^ (PDF). BIPM. 18 November 2022. Archived from the original (PDF) on 18 November 2022. Retrieved 18 November 2022.
  9. ^ "New prefixes for the SI adopted by the General Conference on Weights and Measures". BIPM. Retrieved 11 January 2023.
  10. ^ "Decimal Nature of the Metric System". US Metric Association. 2015. from the original on 15 April 2020. Retrieved 15 April 2020.
  11. ^ a b c Thompson, Ambler; Taylor, Barry N. (March 2008). Guide for the Use of the International System of Units (SI) (Report). National Institute of Standards and Technology. §10.5.3. Retrieved 21 January 2022.
  12. ^ a b "On the extension of the range of SI prefixes". 18 November 2022. Retrieved 5 February 2023.
  13. ^ "Metric (SI) Prefixes". NIST.
  14. ^ "Interpretation of the International System of Units (the Metric System of Measurement) for the United States" (PDF). Federal Register. 73 (96): 28432–28433. 9 May 2008. FR Doc number E8-11058. Retrieved 28 October 2009.
  15. ^ "Avogadro Project". National Physical Laboratory. Retrieved 19 August 2010.
  16. ^ "NIST Mise en Pratique of the New Kilogram Definition". NIST. 2013. from the original on 14 July 2017. Retrieved 9 May 2020.
  17. ^ "Practical realizations of the definitions of some important units". BIPM. 2019. from the original on 9 April 2020. Retrieved 11 April 2020.
  18. ^ "International Committee for Weights and Measures – Proceedings of the 106th meeting" (PDF).
  19. ^ (PDF). 12th Meeting of the CCM. Sèvres: Bureau International des Poids et Mesures. 26 March 2010. Archived from the original (PDF) on 14 May 2013. Retrieved 27 June 2012.
  20. ^ (PDF). 16th Meeting of the CCQM. Sèvres: Bureau International des Poids et Mesures. 15–16 April 2010. Archived from the original (PDF) on 14 May 2013. Retrieved 27 June 2012.
  21. ^ (PDF). 25th Meeting of the CCT. Sèvres: Bureau International des Poids et Mesures. 6–7 May 2010. Archived from the original (PDF) on 14 May 2013. Retrieved 27 June 2012.
  22. ^ United States. National Bureau of Standards (1959). Research Highlights of the National Bureau of Standards. U.S. Department of Commerce, National Bureau of Standards. p. 13. Retrieved 31 July 2019.
  23. ^ "1.16" (PDF). International vocabulary of metrology – Basic and general concepts and associated terms (VIM) (3rd ed.). International Bureau of Weights and Measures (BIPM): Joint Committee for Guides in Metrology. 2012. Retrieved 28 March 2015.
  24. ^ S. V. Gupta, Units of Measurement: Past, Present and Future. International System of Units, p. 16, Springer, 2009. ISBN 3642007384.
  25. ^ "ISO 80000-1:2022 Quantities and units Part 1: General".
  26. ^ "Interpretation of the International System of Units (the Metric System of Measurement) for the United States". Federal Register. 73. National Institute of Standards and Technology: 28432. 16 May 2008. from the original on 16 August 2017. Retrieved 6 December 2022.
  27. ^ . BIPM. Archived from the original on 31 October 2020.
  28. ^ [Official units of measure in Europe 1842]. spasslernen (in German). 1 May 2009. Archived from the original on 25 September 2012. Retrieved 26 March 2011. Text version of Malaisé's book: Malaisé, Ferdinand von (1842). Theoretisch-practischer Unterricht im Rechnen [Theoretical and practical instruction in arithmetic] (in German). München: Verlag des Verf. pp. 307–322. Retrieved 7 January 2013.
  29. ^ a b Page, Chester H.; Vigoureux, Paul, eds. (20 May 1975). The International Bureau of Weights and Measures 1875–1975: NBS Special Publication 420. Washington, D.C.: National Bureau of Standards. p. 12.
  30. ^ Alder, Ken (2002). The Measure of all Things – The Seven-Year-Odyssey that Transformed the World. London: Abacus. ISBN 978-0-349-11507-8.
  31. ^ a b Giunta, Carmen J. (2023). A Brief History of the Metric System: From Revolutionary France to the Constant-Based SI. SpringerBriefs in Molecular Science. Cham: Springer International Publishing. Bibcode:2023bhms.book.....G. doi:10.1007/978-3-031-28436-6. ISBN 978-3-031-28435-9. S2CID 258172637.
  32. ^ Quinn, Terry J. (2012). From artefacts to atoms: the BIPM and the search for ultimate measurement standards. New York Oxford: Oxford University Press. ISBN 978-0-19-530786-3.
  33. ^ Fenna, Donald (2002). Weights, Measures and Units. Oxford University Press. International unit. ISBN 978-0-19-860522-5.
