List of metric units

Metric units are units based on the metre, gram or second and decimal (power of ten) multiples or sub-multiples of these. According to Schadow and McDonald,[1] metric units, in general, are those units "defined 'in the spirit' of the metric system, that emerged in late 18th century France and was rapidly adopted by scientists and engineers. Metric units are in general based on reproducible natural phenomena and are usually not part of a system of comparable units with different magnitudes, especially not if the ratios of these units are not powers of 10. Instead, metric units use multiplier prefixes that magnifies or diminishes the value of the unit by powers of ten." The most widely used examples are the units of the International System of Units (SI). By extension they include units of electromagnetism from the CGS and SI units systems, and other units for which use of SI prefixes has become the norm. Other unit systems using metric units include:

SI units

Main article: International System of Units

The first group of metric units are those that are at present defined as units within the International System of Units (SI). In its most restrictive interpretation, this is what may be meant when the term metric unit is used.

The unit one (1) is the unit of a quantity of dimension one. It is the neutral element of any system of units.[2]

In addition to the unit one, the SI defines 7 base units and associated symbols:

The SI also defines 22 derived units and associated symbols:

  • The hertz (Hz) is equal to one reciprocal second (1 s−1).
  • The radian (rad) is equal to one (1).
  • The steradian (sr) is equal to one (1).
  • The newton (N) is equal to one kilogram-metre per second squared (1 kg⋅m⋅s−2).
  • The pascal (Pa) is equal to one newton per square metre (1 N⋅m−2).
  • The joule (J) is equal to one newton-metre (1 N⋅m).
  • The watt (W) is equal to one joule per second (1 J⋅s−1).
  • The coulomb (C) is equal to one ampere second (1 A⋅s).
  • The volt (V) is equal to one joule per coulomb (1 J⋅C−1).
  • The weber (Wb) is equal to one volt-second (1 V⋅s).
  • The tesla (T) is equal to one weber per square metre (1 Wb⋅m−2).
  • The farad (F) is equal to one coulomb per volt (1 C⋅V−1).
  • The ohm (Ω) is equal to one volt per ampere (1 V⋅A−1).
  • The siemens (S) is equal to one ampere per volt (1 A⋅V−1).
  • The henry (H) is equal to one weber per ampere (1 Wb⋅A−1).
  • The degree Celsius (°C) is equal to one kelvin (1 K).
  • The lumen (lm) is equal to one candela-steradian (1 cd⋅sr).
  • The lux (lx) is equal to one lumen per square metre (1 lm⋅m−2).
  • The becquerel (Bq) is equal to one reciprocal second (1 s−1).
  • The gray (Gy) is equal to one joule per kilogram (1 J⋅kg−1).
  • The sievert (Sv) is equal to one joule per kilogram (1 J⋅kg−1).
  • The katal (kat) is equal to one mole per second (1 mol⋅s−1).

Furthermore, there are twenty-four metric prefixes that can be combined with any of these units except one (1) and kilogram (kg) to form further units of the SI. For mass, the same prefixes are applied to the gram (g) instead of the kilogram.

Non-SI metric units

There are several metric systems, most of which have become disused or are still used in only niche disciplines. Systems are listed with named units that are associated with them.

CGS

Main article: centimetre–gram–second system of units

The centimetre–gram–second system of units (CGS) is based on three base units: centimetre, gram and second. Its subsystems (CGS-ESU, CGS-EMU and CGS-Gaussian) have different defining equations for their systems of quantities for defining electromagnetic quantities and hence the associated units, with CGS-Gaussian units being selected from each of the other two subsystems.

The CGS-to-SI correspondence of electromagnetic units as given was exact prior to the 2019 revision of the SI, until which the magnetic constant μ0 was defined as 4π×10−7 N⋅A−2. As from the redefinition, μ0 has an inexactly known value when expressed in SI units, with the exactness of the electromagnetic unit correspondence given here being affected accordingly.

