Metric units

Metric units are units based on the metre, gram or second and decimal (power of ten) multiples or sub-multiples of these. 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:

Metric units that are part of the SI
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 SI defines 29 named units and associated symbols:

  • The second (s) is the unit of time.
  • The metre (m) is the unit of length.
  • The kilogram (kg) is the unit of mass.
  • The ampere (A) is the unit of electric current.
  • The kelvin (K) is the unit of thermodynamic temperature.
  • The mole (mol) is the unit of amount of substance.
  • The candela (cd) is the unit of luminous intensity.
  • 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/m2).
  • 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).
  • 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).
  • The weber (Wb) is one volt-second (1 V⋅s).
  • The tesla (T) is one weber per square metre (1 Wb/m2).
  • The farad (F) is equal to one coulomb per volt (1 C/V).
  • The ohm (Ω) is equal to one volt per ampere (1 V/A).
  • The siemens (S) is equal to one ampere per volt (1 A/V).
  • The henry (H) is one volt-second per ampere (1 V⋅s/A).
  • 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 on lumen per square metre (1 lm/m2).
  • 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).
  • The sievert (Sv) is equal to one joule per kilogram (1 J/kg).
  • The katal (kat) is equal to one mole per second (1 mol/s).

Further, there are twenty metric prefixes that can be combined with any of these units (with the gram (g) in the case of the kilogram) to form further units that are decimal multiples or submultiples of these to form further SI units.

Metric units that are not part of the SI

Metric units that are not part of the SI include

Spatial

Length
  • The fermi is equal to one femtometre (1 fm).[1]
  • The angstrom (symbol Å) is equal to one hundred picometres (100 pm).
  • The micron (μ) is equal to one micrometre (1 μm).
  • The metric inch is equal to twenty five millimetres (25 mm).
  • The basic module (M) is equal to one hundred millimetres (100 mm).
  • The metric foot is equal to three hundred millimetres (300 mm).
  • The myriametre (mym) is equal to ten kilometres (10 km).
  • The Scandinavian mile (mil) is equal to ten kilometres (10 km).
  • The hebdometre is equal to ten megametres (10 Mm).
  • The spat (S) is equal to one terametre (1 Tm).

Area
  • The shed is equal to 10−24 barns (10−52 m2).
  • The outhouse is equal to 10−6 barns (100 am2 = 10−34 m2).
  • The barn (b) is equal to one hundred femtometres squared (100 fm2 = 10−28 m2).
  • The are (a) is equal to one hundred metres squared (100 m2).
  • The decare (daa) is equal to one thousand metres squared (1000 m2).
  • The dunam is equal to one thousand metres squared (1000 m2).
  • The stremma is equal to one thousand metres squared (1000 m2).
  • The hectare (ha) is equal to ten thousand metres squared (10,000 m2).

Volume

Reciprocal length
  • The dioptre is equal to one inverse metre (1 m−1).
  • The kayser (K) is equal to one hundred inverse metres (100 m−1).

Temporal

Time

Frequency

Other
  • The eotvos (E) is equal to 10−9 Gal/cm (10−9 s−2).

Combined spatial and temporal

For the stokes, a unit of dimension L2 T−1, see § Viscosity.

Speed
  • The benz is equal to one metre per second (1 m/s).

Acceleration
  • The gal (Gal) is a CGS unit of acceleration equal to one centimetre per second squared (1 cm/s2).[2]
  • The leo is equal to 10 m⋅s−2.[3]

Volume flow rate
  • The normal litre per minute (NLPM) is approximately equal to (0.001/60) m3/s.
  • The standard litre per minute (SLPM) is approximately equal to (0.001/60) m3/s.
  • The sverdrup (Sv) is equal to one million metres cubed per second (106 m3/s) [4]

Mechanics

Mass
  • The undecimogramme is equal to ten picograms (10 pg).
  • The gamma (γ) is equal to one microgram (1 μg).
  • The carat (ct) is equal to 200 mg.
  • The grave is equal to one kilogram (1 kg).
  • The normal litre (NL) is a unit of mass used in gas flow equal to the product of 1 litre and the density of the gas in specified standard conditions. [5]
  • The hyl is equal to 9.80665 kg (or 9.80665 g).
  • The metric quintal (q) is equal to one hundred kilograms (100 kg).
  • The tonne (t) is an MTS unit equal to one megagram (1 Mg).

Linear mass density
  • The tex (tex) is equal to one gram per kilometre (1 g/km).[6]
  • The number metric (Nm) is equal to 1000 metres per kilogram (1000 m/kg).