  34. ^ Maxwell, J. C. (1873). A treatise on electricity and magnetism. Vol. 2. Oxford: Clarendon Press. pp. 242–245. Retrieved 12 May 2011.
  35. ^ . International Electrotechnical Commission. 2011. Archived from the original on 15 May 2011. Retrieved 5 April 2011.
  36. ^ "BIPM – Resolution 6 of the 9th CGPM". Bipm.org. 1948. Retrieved 22 August 2017.
  37. ^ "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 6 November 2012.
  38. ^ "Redefining the kilogram". UK National Physical Laboratory. Retrieved 30 November 2014.
  39. ^ "A Turning Point for Humanity: Redefining the World's Measurement System". NIST. 12 May 2018. Retrieved 16 January 2024.
  40. ^ "Appendix 1. Decisions of the CGPM and the CIPM" (PDF). BIPM. p. 188. Retrieved 27 April 2021.
  41. ^ 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.
  42. ^ "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". Eur-Lex. 23 July 2019. Retrieved 28 August 2019.
  43. ^ Olthoff, Jim (2018). "For All Times, For All Peoples: How Replacing the Kilogram Empowers Industry". NIST. from the original on 16 March 2020. Retrieved 14 April 2020. ... the International System of Units (SI), popularly known as the metric system.

Further reading edit

External links edit

 
Wikimedia Commons has media related to International System of Units.
  • BIPM (International Bureau of Weights and Measures) official web site

January 01, 1970
international, system, units, redirects, here, other, uses, disambiguation, internationally, known, abbreviation, from, french, système, international, unités, modern, form, metric, system, world, most, widely, used, system, measurement, coordinated, internati. SI redirects here For other uses see Si disambiguation The International System of Units internationally known by the abbreviation SI from French Systeme international d unites is the modern form of the metric system and the world s most widely used system of measurement Coordinated by the International Bureau of Weights and Measures abbreviated BIPM from French Bureau international des poids et mesures it is the only system of measurement with an official status in nearly every country in the world employed in science technology industry and everyday commerce SI base units outer ring and constants inner ring SI base units Symbol Name Quantity s second time m metre length kg kilogram mass A ampere electric current K kelvin thermodynamic temperature mol mole amount of substance cd candela luminous intensity The SI comprises a coherent system of units of measurement starting with seven base units which are the second symbol s the unit of time metre m length kilogram kg mass ampere A electric current kelvin K thermodynamic temperature mole mol amount of substance and candela cd luminous intensity The system can accommodate coherent units for an unlimited number of additional quantities These are called coherent derived units which can always be represented as products of powers of the base units Twenty two coherent derived units have been provided with special names and symbols The seven base units and the 22 coherent derived units with special names and symbols may be used in combination to express other coherent derived units Since the sizes of coherent units will be convenient for only some applications and not for others the SI provides twenty four prefixes which when added to the name and symbol of a coherent unit produce twenty four additional non coherent SI units for the same quantity these non coherent units are always decimal i e power of ten multiples and sub multiples of the coherent unit The current way of defining the SI is a result of a decades long move towards increasingly abstract and idealised formulation in which the realisations of the units are separated conceptually from the definitions A consequence is that as science and technologies develop new and superior realisations may be introduced without the need to redefine the unit One problem with artefacts is that they can be lost damaged or changed another is that they introduce uncertainties that cannot be reduced by advancements in science and technology The original 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 Conference generale 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 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 and is based on the metre kilogram second system of units MKS combined with ideas from the development of the CGS system Contents 1 Definition 1 1 SI defining constants 1 2 SI base units 1 3 Derived units 1 4 Prefixes 1 5 Coherent and non coherent SI units 2 Lexicographic conventions 2 1 Unit names 2 2 Unit symbols and the values of quantities 3 Realisation of units 4 Organizational status 4 1 International System of Quantities 4 2 Controlling authority 5 History 5 1 CGS and MKS systems 5 2 Metre Convention 5 3 Giovanni Giorgi and the problem of electrical units 5 4 9th CGPM the precursor to SI 5 5 Birth of the SI 5 6 2019 redefinition 6 Related units 6 1 Non SI units accepted for use with SI 6 2 Metric units not recognised by SI 6 3 Unacceptable uses 7 See also 8 Notes 9 References 10 Further reading 11 External linksDefinition editThe International System of Units consists of a set of defining constants with corresponding base units derived units and a set of decimal based multipliers that are used as prefixes 1 125 SI defining constants edit SI defining constants Symbol Defining constant Exact value DnCs hyperfine transition frequency of Cs 9192 631 770 Hz c speed of light 299792 458 m s h Planck constant 6 626070 15 10 34 J s e elementary charge 1 602176 634 10 19 C k Boltzmann constant 1 380649 10 23 J K NA Avogadro constant 6 022140 76 1023 mol 1 Kcd luminous efficacy of 540 THz radiation 683 lm W The seven defining constants are the most fundamental feature of the definition of the system of units 1 