International System of Units
|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|
|mol||mole||amount of substance|
The International System of Units, known by the international abbreviation SI[a] in all languages: 125 : iii  and sometimes pleonastically as the SI system,[b] is the modern form: 117  of the metric system[g] and the world's most widely used system of measurement.: 123  Established and maintained by the General Conference on Weights and Measures[j] (CGPM[k]), it is the only system of measurement with an official status[m] in nearly every country in the world,[n] employed in science, technology, industry, and everyday commerce.
The SI comprises a
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.[r] 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[s] 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.[t][u] 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.
Since 2019, the magnitudes of all SI units have been defined by declaring that seven defining 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. Prior to 2019, h, e, k, and NA were not defined a priori but were rather very precisely measured quantities. In 2019, their values were fixed by definition to their best estimates at the time, ensuring continuity with previous definitions of the base units.
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 last artefact used by the SI was the International Prototype of the Kilogram, a cylinder of platinum–iridium.
The original motivation for the development of the SI was the diversity of units that had sprung up within the
The International System of Units, or SI,
The only other types of measurement system that still have widespread use across the world are the Imperial and US customary measurement systems,[z] and they are legally defined in terms of the SI.[aa] There are other, less widespread systems of measurement that are occasionally used in particular regions of the world. In addition, there are many individual non-SI units that don't belong to any comprehensive system of units, but that are nevertheless still regularly used in particular fields and regions. Both of these categories of unit are also typically defined legally in terms of SI units.[ab]
The SI was established and is maintained by the
All the decisions and recommendations concerning units are collected in a brochure called The International System of Units (SI),[ad] which is published by the International Bureau of Weights and Measures (BIPM[ae]) and periodically updated.
Overview of the units
SI base units
The SI selects seven units to serve as base units, corresponding to seven base physical quantities.[af][ag] 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). 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.
SI derived units
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.[ah] The base and coherent derived units of the SI together form a coherent system of units (the set of coherent SI units).[ai] Twenty-two coherent derived units have been provided with special names and symbols.[q] The seven base units and the 22 derived units with special names and symbols may be used in combination to express other derived units,[r] which are adopted to facilitate measurement of diverse quantities.
Why SI kept the distinction between base and derived units
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[aj] specifies base and derived quantities that necessarily have the corresponding SI units.: 129
SI metric prefixes and the decimal nature of the SI
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, while the coherent unit of length is the metre,[ak] the SI provides a full range of smaller and larger units of length, any of which may be more convenient for any given application – 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.[al]
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.: 143–4  Most prefixes correspond to integer powers of 1000; the only ones that do not are those for 10, 1/10, 100, and 1/100.
In general, given any coherent unit with a separate name and symbol,[am] one forms a new unit by simply adding an appropriate metric prefix to the name of the coherent unit (and a corresponding prefix symbol to the coherent unit's symbol).[an] Since the metric prefix signifies a particular power of ten, the new unit is always a power-of-ten multiple or sub-multiple of the coherent unit. Thus, the conversion between different SI units for one and the same physical quantity is always through a power of ten.[ao] This is why the SI (and metric systems more generally) are called decimal systems of measurement units.[ap]
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 and can be combined with other unit symbols to form compound unit symbols.: 143 For example, g/cm3 is an SI unit of density, where cm3 is to be interpreted as (cm)3.
Coherent and non-coherent SI units
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.: 137 The one exception is the kilogram, the only coherent SI unit whose name and symbol, for historical reasons, include a prefix.[an]
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.
Moreover, the metre is the only coherent SI unit of length. Every physical quantity has exactly one coherent SI unit, although this unit may be expressible in different forms by using some of the special names and symbols.: 140 For example, the coherent SI unit of linear momentum may be written as either kg⋅m/s or as N⋅s, and both forms are in use (e.g. compare respectively here:205 and here:135).
