Metric system

Four metric measuring devices: a tape measure in centimetres, a thermometer in degrees Celsius, a kilogram weight and a multimeter that measures volts, amperes and ohms

The metric system is an internationally recognised decimalised system of measurement. It is in widespread use, and where it is adopted, it is the only or most common system of weights and measures (see metrication). It is now known as the International System of Units (SI). It is used to measure everyday things such as the mass of a sack of flour, the height of a person, the speed of a car, and the volume of fuel in its tank. It is also used in science, industry and trade.

In its modern form, it consists of a set of base units including metre for length, kilogram for mass, second for time and ampere for electrical current, and a few others, which together with their derived units, can measure any physical quantity. Metric system may also refer to other systems of related base and derived units defined before the middle of the 20th century, some of which are still in limited use today.

The metric system was designed to have properties that make it easy to use and widely applicable, including units based on the natural world, decimal ratios, prefixes for multiples and sub-multiples, and a structure of base and derived units. It is also a coherent system, which means that its units do not introduce conversion factors not already present in equations relating quantities. It has a property called rationalisation that eliminates certain constants of proportionality in equations of physics.

The units of the metric system, originally taken from observable features of nature, are now defined by phenomena such as the microwave frequency of a caesium atomic clock which accurately measures seconds. One unit, the kilogram, was defined in terms of a man-made artefact until recently, but its precise definition now depends on a fixed numerical value for Planck's constant. The new definition was formally propagated on 20 May 2019.

While there are numerous named derived units of the metric system, such as the watt and lumen, other common quantities such as velocity and acceleration do not have their own unit, but are defined in terms of existing base and derived units such as metres per second for velocity.

Units of the British imperial system and the related US customary system are officially defined in terms of the metric system. Notably, as per the International Yard and Pound Agreement the base units of the Imperial and Customary system are defined in terms of the metre and kilogram.

The metric system is also extensible, and new derived units are defined as needed in fields such as radiology and chemistry. The most recent derived unit, the katal, for catalytic activity, was added in 1999. Recent changes are directed toward defining base units in terms of invariant constants of physics to provide more precise realisations of units for advances in science and industry.


Base units

The modern metric system consists of four electromechanical base units representing seven fundamental dimensions of measure: length, mass, time, electromagnetism, thermodynamic temperature, luminous intensity, and quantity of substance. The units are:

Together they are sufficient for measuring any known quantity,[1] without reference to further quantities or phenomena.

The metre, ampere, candela, and mole are all defined in terms of other base units. For example, the speed of light is defined as 299,792,458 metres per second, and the metre is derived from that constant and the definition of a second. As a result, in dimensional analysis, they remain wholly separate concepts.

Derived units with special names

There are currently 22 derived units with special names in the metric system, these are defined in terms of the base units or other named derived units.

Eight of these units are electromagnetic quantities:

  • volt, a unit of electrical potential
  • ohm, a unit of electrical resistance
  • tesla, a unit of magnetic flux density
  • weber, a unit of magnetic flux
  • farad, a unit of electrical capacitance
  • henry, a unit of electrical inductance
  • siemens, a unit of electrical conductance (the inverse of ohm)
  • coulomb, a unit of electrical charge

Four of these units are mechanical quantities:

  • watt, a unit of mechanical or electrical power
  • newton, a unit of mechanical force
  • joule, a unit of mechanical, electrical or thermodynamic energy
  • pascal, a unit of pressure

Five units represent measures of electromagnetic radiation and radioactivity:

  • becquerel, a unit of radioactive decay
  • sievert, a unit of absorbed ionising radiation
  • gray, a unit of ionising radiation
  • lux, a unit of luminous flux
  • lumen, a unit of luminous intensity

Two units are measures of circular arcs and spherical surfaces:

Three units are miscellaneous:

  • degree Celsius, a unit of thermodynamic temperature
  • katal, a unit of catalytic activity (enzymatic)
  • hertz, a unit of cycles per second (inverse of second)

Auxiliary and accessory units

Although SI, as published by the CGPM, should, in theory, meet all the requirements of commerce, science, and technology, certain customary units of measure have acquired established positions within the world community. In order that such units are used consistently around the world, the CGPM catalogued such units in Tables 6 to 9 of the SI brochure. These categories are:[2]

  • Non-SI units accepted for use with the International System of Units (Table 6). This list includes the hour and minute, the angular measures (Degree, Minute and second of arc), and the historic [non-coherent] metric units, the litre, tonne, and hectare (originally agreed by the CGPM in 1879)
  • Non-SI units whose values in SI units must be obtained experimentally (Table 7). This list includes various units of measure used in atomic and nuclear physics and in astronomy such as the dalton, the electron mass, the electron volt, the astronomical unit, the solar mass, and a number of other units of measure that are well-established, but dependent on experimentally-determined physical quantities.
  • Other non-SI units (Table 8). This list catalogues a number of units of measure that have been used internationally in certain well-defined spheres including the bar for pressure, the ångström for atomic physics, the nautical mile and the knot in navigation.
  • Non-SI units associated with the CGS and the CGS-Gaussian system of units (Table 9). This table catalogues a number of units of measure based on the CGS system and dating from the nineteenth century. They appear frequently in the literature, but their continued use is discouraged by the CGPM.

The SI symbols for the metric units are intended to be identical, regardless of the language used[3] but unit names are ordinary nouns and use the character set and follow the grammatical rules of the language concerned. For example, the SI unit symbol for kilometre is "km" everywhere in the world, even though the local language word for the unit name may vary. Language variants for the kilometre unit name include: chilometro (Italian), Kilometer (German),[Note 1] kilometer (Dutch), kilomètre (French), χιλιόμετρο (Greek), quilómetro/quilômetro (Portuguese), kilómetro (Spanish) and километр (Russian).[4][5]

Variations are also found with the spelling of unit names in countries using the same language, including differences in American English and British spelling. For example, meter and liter are used in the United States whereas metre and litre are used in other English-speaking countries. In addition, the official US spelling for the rarely used SI prefix for ten is deka. In American English the term metric ton is the normal usage whereas in other varieties of English tonne is common. Gram is also sometimes spelled gramme in English-speaking countries other than the United States, though this older usage is declining.[6]

In SI, the unit of power is the "watt", which is defined as "one joule per second".[7] In the US customary system of measurement the unit of power is the "horsepower", which is defined as "550-foot-pounds per second" (the pound in this context being the pound-force).[8] Similarly, neither the US gallon nor the imperial gallon is one cubic foot or one cubic yard— the US gallon is 231 cubic inches and the imperial gallon is 277.42 cubic inches.[9]

The concept of coherence was only introduced into the metric system in the third quarter of the 19th century;[10] in its original form the metric system was non-coherent—in particular the litre was 0.001 m3 and the are (from which the hectare derives) was 100 m2. However the units of mass and length were related to each other through the physical properties of water, the gram having been designed as being the mass of one cubic centimetre of water at its freezing point.[11]