125 The magnitudes of all SI units are defined by declaring that seven constants have certain exact numerical values when expressed in terms of their SI units These defining constants are the speed of light in vacuum c the hyperfine transition frequency of caesium DnCs the Planck constant h the elementary charge e the Boltzmann constant k the Avogadro constant NA and the luminous efficacy Kcd The nature of the defining constants ranges from fundamental constants of nature such as c to the purely technical constant Kcd The values assigned to these constants were fixed to ensure continuity with previous definitions of the base units 1 128 SI base units edit Main article SI base unit The SI selects seven units to serve as base units corresponding to seven base physical quantities They are the second with the symbol s which is the SI unit of the physical quantity of time the metre symbol m the SI unit of length kilogram kg the unit of mass ampere A electric current kelvin K thermodynamic temperature mole mol amount of substance and candela cd luminous intensity 1 The base units are defined in terms of the defining constants For example the kilogram is defined by taking the Planck constant h to be 6 626070 15 10 34 J s giving the expression in terms of the defining constants 1 131 1 kg 299792 458 2 6 626070 15 10 34 9192 631 770 h DnCs c 2 All units in the SI can be expressed in terms of the base units and the base units serve as a preferred set for expressing or analysing the relationships between units The choice of which and even how many quantities to use as base quantities is not fundamental or even unique it is a matter of convention 1 126 SI base units 1 136 Unit name Unit symbol Dimension symbol Quantity name Typical symbols Definition second s T displaystyle mathsf T nbsp time t displaystyle t nbsp The duration of 9192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom metre m L displaystyle mathsf L nbsp length l displaystyle l nbsp x displaystyle x nbsp r displaystyle r nbsp etc The distance travelled by light in vacuum in 1 299792 458 second kilogram n 1 kg M displaystyle mathsf M nbsp mass m displaystyle m nbsp The kilogram is defined by setting the Planck constant h to 6 626070 15 10 34 J s J kg m2 s 2 given the definitions of the metre and the second 2 ampere A I displaystyle mathsf I nbsp electric current I i displaystyle I i nbsp The flow of 1 1 602176 634 10 19 times the elementary charge e per second which is approximately 6 241509 0744 1018 elementary charges per second kelvin K 8 displaystyle mathsf Theta nbsp thermodynamictemperature T displaystyle T nbsp The kelvin is defined by setting the fixed numerical value of the Boltzmann constant k to 1 380649 10 23 J K 1 J kg m2 s 2 given the definition of the kilogram the metre and the second mole mol N displaystyle mathsf N nbsp amount of substance n displaystyle n nbsp The amount of substance of 6 022140 76 1023 elementary entities n 2 This number is the fixed numerical value of the Avogadro constant NA when expressed in the unit mol 1 candela cd J displaystyle mathsf J nbsp luminous intensity I v displaystyle I rm v nbsp The luminous intensity in a given direction of a source that emits monochromatic radiation of frequency 5 4 1014 hertz and that has a radiant intensity in that direction of 1 683 watt per steradian Notes Despite 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 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 Derived units edit Main article SI derived unit The system allows for an unlimited number of additional units called derived units which can always be represented as products of powers of the base units possibly with a nontrivial numeric multiplier When that multiplier is one the unit is called a coherent derived unit For example the coherent derived SI unit unit of velocity is the metre per second with the symbol m s 1 139 The base and coherent derived units of the SI together form a coherent system of units the set of coherent SI units A useful property of a coherent system is that when the numerical values of physical quantities are expressed in terms of the units of the system then the equations between the numerical values have exactly the same form including numerical factors as the corresponding equations between the physical quantities 3 6 Twenty two coherent derived units have been provided with special names and symbols as shown in the table below The radian and steradian have no base units but are treated as derived units for historical reasons 1 137 The 22 SI derived units with special names and symbols 4 15 Name Symbol Quantity In SI base units In other SI units radian N 1 rad plane angle m m 1 steradian N 1 sr solid angle m2 m2 1 hertz Hz frequency s 1 newton N force weight kg m s 2 pascal Pa pressure stress kg m 1 s 2 N m2 J m3 joule J energy work heat kg m2 s 2 N m Pa m3 watt W power radiant flux kg m2 s 3 J s coulomb C electric charge s A volt V electric potential voltage emf kg m2 s 3 A 1 W A J C farad F capacitance kg 1 m 2 s4 A2 C V C2 J ohm W resistance impedance reactance kg m2 s 3 A 2 V A J s C2 siemens S electrical conductance kg 1 m 2 s3 A2 W 1 weber Wb magnetic flux kg m2 s 2 A 1 V s tesla T magnetic flux density kg s 2 A 1 Wb m2 henry H inductance kg m2 s 2 A 2 Wb A degree Celsius C temperature relative to 273 15 K K lumen lm luminous flux cd m2 m2 cd sr lux lx illuminance cd m2 m4 lm m2 cd sr m 2 becquerel Bq activity referred to a radionuclide decays per unit time s 1 gray Gy absorbed dose of ionising radiation m2 s 2 J kg sievert Sv equivalent dose of ionising radiation m2 s 2 J kg katal kat catalytic activity mol s 1 Notes a b The radian and steradian are defined as dimensionless 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 5 103 4 14 16 nbsp Arrangement of the principal measurements in physics based on the mathematical