CGS nonelectromagnetic units

CGS-ESU electromagnetic units

CGS-EMU electromagnetic units

CGS-Gaussian electromagnetic units

MTS

Main article: metre–tonne–second system of units

MKSA

Main article: MKS system of units

MKpS units

Main article: Gravitational metric system

Other metric units

Length

Area

  • The shed is a unit of area used in nuclear physics equal to 10−24 barns (100 rm2 = 10−52 m2).
  • The outhouse is a unit of area used in nuclear physics equal to 10−6 barns (100 am2 = 10−34 m2).
  • The barn (b) is a unit of area used in nuclear physics equal to one hundred femtometres squared (100 fm2 = 10−28 m2).
  • The are (a) is a unit of area equal to 100 m2.
  • The decare (daa) is a unit of area equal to 1000 m2.
  • The hectare (ha) is a unit of area equal to 10000 m2 (0.01 km2).

Volume

  • The lambda (λ) is a unit of volume equal to one cubic millimetre (1 mm3).
  • The litre (symbol l or L) is a unit of volume equal to one cubic decimetre (1 dm3).
  • The stere (st) is a unit of volume equal to 1 m3.

Reciprocal length

Time

Reciprocal time

Reciprocal time squared

Speed

  • The benz is a unit of speed equal to one metre per second (1 m/s).

Acceleration

  • The leo is a unit of acceleration equal to 10 m⋅s−2.[10]

Flow rate

  • The sverdrup (Sv) is a unit of volume flow rate equal to one million metres cubed per second (106 m3/s).[11]

Mass

  • The undecimogramme is a unit of mass equal to ten picograms (10 pg).
  • The gamma (γ) is a unit of mass equal to one microgram (1 μg).
  • The gravet is a unit of mass equal to one gram (1 g).
  • The grave is a unit of mass equal to one kilogram (1 kg).
  • The bar is a unit of mass equal to one megagram (1 Mg).

Linear mass density

Pressure

Energy

  • The foe is a unit of energy equal to 1051 erg (1044 J).

Viscosity

Electrical

Electromagnetic radiation

Radioactivity

Concentration

  • The molar (M) is equal to one mole per litre (1 mol/dm3).

Acoustics

  • The acoustic ohm is a unit of acoustic impedance equal to 1 Pa·s/m3.

See also

Notes

  1. ^ Note that the source has a sign error in the decimal exponent.

References

  1. ^ Gunther Schadow, Clement J. McDonald, The Unified Code for Units of Measure, Version 1.4b, June 6, 2002
  2. ^ The International System of Units (PDF) (9th ed.), International Bureau of Weights and Measures, Dec 2022, p. 136, ISBN 978-92-822-2272-0
  3. ^ a b c d e f Table 9, BIPM brochure, 8th Ed
  4. ^ a b c d e The International System of Units (PDF) (8th ed.). Archived from the original (PDF) on 2017-08-14. Retrieved 2020-02-13.
  5. ^ CL Morfey, Dictionary of Acoustics
  6. ^ a b c d e f g Gyllenbok, Jan (2018), Encyclopaedia of Historical Metrology, Weights, and Measures: Volume 1, Birkhäuser, ISBN 9783319575988
  7. ^ a b c System of Electric Units – Francis B. Sildbee (1962), p. 172
  8. ^ Donald Fenna (2002), A Dictionary of Weights, Measures, and Units, Oxford University Press
  9. ^ Nuclear Size and Shape
  10. ^ Donald Fenna (2002), A Dictionary of Weights, Measures, and Units, Oxford University Press
  11. ^ Aldersey-Williams, 2016
  12. ^ François Cardarelli (2004). Encyclopaedia of Scientific Units, Weights and Measures. Springer-Verlag London Ltd. ISBN 978-1852336820
  13. ^ François Cardarelli (2004). Encyclopaedia of Scientific Units, Weights and Measures. Springer-Verlag London Ltd. ISBN 978-1852336820
  14. ^ NIST Guide to the SI, Chapter 5: Units Outside the SI