On the other hand, 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 is why it is important not to use the unit alone to specify the quantity.[aq]
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.: 140 As perhaps a more familiar example, consider rainfall, defined as volume of rain (measured in m3) that fell per unit area (measured in m2). Since m3/m2 = m, it follows that the coherent derived SI unit of rainfall is the metre, even though the metre is also the base SI unit of length.[ar]
Permitted non-SI units
There is a special group of units that are called "non-SI units that are accepted for use with the SI".: 145 See Non-SI units mentioned in the SI for a full list. Most of these, in order to be converted to the corresponding SI unit, require conversion factors that are not powers of ten. Some common examples of such units are the customary units of time, namely the minute (conversion factor of 60 s/min, since 1 min = 60 s), the hour (3600 s), and the day (86400 s); the degree (for measuring plane angles, 1° = π/180 rad); and the electronvolt (a unit of energy, 1 eV = 1.602176634×10−19 J).
The SI is intended to be an evolving system; units[as] and prefixes are created and unit definitions are modified through international agreement as the technology of measurement progresses and the precision of measurements improves.
Defining magnitudes of units
Since 2019, the magnitudes of all SI units have been defined in an abstract way, which is conceptually separated from any practical realisation of them.: 126 [at] Namely, the SI units are defined by declaring that seven defining constants: 125–9 have certain exact numerical values when expressed in terms of their SI units. Probably the most widely known of these constants is the speed of light in vacuum, c, which in the SI by definition has the exact value of c = 299792458 m/s. The other six constants are ΔνCs, the hyperfine transition frequency of caesium; h, the Planck constant; e, the elementary charge; k, the Boltzmann constant; NA, the Avogadro constant; and Kcd, the luminous efficacy of monochromatic radiation of frequency 540×1012 Hz.[au] The nature of the defining constants ranges from fundamental constants of nature such as c to the purely technical constant Kcd.: 128–9 Prior to 2019, h, e, k, and NA were not defined a priori but were rather very precisely measured quantities. In 2019, their values were fixed by definition to their best estimates at the time, ensuring continuity with previous definitions of the base units.
As far as realisations, what are believed to be the current best practical realisations of units are described in the mises en pratique,[av] which are also published by the BIPM. The abstract nature of the definitions of units is what makes it possible to improve and change the mises en pratique as science and technology develop without having to change the actual definitions themselves.[ay]
In a sense, this way of defining the SI units is no more abstract than the way derived units are traditionally defined in terms of the base units. Consider a particular derived unit, for example, the joule, the unit of energy. Its definition in terms of the base units is kg⋅m2/s2. Even if the practical realisations of the metre, kilogram, and second are available, a practical realisation of the joule would require some sort of reference to the underlying physical definition of work or energy—some actual physical procedure for realising the energy in the amount of one joule such that it can be compared to other instances of energy (such as the energy content of gasoline put into a car or of electricity delivered to a household).
The situation with the defining constants and all of the SI units is analogous. In fact, purely mathematically speaking, the SI units are defined as if we declared that it is the defining constant's units that are now the base units, with all other SI units being derived units. To make this clearer, first note that each defining constant can be taken as determining the magnitude of that defining constant's unit of measurement;: 128 for example, the definition of c defines the unit m/s as 1 m/s = c/299792458 ('the speed of one metre per second is equal to one 299792458th of the speed of light'). In this way, the defining constants directly define the following seven units:
Further, one can show, using dimensional analysis, that every coherent SI unit (whether base or derived) can be written as a unique product of powers of the units of the SI defining constants (in complete analogy to the fact that every coherent derived SI unit can be written as a unique product of powers of the base SI units). For example, the kilogram can be written as kg = (Hz)(J⋅s)/(m/s)2.[az] Thus, the kilogram is defined in terms of the three defining constants ΔνCs, c, and h because, on the one hand, these three defining constants respectively define the units Hz, m/s, and J⋅s,[ba] while, on the other hand, the kilogram can be written in terms of these three units, namely, kg = (Hz)(J⋅s)/(m/s)2.[bb] While the question of how to actually realise the kilogram in practice would, at this point, still be open, that is not really different from the fact that the question of how to actually realise the joule in practice is still in principle open even once one has achieved the practical realisations of the metre, kilogram, and second.