manipulation of length time and mass Derived units apply to some 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 a Other useful derived quantities can be specified in terms of the SI base and derived units that have no named units in the SI such as acceleration which has the SI unit m s2 1 139 A combination of base and derived units may be used to express a derived unit 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 m2 6 Prefixes edit Main article Metric prefix Like all metric systems the SI uses metric prefixes to systematically construct for the same physical quantity a set of units that are decimal multiples of each other over a wide range For example driving distances are normally given in kilometres symbol km rather than in metres Here the metric prefix kilo symbol k stands for a factor of 1000 thus 1 km 1000 m The current version of the SI provides twenty four metric prefixes that signify decimal powers ranging from 10 30 to 1030 the most recent being adopted in 2022 1 143 144 7 8 9 Most prefixes correspond to integer powers of 1000 the only ones that do not are those for 10 1 10 100 and 1 100 The conversion between different SI units for one and the same physical quantity is always through a power of ten This is why the SI and metric systems more generally are called decimal systems of measurement units 10 The grouping formed by a prefix symbol attached to a unit symbol e g km cm constitutes a new inseparable unit symbol This new symbol can be raised to a positive or negative power It can also be combined with other unit symbols to form compound unit symbols 1 143 For example g cm3 is an SI unit of density where cm3 is to be interpreted as cm 3 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 5 122 11 14 The BIPM specifies 24 prefixes for the International System of Units SI SI prefixesvte Prefix Base 10 Decimal Adoption nb 1 Name Symbol quetta Q 1030 1000 000 000 000 000 000 000 000 000 000 2022 12 ronna R 1027 1000 000 000 000 000 000 000 000 000 yotta Y 1024 1000 000 000 000 000 000 000 000 1991 zetta Z 1021 1000 000 000 000 000 000 000 exa E 1018 1000 000 000 000 000 000 1975 13 peta P 1015 1000 000 000 000 000 tera T 1012 1000 000 000 000 1960 giga G 109 1000 000 000 mega M 106 1000 000 1873 kilo k 103 1000 1795 hecto h 102 100 deca da 101 10 100 1 deci d 10 1 0 1 1795 centi c 10 2 0 01 milli m 10 3 0 001 micro m 10 6 0 000001 1873 nano n 10 9 0 000000 001 1960 pico p 10 12 0 000000 000 001 femto f 10 15 0 000000 000 000 001 1964 atto a 10 18 0 000000 000 000 000 001 zepto z 10 21 0 000000 000 000 000 000 001 1991 yocto y 10 24 0 000000 000 000 000 000 000 001 ronto r 10 27 0 000000 000 000 000 000 000 000 001 2022 12 quecto q 10 30 0 000000 000 000 000 000 000 000 000 001 Notes Prefixes adopted before 1960 already existed before SI The introduction of the CGS system was in 1873 Coherent and non coherent SI units edit Further information Coherent unit The base units and the derived units formed as the product of powers of the base units with a numerical factor of one form a coherent system of units Every physical quantity has exactly one coherent SI unit For example 1 m s 1 m 1 s is the coherent derived unit for velocity 1 139 With the exception of the kilogram for which the prefix kilo is required for a coherent unit when prefixes are used with the coherent SI units the resulting units are no longer coherent because the prefix introduces a numerical factor other than one 1 137 For example the metre kilometre centimetre nanometre etc are all SI units of length though only the metre is a coherent SI unit The complete set of SI units consists of both the coherent set and the multiples and sub multiples of coherent units formed by using the SI prefixes 1 138 The kilogram is the only coherent SI unit whose name and symbol include a prefix For historical reasons the names and symbols for multiples and sub multiples of the unit of mass are formed as if the gram were the base unit Prefix names and symbols are attached to the unit name gram and the unit symbol g respectively For example 10 6 kg is written milligram and mg not microkilogram and mkg 1 144 Several different quantities may share the same coherent SI unit For example the joule per kelvin symbol J K is the coherent SI unit for two distinct quantities heat capacity and entropy another example is the ampere which is the coherent SI unit for both electric current and magnetomotive force This illustrates why it is important not to use the unit alone to specify the quantity As the SI Brochure states 1 140 this applies not only to technical texts but also for example to measuring instruments i e the instrument read out needs to indicate both the unit and the quantity measured Furthermore the same coherent SI unit may be a base unit in one context but a coherent derived unit in another For example the ampere is a base unit when it is a unit of electric current but a coherent derived unit when it is a unit of magnetomotive force 1 140 Examples of coherent derived units in terms of base units 4 17 Name Symbol Derived quantity Typical symbol square metre m2 area A cubic metre m3 volume V metre per second m s speed velocity v metre per second squared m s2 acceleration a reciprocal metre m 1 wavenumber s ṽ vergence optics V 1 f kilogram per cubic metre kg m3 density r kilogram per square metre kg m2 surface density rA cubic metre per kilogram m3 kg specific volume v ampere per square metre A m2 current density j ampere per metre A m magnetic field strength H mole per cubic metre mol m3 concentration c kilogram per cubic metre kg m3 mass concentration r g candela per square metre cd m2 luminance Lv Examples of derived units that include units with special names 4 18 Name Symbol Quantity In SI base units pascal second Pa s dynamic viscosity m 1 kg s 1 newton metre N m moment of force m2 