Force

Pressure
  • The barye (Ba) is a CGS unit equal to one dyne per centimeter squared (1 dyn cm−2 = 100 mPa).
  • The centimetre of water (cmH2O) is approximately 98.0665 pascals (98.0665 Pa).
  • The millimetre of mercury (mmHg or mm Hg) is approximately 133.3224 pascals (133.3224 Pa).
  • The torr is approximately 133.3224 pascals.
  • The pièze (pz) is an MTS unit equal to one sthène per metre squared (1 sn m−2 = 1 kPa).
  • The centimetre of mercury (cmHg or cm Hg) is approximately 1333.224 pascals (1333.224 Pa).
  • The metre sea water (msw) is equal to ten kilopascals (10 kPa).
  • The bar (bar) is equal to one hundred kilopascals (100 kPa).
  • The technical atmosphere (at) is equal to 98066.5 pascals (1 at = 1 kgf⋅cm−2).

Energy
  • The electronvolt (eV) is equal to 1.602176634×10−19 J = 160.2176634 zJ.
  • The erg (erg) is a CGS unit equal to one dyne centimeter (1 dyn cm = 100 nJ).[9]
  • The calorie (cal) is 4.184 J.
  • The watt hour (W h) is equal to 3.6 kJ.
  • The foe is equal to 1044 joules.

Power
  • The watt hour per day (W⋅h/d) is equal to 3.6 kJ/(24 h) = 1/24 W.
  • The poncelet (p) is equal to 980.665 W.

Viscosity
  • The poise (P) is a unit of dynamic viscosity equal to one gram per (centimeter second) or one hundred grams per (metre second) (1 g⋅cm−1⋅s−1 = 100 g⋅m−1 s−1).[10]
  • The poiseuille is a unit of dynamic viscosity equal to one pascal-second (1 Pa⋅s).[11]
  • The stokes (St) is a unit of kinematic viscosity equal to one centimetre squared per second or one hundred millimetres squared per second (1 cm2/s = 1 P⋅g⋅cm−3 = 100 mm2/s).[12]

Electromagnetism

Electricity
Current
Charge
  • The statcoulomb (statC) is a unit of electric charge equal to 1 dyn1/2⋅cm, corresponding to approximately 3.33564×10−10 C.
  • The abcoulomb (abC) is a CGS unit of electric charge corresponding to ten coulombs (10 C).
  • The ampere-hour is a unit of electric charge equal to 3.6 kC.
Capacitance
Resistance
  • The abohm (abΩ) is a unit of electrical resistance corresponding to one nanoohm (1 nΩ).
  • The statohm is a unit of electrical resistance corresponding to approximately 898.7551787 GΩ.
Potential difference
  • The abvolt (abV) is a unit of potential difference corresponding to ten nanovolts (10 nV).
  • The statvolt (statV) is a unit of potential difference equal to 1 cm1/2⋅g1/2⋅s−1, corresponding to 299.792458 V.

Light
  • The nox (nx) is a unit of illuminance equal to 1 millilux (1 mlx).
  • The phot (ph) is a unit of illuminance equal to 10 kilolux (10 klx).[13]
  • The nit (nt) is a unit of luminance equal to one candela per metre squared (1 cd⋅m−2).
  • The stilb (sb) is a unit of luminance equal to ten kilocandelas per metre squared (10 kcd⋅m−2).[14]
  • The einstein (E) is a unit of amount of photons, equal to one mole (1 mol) of photons.

Radioactivity

Other

Information and computing

Dimensionless units
  • The percent (%) is equal to one part in a hundred (0.01).
  • The permille (‰) is equal to one part in a thousand (0.001).
  • The permyriad (‱) is equal to one part in ten thousand (0.0001).
  • The part per million (ppm) is equal to one part in a million (0.000001).
  • The part per billion (ppb) is equal to one part in a billion (0.000000001).
  • The part per trillion (ppt) is equal to one part in a trillion (0.000000000001).
  • The part per quadrillion (ppq) is equal to one part in a quadrillion (0.000000000000001).

See also

References
  1. Nuclear Size and Shape
  2. Table 9, BIPM brochure, 8th Ed
  3. Donald Fenna (2002), A Dictionary of Weights, Measures, and Units, Oxford University Press
  4. Aldersey-Williams, 2016
  6. François Cardarelli (2004). Encyclopaedia of Scientific Units, Weights and Measures. Springer-Verlag London Ltd. ISBN 978-1852336820
  7. Table 9, BIPM brochure, 8th Ed
  8. Donald Fenna (2002), A Dictionary of Weights, Measures, and Units, Oxford University Press
  9. Table 9, BIPM brochure, 8th Ed
  10. Table 9, BIPM brochure, 8th Ed
  11. François Cardarelli (2004). Encyclopaedia of Scientific Units, Weights and Measures. Springer-Verlag London Ltd. ISBN 978-1852336820
  12. Table 9, BIPM brochure, 8th Ed
  13. Table 9, BIPM brochure, 8th Ed
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