Specifying fundamental constants vs. other methods of definition
The current way of defining the SI is the 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.: 126
The great advantage of doing it this way is that as science and technologies develop, new and superior realisations may be introduced without the need to redefine the units.[aw] Units can now be realised with an accuracy that is ultimately limited only by the quantum structure of nature and our technical abilities but not by the definitions themselves.[ax] Any valid equation of physics relating the defining constants to a unit can be used to realise the unit, thus creating opportunities for innovation... with increasing accuracy as technology proceeds.': 122 In practice, the CIPM Consultative Committees provide so-called "mises en pratique" (practical techniques), which are the descriptions of what are currently believed to be best experimental realisations of the units.
This system lacks the conceptual simplicity of using artefacts (referred to as prototypes) as realisations of units to define those units: with prototypes, the definition and the realisation are one and the same.
In the past, there were also various other approaches to the definitions of some of the SI units. One made use of a specific physical state of a specific substance (the triple point of water, which was used in the definition of the kelvin: 113–4 ); others referred to idealised experimental prescriptions: 125 (as in the case of the former SI definition of the ampere: 113 and the former SI definition (originally enacted in 1979) of the candela: 115 ).
In the future, the set of defining constants used by the SI may be modified as more stable constants are found, or if it turns out that other constants can be more precisely measured.[bk]
The original motivation for the development of the SI was the diversity of units that had sprung up within the
Adopted in 1889, use of the MKS system of units succeeded the centimetre–gram–second system of units (CGS) in commerce and engineering. The metre and kilogram system served as the basis for the development of the International System of Units (abbreviated SI), which now serves as the international standard. Because of this, the standards of the CGS system were gradually replaced with metric standards incorporated from the MKS system.
In 1901, Giovanni Giorgi proposed to the Associazione elettrotecnica italiana (AEI) that this system, extended with a fourth unit to be taken from the units of electromagnetism, be used as an international system. This system was strongly promoted by electrical engineer
The International System was published in 1960, based on the MKS units, as a result of an initiative that began in 1948.
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[k]), the International Committee for Weights and Measures (CIPM[ac]), and the International Bureau of Weights and Measures (BIPM[ae]). The ultimate authority rests with the CGPM, which is a plenary body through which its Member States[bl] act together on matters related to measurement science and measurement standards; it usually convenes every four years. The CGPM elects the CIPM, which is an 18-person committee of eminent scientists. The CIPM operates based on the advice of a number of its Consultative Committees, which bring together the world's experts in their specified fields as advisers on scientific and technical matters.[bm] One of these committees is the Consultative Committee for Units (CCU), which is responsible for matters related to the development of the International System of Units (SI), preparation of successive editions of the SI brochure, and advice to the CIPM on matters concerning units of measurement. It is the CCU which considers in detail all new scientific and technological developments related to the definition of units and the SI. In practice, when it comes to the definition of the SI, the CGPM simply formally approves the recommendations of the CIPM, which, in turn, follows the advice of the CCU.
The CCU has the following as members: national laboratories of the Member States of the CGPM charged with establishing national standards;[bn] relevant intergovernmental organisations and international bodies;[bo] international commissions or committees;[bp] scientific unions;[bq] personal members;[br] and, as an ex officio member of all Consultative Committees, the Director of the BIPM.
Units and prefixes
The International System of Units consists of a set of
Derived units apply to derived quantities, which may by definition be expressed in terms of base quantities, and thus are not independent; for example,
The SI base units are the building blocks of the system and all the other units are derived from them.
|Unit name||Unit symbol||Dimension symbol||Quantity name||Typical symbols||Definition|
|s||T||time||The duration of 9192631770 periods of the radiation corresponding to the transition between the two |
|metre||m||L||length||, , , , , , , etc.[n 2]||The distance travelled by light in a vacuum in 1/299792458 seconds.|
|kg||M||mass||The kilogram is defined by setting the Planck constant h exactly to 6.62607015×10−34 J⋅s (J = kg⋅m2⋅s−2), given the definitions of the metre and the second.|
|ampere||A||I||electric current||The flow of exactly 1/1.602176634×10−19 times the elementary charge e per second.