kg s 2 newton per metre N m surface tension kg s 2 radian per second rad s angular velocity angular frequency s 1 radian per second squared rad s2 angular acceleration s 2 watt per square metre W m2 heat flux density irradiance kg s 3 joule per kelvin J K entropy heat capacity m2 kg s 2 K 1 joule per kilogram kelvin J kg K specific heat capacity specific entropy m2 s 2 K 1 joule per kilogram J kg specific energy m2 s 2 watt per metre kelvin W m K thermal conductivity m kg s 3 K 1 joule per cubic metre J m3 energy density m 1 kg s 2 volt per metre V m electric field strength m kg s 3 A 1 coulomb per cubic metre C m3 electric charge density m 3 s A coulomb per square metre C m2 surface charge density electric flux density electric displacement m 2 s A farad per metre F m permittivity m 3 kg 1 s4 A2 henry per metre H m permeability m kg s 2 A 2 joule per mole J mol molar energy m2 kg s 2 mol 1 joule per mole kelvin J mol K molar entropy molar heat capacity m2 kg s 2 K 1 mol 1 coulomb per kilogram C kg exposure x and g rays kg 1 s A gray per second Gy s absorbed dose rate m2 s 3 watt per steradian W sr radiant intensity m2 kg s 3 watt per square metre steradian W m2 sr radiance kg s 3 katal per cubic metre kat m3 catalytic activity concentration m 3 s 1 molLexicographic conventions editSee also ISO 31 0 Typographic conventions and Space punctuation Unit symbols and numbers nbsp Example of lexical conventions In the expression of acceleration due to gravity a space separates the value and the units both the m and the s are lowercase because neither the metre nor the second are named after people and exponentiation is represented with a superscript 2 Unit names edit According to the SI Brochure 1 148 unit names should be treated as common nouns of the context language This means that they should be typeset in the same character set as other common nouns e g Latin alphabet in English Cyrillic script in Russian etc following the usual grammatical and orthographical rules of the context language For example in English and French even when the unit is named after a person and its symbol begins with a capital letter the unit name in running text should start with a lowercase letter e g newton hertz pascal and is capitalised only at the beginning of a sentence and in headings and publication titles As a nontrivial application of this rule the SI Brochure notes 1 148 that the name of the unit with the symbol C is correctly spelled as degree Celsius the first letter of the name of the unit d is in lowercase while the modifier Celsius is capitalised because it is a proper name 1 148 The English spelling and even names for certain SI units and metric prefixes depend on the variety of English used US English uses the spelling deka meter and liter and International English uses deca metre and litre The name of the unit whose symbol is t and which is defined according to 1 t 103 kg is metric ton in US English and tonne in International English 4 iii Unit symbols and the values of quantities edit Symbols of SI units are intended to be unique and universal independent of the context language 5 130 35 The SI Brochure has specific rules for writing them 5 130 35 In addition the SI Brochure provides style conventions for among other aspects of displaying quantities units the quantity symbols formatting of numbers and the decimal marker expressing measurement uncertainty multiplication and division of quantity symbols and the use of pure numbers and various angles 1 147 In the United States the guideline produced by the National Institute of Standards and Technology NIST 11 37 clarifies language specific details for American English that were left unclear by the SI Brochure but is otherwise identical to the SI Brochure 14 For example 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 English style handwriting The American NIST recommends that within the United States L be used rather than l 11 Realisation of units editMain article Realisation metrology nbsp Silicon sphere for the Avogadro project used for measuring the Avogadro constant to a relative standard uncertainty of 2 10 8 or less held by Achim Leistner 15 Metrologists carefully distinguish between the definition of a unit and its realisation The SI units are defined by declaring that seven defining constants 1 125 129 have certain exact numerical values when expressed in terms of their SI units 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 1 135 For each base unit the BIPM publishes a mises en pratique French for putting into practice implementation 16 describing the current best practical realisations of the unit 17 The separation of the defining constants from the definitions of units means that improved measurements can be developed leading to changes in the mises en pratique as science and technology develop without having to revise the definitions 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 5 111 Various consultative committees of the CIPM decided in 2016 that more than one mise en pratique would be developed for determining the value of each unit 18 These methods include the following 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 5 10 8 and at least one of these values should be better than 2 10 8 Both the Kibble balance and the Avogadro project should be included in the experiments and any differences between these be reconciled 19 20 The definition of the kelvin measured with a 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 10 6 and that these values be corroborated by other measurements 21 Organizational status edit nbsp Countries using the metric SI imperial and US customary systems as of 2019 The International System of Units or SI 1 123 is a decimal and metric system of units established in 1960 and periodically updated since then The SI has an official status in most countries