International System of Units
The International System of Units, internationally known by the abbreviation SI, is the modern form of the metric system and the world's most widely used system of measurement. It is the only system of measurement with official status in nearly every country in the world, employed in science, technology, industry, and everyday commerce. The SI system is coordinated by the International Bureau of Weights and Measures, which is abbreviated BIPM from.
File:SI Illustration Base Units and Constants Colour Full.svg|thumb|SI [|base units] and [|constants]
| 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, metre, kilogram, ampere, kelvin, mole, and candela. 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 24 prefixes which, when added to the name and symbol of a coherent unit produce 24 additional SI units for the same quantity; these non-coherent units are always decimal 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 potentially 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 systems and the lack of coordination between the various disciplines that used them. The General Conference on Weights and Measures, 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 combined with ideas from the development of the CGS system.
Definition
The International System of Units consists of a set of seven defining constants with seven corresponding base units, derived units, and a set of decimal-based multipliers that are used as prefixes.SI defining constants
| Symbol | Defining constant | Exact value |
| hyperfine transition frequency of 133Cs | ||
| speed of light | ||
| Planck constant | ||
| elementary charge | ||
| Boltzmann constant | ||
| Avogadro constant | ||
| luminous efficacy of radiation |
The seven defining constants are the most fundamental feature of the definition of the system of units.
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, the hyperfine transition frequency of caesium, the Planck constant, the elementary charge, the Boltzmann constant, the Avogadro constant, and the luminous efficacy. The nature of the defining constants ranges from fundamental constants of nature such as to the purely technical constant. The values assigned to these constants were fixed to ensure continuity with previous definitions of the base units.
SI base units
The SI selects seven units to serve as base units, corresponding to seven base physical quantities. They are the second for time, metre for length, kilogram for mass, ampere for electric current, kelvin for thermodynamic temperature, mole for amount of substance, and candela for luminous intensity.The base units are defined in terms of the defining constants. For example, the kilogram is defined by taking the Planck constant to be, giving the expression in terms of the defining constants
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.
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. For example, the coherent derived SI unit of velocity is the metre per second, with the symbol. The base and coherent derived units of the SI together form a coherent system of 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.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.
The derived units in the SI are formed by powers, products, or quotients of the base units and are unlimited in number.
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. 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.
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, the SI unit of pressure is the pascal – and the pascal can be defined as one newton per square metre.
Prefixes
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 rather than in metres. Here the metric prefix 'kilo-' stands for a factor of 1000; thus, =.The SI provides twenty-four metric prefixes that signify decimal powers ranging from 10−30 to 1030, the most recent being adopted in 2022. 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 are called decimal systems of measurement units.
The grouping formed by a prefix symbol attached to a unit symbol 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. For example, is an SI unit of density, where is to be interpreted as.
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.
The BIPM specifies 24 prefixes for the International System of Units :
Coherent and non-coherent SI units
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, is the coherent derived unit for velocity. With the exception of the kilogram, 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. For example, the metre, kilometre, centimetre, nanometre, etc. are all SI units of length, though only the metre is a 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.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, is written milligram and, not microkilogram and.
The same coherent SI unit may be used for different physical quantities. For example, the joule per kelvin is the coherent SI unit for two distinct quantities, heat capacity and entropy, and the ampere is the coherent SI unit for both electric current and magnetomotive force.
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.
| Name | Symbol | Derived quantity | Typical symbol |
| square metre | area | ||
| cubic metre | volume | ||
| metre per second | speed, velocity | ||
| metre per second squared | acceleration | ||
| reciprocal metre | wavenumber | , | |
| reciprocal metre | vergence | , 1/ | |
| kilogram per cubic metre | density | ||
| kilogram per square metre | surface density | ||
| cubic metre per kilogram | specific volume | ||
| ampere per square metre | current density | ||
| ampere per metre | magnetic field strength | ||
| mole per cubic metre | concentration | ||
| kilogram per cubic metre | mass concentration | , | |
| candela per square metre | luminance |
| 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/ | 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/ | 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/ | molar entropy, molar heat capacity | m2⋅kg⋅s−2⋅K−1⋅mol−1 |
| coulomb per kilogram | C/kg | exposure | 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/ | radiance | kg⋅s−3 |
| katal per cubic metre | kat/m3 | catalytic activity concentration | m−3⋅s−1⋅mol |