Equalling approximately 6.2415090744×1018 elementary charges per second.
|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||amount of substance||The amount of substance of exactly 6.02214076×1023 elementary entities.[n 4] This number is the fixed numerical value of the Avogadro constant, NA, when expressed in the unit mol−1.|
|candela||cd||J||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.|
The derived units in the SI are formed by powers, products, or quotients of the base units and are potentially unlimited in number.: 103 : 14, 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)—and the pascal can be defined as one newton per square metre (N/m2).
|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|
|kg⋅m2⋅s−2||N⋅m = Pa⋅m3|
|watt||W||power, radiant flux||kg⋅m2⋅s−3||J/s|
|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|
|kg⋅m2⋅s−3⋅A−2||V/A = J⋅s/C2|
magnetic flux density
|°C||temperature relative to 273.15 K||K|
|becquerel||Bq||activity referred to a radionuclide (decays per unit time)||s−1|
|Name||Symbol||Derived quantity||Typical symbol|
|metre per second||m/s||speed, velocity||v|
|metre per second squared||m/s2||acceleration||a|
|vergence (optics)||V, 1/f|
|kilogram per cubic metre||kg/m3||density||ρ|
|kilogram per square metre||kg/m2||
|cubic metre per kilogram||m3/kg||specific volume||v|
|ampere per square metre||A/m2||current density||j|
ampere per metre
magnetic field strength
|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|
|Name||Symbol||Quantity||In SI base units|
moment of force
|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
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)||
|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
|coulomb per cubic metre||C/m3||
electric charge density
|coulomb per square metre||C/m2||
|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
|coulomb per kilogram||C/kg||exposure (x- and γ-rays)||kg−1⋅s⋅A|
|gray per second||Gy/s||
absorbed dose rate
|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
Prefixes are added to unit names to produce multiples and
The BIPM specifies 24 prefixes for the International System of Units (SI):
|Prefix||Base 10||Decimal||English word||Adoption|
|Name||Symbol||Short scale||Long scale|
Non-SI units accepted for use with SI
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
Some units of time, angle, and legacy non-SI units have a long history of use. Most societies have used the solar day and its non-decimal subdivisions as a basis of time and, unlike the foot or the pound, these were the same regardless of where they were being measured. The radian, being 1/2π of a revolution, has mathematical advantages but 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:
|Quantity||Name||Symbol||Value in SI units|
|time||minute||min||1 min = 60 s|
|hour||h||1 h = 60 min = 3600 s|
|day||d||1 d = 24 h = 86400 s|
|length||astronomical unit||au||1 au = 149597870700 m|
|degree||°||1° = π/180 rad|
|arcminute||′||1′ = 1/60° = π/10800 rad|
|arcsecond||″||1″ = 1/60′ = π/648000 rad|
|area||hectare||ha||1 ha = 1 hm2 = 104 m2|
|volume||litre||l, L||1 l = 1 L = 1 dm3 = 103 cm3 = 10−3 m3|
|mass||tonne (metric ton)||t||1 t = 1 Mg = 103 kg|
|dalton||Da||1 Da = 1.660539040(20)×10−27 kg|
|energy||electronvolt||eV||1 eV = 1.602176634×10−19 J|
|neper||Np||In using these units it is important that the nature of the quantity be specified and that any reference value used be specified.|
These units are used in combination with SI units in common units such as the kilowatt-hour (1 kW⋅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 – 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.[bu]
- 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.[bv]
- The length of the equator is close to 40000000 m (more precisely 40075014.2 m). In fact, the dimensions of our planet were used by the French Academy in the original definition of the metre.
- The metre is close to the length of a pendulum that has a period of 2 seconds;[bw] most dining tabletops are about 0.75 metres high; a very tall human (basketball forward) is about 2 metres tall.
- 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 1-euro coin weighs 7.5 g; a Sacagawea US 1-dollar coin weighs 8.1 g; a UK 50-pence coin weighs 8.0 g.