including the United States Canada and the United Kingdom although these three countries are among the handful of nations that to various degrees also continue to use their customary systems Nevertheless with this nearly universal level of acceptance the SI has been used around the world as the preferred system of units the basic language for science technology industry and trade 1 123 126 The only other types of measurement system that still have widespread use across the world are the imperial and US customary measurement systems The international yard and pound are defined in terms of the SI 22 International System of Quantities edit Main article International System of Quantities 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 ISQ 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 non contradictory equations The ISQ defines the quantities that are measured with the SI units 23 The ISQ is formalised in part in the international standard ISO IEC 80000 which was completed in 2009 with the publication of ISO 80000 1 24 and has largely been revised in 2019 2020 25 Controlling authority edit Main articles General Conference on Weights and Measures and International Bureau of Weights and Measures The SI is regulated and continually developed by three international organisations that were established in 1875 under the terms of the Metre Convention They are the General Conference on Weights and Measures CGPM b 26 the International Committee for Weights and Measures CIPM c and the International Bureau of Weights and Measures BIPM d All the decisions and recommendations concerning units are collected in a brochure called The International System of Units SI 1 which is published in French and English by the BIPM and periodically updated The writing and maintenance of the brochure is carried out by one of the committees of the 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 27 The brochure leaves some scope for local variations particularly regarding unit 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 usage for English language publications that use American English 4 History edit nbsp Stone marking the Austro Hungarian Italian border at Pontebba displaying myriametres a unit of 10 km used in Central Europe in the 19th century but since deprecated 28 For broader coverage of this topic see History of the metric system CGS and MKS systems edit See also CGS system of units nbsp Closeup of the National Prototype Metre serial number 27 allocated to the United States The concept of a system of units emerged a hundred years before the SI 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 building on previous work of Carl Gauss developed the centimetre gram second system of units or cgs system in 1874 The systems formalised the concept of a collection of related units called a coherent system of units In a coherent system base units combine to define derived units without extra factors 4 2 For example using meters per second is coherent in a system that uses meter for length and seconds for time but kilometre per hour is not coherent 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 29 Metre Convention edit Main articles Metre Convention and MKS system of units A French inspired 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 e 30 353 354 The General Conference on Weights and Measures French Conference generale des poids et mesures CGPM which was established by the Metre Convention 29 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 31 37 32 Initially the convention only covered standards for the metre and the kilogram This became the foundation of the MKS system of units 4 2 Giovanni Giorgi and the problem of electrical units edit At the close of the 19th century three different systems of units of measure existed for electrical measurements a CGS based system for electrostatic units also known as the Gaussian or ESU system a CGS based system for electromechanical units EMU and an International system based on units defined by the Metre Convention 33 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 34 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 35 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 When combined with the MKS the new system known as MKSA was approved in 1946 4 9th CGPM the precursor to SI edit 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 36 This working document was Practical system of units of measurement Based on this study the 10th CGPM in 1954 defined an international system derived six base units 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 37 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 5 104 130 Birth of the SI edit The 10th CGPM in 1954 resolved to create an international system of units 31 41 and in 1960 the 11th CGPM published a long detailed report including the decision to name system the International System of Units abbreviated SI from the French name Le Systeme international d unites 5 110 The International Bureau of Weights and Measures BIPM has described SI as the modern form of metric system 5 95 In 1971 the mole became the seventh base unit of the SI 4 2 2019 redefinition edit nbsp Reverse dependencies of the SI base units on seven physical constants which are assigned exact numerical values in the 2019 redefinition Unlike in the previous definitions the base units are all derived exclusively from constants of nature Here a b displaystyle a rightarrow b nbsp means that a displaystyle a nbsp is used to define b displaystyle b nbsp Main article 2019 redefinition of the SI base units After the metre was redefined in 1960 the International Prototype of the Kilogram IPK was the only physical artefact upon which base units directly the kilogram and indirectly the ampere mole and candela depended for their definition making these units subject to periodic