- A candela is about the luminous intensity of a moderately bright candle, or 1 candle power; a 60 W tungsten-filament incandescent light bulb has a luminous intensity of about 64 candelas.[bx]
- 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 near-perfect gas relative to air can be obtained to a good approximation by dividing its molecular mass by 29 (because 4/5 × 28 + 1/5 × 32 = 28.8 ≈ 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 °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 230 V (European mains voltage) consumes 0.26 A at this voltage.[by]
According to the SI Brochure,
The English spelling and even names for certain SI units and metric prefixes depend on the variety of English used.
Unit symbols and the values of quantities
Symbols of SI units are intended to be unique and universal, independent of the context language.: 130–135 The SI Brochure has specific rules for writing them.: 130–135 The guideline produced by the National Institute of Standards and Technology (NIST) clarifies language-specific details for American English that were left unclear by the SI Brochure, but is otherwise identical to the SI Brochure.
General rules[ca] 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, 7.3×102 m2, 22 K. This rule explicitly includes the percent sign (%): 134 and the symbol for degrees Celsius (°C).: 133 Exceptions are the symbols for plane angular degrees, minutes, and seconds (°, ′, and ″, respectively), 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, μ in μg). 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(⋅) or a non-breaking space; e.g., N⋅m or N m.
- Symbols for derived units formed by division are joined with a exponent. E.g., the "metre per second" can be written m/s, m s−1, m⋅s−1, or m/s. In cases where a solidus is followed by a centre dot (or space), or more than one solidus is present, parentheses must be used to avoid ambiguity; e.g., kg/(m⋅s2), kg⋅m−1⋅s−2, and (kg/m)/s2 are acceptable, but kg/m/s2 and kg/m⋅s2 are ambiguous and unacceptable.
- The first letter of symbols for units derived from the name of a person is written in
- Symbols do not have a plural form, e.g., 25 kg, not 25 kgs.
- Uppercase and lowercase prefixes are not interchangeable. E.g., the quantities 1 mW and 1 MW represent two different quantities (milliwatt and megawatt).
- The symbol for the
- Spaces should be used as a thousands separator(1000000) 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 line-break 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 80000-1:2009.
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
Realisation of units
Metrologists carefully distinguish between the definition of a unit and its realisation. The definition of each base unit of the SI is drawn up so that it is unique and provides a sound theoretical basis on which the most accurate and reproducible measurements can be made. The realisation of the definition of a unit is the procedure by which the definition may be used to establish the value and associated uncertainty of a quantity of the same kind as the unit. A description of the mise en pratique[cc] of the base units is given in an electronic appendix to the SI Brochure.: 168–169
The published mise en pratique is not the only way in which a base unit can be determined: the SI Brochure states that "any method consistent with the laws of physics could be used to realise any SI unit.": 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. These methods include the following:
- At least three separate experiments be carried out yielding values having a relative
- The definition of the thermometry and dielectric constant gas thermometry be better than one part in 10−6 and that these values be corroborated by other measurements.
Evolution of the SI
Changes to the SI
The International Bureau of Weights and Measures (BIPM) has described SI as "the modern form of metric system".: 95 Changing technology has led to an evolution of the definitions and standards that has followed two principal strands – changes to SI itself, and clarification of how to use units of measure that are not part of SI but are still nevertheless used on a worldwide basis.
Since 1960 the CGPM has made a number of changes to the SI to meet the needs of specific fields, notably chemistry and radiometry. These are mostly additions to the list of named derived units, and include the : 165
The 1960 definition of the standard metre in terms of wavelengths of a specific emission of the krypton-86 atom was replaced in 1983 with the distance that light travels in vacuum in exactly 1/299792458 second, so that the speed of light is now an exactly specified constant of nature.
A few changes to notation conventions have also been made to alleviate lexicographic ambiguities. An analysis under the aegis of CSIRO, published in 2009 by the Royal Society, has pointed out the opportunities to finish the realisation of that goal, to the point of universal zero-ambiguity machine readability.
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. 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 – 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.