comparisons of national standard kilograms with the IPK 38 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 39 By avoiding the use of an artifact to define units all issues with the loss damage and change of the artifact are avoided 1 125 A proposal was made that 40 In addition to the speed of light four constants of nature the Planck constant an elementary charge the Boltzmann constant and the Avogadro constant be defined to have exact values The International Prototype of the 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 new definitions were adopted at the 26th CGPM on 16 November 2018 and came into effect on 20 May 2019 41 The change was adopted by the European Union through Directive EU 2019 1258 42 Prior to its redefinition in 2019 the SI was defined through the seven base units from which the derived units were constructed as products of powers of the base units After the redefinition the SI is defined by fixing the numerical values of seven defining constants This has the effect that the distinction between the base units and derived units is in principle not needed since all units base as well as derived may be constructed directly from the defining constants Nevertheless the distinction is retained because it is useful and historically well established and also because the ISO IEC 80000 series of standards which define the International System of Quantities ISQ specifies base and derived quantities that necessarily have the corresponding SI units 1 129 Related units editNon SI units accepted for use with SI edit Main article Non SI units mentioned in the SI nbsp While not an SI unit the litre may be used with SI units It is equivalent to 10 cm 3 1 dm 3 10 3 m3 Many non SI 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 non SI units accepted for use with SI 5 including the hour minute degree of angle litre and decibel Metric units not recognised by SI edit Main article List of metric units Although the term metric system is often used as an informal alternative name for the International System of Units 43 other metric systems exist some of which were in widespread use in the past or are even still used in particular areas There are also individual metric units such as the sverdrup and the darcy that exist outside of any system of units Most of the units of the other metric systems are not recognised by the SI Unacceptable uses edit Sometimes SI unit name variations are introduced mixing information about the corresponding physical quantity or the conditions of its measurement however this practice is unacceptable with the SI Unacceptability of mixing information with units When one gives the value of a quantity any information concerning the quantity or its conditions of measurement must be presented in such a way as not to be associated with the unit 5 Instances include watt peak and watt RMS geopotential metre and vertical metre standard cubic metre atomic second ephemeris second and sidereal second See also editConversion of units Comparison of various scales List of international common standards Metrication Outline of the metric system Overview of and topical guide to the metric system Organisations International Bureau of Weights and Measures Intergovernmental measurement science and measurement standards setting organisation Institute for Reference Materials and Measurements EU National Institute of Standards and Technology Measurement standards laboratory in the United States US Standards and conventions Conventional electrical unit Historical high precision units of measurement Coordinated Universal Time UTC Primary time standard Unified Code for Units of Measure System of codes for unambiguously representing measurement unitsNotes edit Ohm s law 1 W 1 V A from the relationship E I R where E is electromotive force or voltage unit volt I is current unit ampere and R is resistance unit ohm From French Conference generale des poids et mesures from French Comite international des poids et mesures from French Bureau international des poids et mesures Argentina Austria Hungary Belgium Brazil Denmark France German Empire Italy Peru Portugal Russia Spain Sweden and Norway Switzerland Ottoman Empire United States and Venezuela Attribution 1 nbsp This article incorporates text from this source which is available under the CC BY 3 0 license References edit 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 aa ab ac ad International Bureau of Weights and Measures December 2022 The International System of Units SI PDF vol 2 9th ed ISBN 978 92 822 2272 0 archived from the original on 18 October 2021 Materese Robin 16 November 2018 Historic Vote Ties Kilogram and Other Units to Natural Constants NIST Retrieved 16 November 2018 ISO 80000 1 2009 Quantities and units Part 1 General a b c d e f g h i j David B Newell Eite Tiesinga eds 2019 The International System of Units SI PDF NIST Special publication 330 2019 ed Gaithersburg MD NIST Retrieved 30 November 2019 a b c d e f g h i j International Bureau of Weights and Measures 2006 The International System of Units SI PDF 8th ed ISBN 92 822 2213 6 archived PDF from the original on 4 June 2021 retrieved 16 December 2021 Units amp Symbols for Electrical amp Electronic Engineers Institution of Engineering and Technology 1996 pp 8 11 Archived from the original on 28 June 2013 Retrieved 19 August 2013 Earth now weighs six ronnagrams New metric prefixes voted in phys org 18 November 2022 List of Resolutions for the 27th meeting of the General Conference on Weights and Measures PDF BIPM 18 November 2022 Archived from the original PDF on 18 November 2022 Retrieved 18 November 2022 New prefixes for the SI adopted by the General Conference on Weights and Measures BIPM Retrieved 11 January 2023 Decimal Nature of the Metric System US Metric Association 2015 Archived from the original on 15 April 2020 Retrieved 15 April 2020 a b c Thompson Ambler Taylor Barry N March 2008 Guide for the Use of the International System of Units SI Report National Institute of Standards and Technology 10 5 3 Retrieved 21 January 2022 a b On the extension of the range of SI prefixes 18 November 2022 Retrieved 5 February 2023 Metric SI Prefixes NIST Interpretation of the International System of Units the Metric System of Measurement for the United States PDF Federal Register 73 96 28432 28433 9 May 2008 FR Doc number E8 11058 Retrieved 28 October 2009 Avogadro Project National Physical Laboratory Retrieved 19 August 2010 NIST Mise en Pratique of the New Kilogram Definition NIST 2013 Archived from the original on 14 July 2017 Retrieved 9 May 2020 Practical realizations of the definitions of some important units BIPM 2019 Archived from the original on 9 April 2020 Retrieved 11 April 2020 International Committee for Weights and Measures Proceedings of the 106th meeting PDF Recommendations of the Consultative Committee for Mass and Related Quantities to the International Committee for Weights and Measures PDF 12th Meeting of the CCM Sevres Bureau International des Poids et Mesures 26 March 2010 Archived from the original PDF on 14 May 2013 Retrieved 27 June 2012 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 Sevres Bureau International des Poids et Mesures 15 16 April 2010 Archived from the original PDF on 14 May 2013 Retrieved 27 June 2012 Recommendations of the Consultative Committee for Thermometry to the International Committee for Weights and Measures PDF 25th Meeting of the CCT Sevres Bureau International des Poids et Mesures 6 7 May 2010 Archived from the original PDF on 14 May 2013 Retrieved 27 June 2012 United States National Bureau of Standards 1959 Research Highlights of the National Bureau of Standards U S Department of Commerce National Bureau of Standards p 13 Retrieved 31 July 2019 1 16 PDF International vocabulary of metrology Basic and general concepts and associated terms VIM 3rd ed International Bureau of Weights and Measures BIPM Joint Committee for Guides in Metrology 2012 Retrieved 28 March 2015 S V Gupta Units of Measurement Past Present and Future International System of Units p 16 Springer 2009 ISBN 3642007384 ISO 80000 1 2022 Quantities and units Part 1 General Interpretation of the International System of Units the Metric System of Measurement for the United States Federal Register 73 National Institute of Standards and Technology 28432 16 May 2008 Archived from the original on 16 August 2017 Retrieved 6 December 2022 VIM3 International Vocabulary of Metrology BIPM Archived from the original on 31 October 2020 Amtliche Masseinheiten in Europa 1842 Official units of measure in Europe 1842 spasslernen in German 1 May 2009 Archived from the original on 25 September 2012 Retrieved 26 March 2011 Text version of Malaise s book Malaise Ferdinand von 1842 Theoretisch practischer Unterricht im Rechnen Theoretical and practical instruction in arithmetic in German Munchen Verlag des Verf pp 307 322 Retrieved 7 January 2013 a b Page Chester H Vigoureux Paul eds 20 May 1975 The International Bureau of Weights and Measures 1875 1975 NBS Special Publication 420 Washington D C National Bureau of Standards p 12 Alder Ken 2002 The Measure of all Things The Seven Year Odyssey that Transformed the World London Abacus ISBN 978 0 349 11507 8 a b Giunta Carmen J 2023 A Brief History of the Metric System From Revolutionary France to the Constant Based SI SpringerBriefs in Molecular Science Cham Springer International Publishing Bibcode 2023bhms book G doi 10 1007 978 3 031 28436 6 ISBN 978 3 031 28435 9 S2CID 258172637 Quinn Terry J 2012 From artefacts to atoms the BIPM and the search for ultimate measurement standards New York Oxford Oxford University Press ISBN 978 0 19 530786 3 Fenna Donald 2002 Weights Measures and Units Oxford University Press International unit ISBN 978 0 19 860522 5 Maxwell J C 1873 A treatise on electricity and magnetism Vol 2 Oxford Clarendon Press pp 242 245 Retrieved 12 May 2011 Historical figures Giovanni Giorgi International Electrotechnical Commission 2011 Archived from the original on 15 May 2011 Retrieved 5 April 2011 BIPM Resolution 6 of the 9th CGPM Bipm org 1948 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 6 November 2012 Redefining the kilogram UK National Physical Laboratory Retrieved 30 November 2014 A Turning Point for Humanity Redefining the World s Measurement System NIST 12 May 2018 Retrieved 16 January 2024 Appendix 1 Decisions of the CGPM and the CIPM PDF BIPM p 188 Retrieved 27 April 2021 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 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 Eur Lex 23 July 2019 Retrieved 28 August 2019 Olthoff Jim 2018 For All Times For All Peoples How Replacing the Kilogram Empowers Industry NIST Archived from the original on 16 March 2020 Retrieved 14 April 2020 the International System of Units SI popularly known as the metric system Further reading editInternational Union of Pure and Applied Chemistry 1993 Quantities Units and Symbols in Physical Chemistry 2nd edition Oxford Blackwell Science ISBN 0 632 03583 8 Electronic version Unit Systems in Electromagnetism MW Keller et al PDF Metrology Triangle Using a Watt Balance a Calculable Capacitor and a Single Electron Tunneling Device The Current SI Seen From the Perspective of the Proposed New SI PDF 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 edit nbsp Wikimedia Commons has media related to International System of Units BIPM International Bureau of Weights and Measures official web site Portal nbsp Physics Retrieved from https en wikipedia org w index php title International System of Units amp oldid 1223112784 Prefixes, wikipedia, wiki, book, books, library,

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