• Metric System

    Metric System

    • Metric prefixes in everyday use
      Text Symbol Factor Power
      exa E 1000000000000000000 1018
      peta P 1000000000000000 1015
      tera T 1000000000000 1012
      giga G 1000000000 109
      mega M 1000000 106
      kilo k 1000 103
      hecto h 100 102
      deca da 10 101
      (none) (none) 1 100
      deci d 0.1 10−1
      centi c 0.01 10−2
      milli m 0.001 10−3
      micro μ 0.000001 10−6
      nano n 0.000000001 10−9
      pico p 0.000000000001 10−12
      femto f 0.000000000000001 10−15
      atto a 0.000000000000000001 10−18
      Variants of the metric system
      Quantity CGS MKS MTS
      distance, displacement,
      length, height, etc.
      (d, x, l, h, etc.)
      centimetre (cm) metre (m) metre
      mass (m) gram (g) kilogram (kg) tonne (t)
      time (t) second (s) second second
      speed, velocity (v, v) cm/s m/s m/s
      acceleration (a) gal (Gal) m/s2 m/s2
      force (F) dyne (dyn) newton (N) sthene (sn)
      pressure (P or p) barye (Ba) pascal (Pa) pièze (pz)
      energy (E, Q, W) erg (erg) joule (J) kilojoule (kJ)
      power (P) erg/s watt (W) kilowatt (kW)
      viscosity (µ) poise (p) Pa·s pz·s

      The metric system is an internationally agreed decimal system of measurement. It was originally based on the mètre des Archives and the kilogramme des Archives introduced by the French First Republic in 1799, but over the years the definitions of the metre and the kilogram have been refined, and the metric system has been extended to incorporate many more units. Although a number of variants of the metric system emerged in the late nineteenth and early twentieth centuries, the term is now often used as a synonym for "SI" or the "International System of Units"—the official system of measurement in almost every country in the world.

      The metric system has been officially sanctioned for use in the United States since 1866, but the US remains the only industrialised country that has not adopted the metric system as its official system of measurement: although In 1988, Congress passed the Omnibus Trade and Competitiveness Act, which designates "the metric system of measurement as the preferred system of weights and measures for United States trade and commerce". Among many other things, the act requires federal agencies to use metric measurements in nearly all of their activities, although there are still exceptions allowing traditional units to be used in documents intended for consumers. Many sources also cite Liberia and Myanmar as the only other countries not to have done so. Although the United Kingdom uses the metric system for most administrative and trade purposes, imperial units are widely used by the public and are permitted or obligatory for some purposes, such as road signs.

      Although the originators intended to devise a system that was equally accessible to all, it proved necessary to use prototype units in the custody of national or local authorities as standards. Control of the prototype units of measure was maintained by the French government until 1875, when it was passed to an intergovernmental organisation, the General Conference on Weights and Measures (CGPM).

      Quantity CGS MKS MTS
      distance, displacement,
      length, height, etc.
      (d, x, l, h, etc.)
      centimetre (cm) metre (m) metre
      mass (m) gram (g) kilogram (kg) tonne (t)
      time (t) second (s) second second
      speed, velocity (v, v) cm/s m/s m/s
      acceleration (a) gal (Gal) m/s2 m/s2
      force (F) dyne (dyn) newton (N) sthene (sn)
      pressure (P or p) barye (Ba) pascal (Pa) pièze (pz)
      energy (E, Q, W) erg (erg) joule (J) kilojoule (kJ)
      power (P) erg/s watt (W) kilowatt (kW)
      viscosity (µ) poise (p) Pa·s pz·s
      Quantity Dimension SI unit and symbol Legacy unit and symbol Conversion
      Time T second (s) second (s) 1
      Length L metre (m) centimetre (cm)
      ångström (Å)
      Mass M kilogram (kg) gram (g) 0.001
      Electric current I ampere (A) international ampere
      abampere or biot
      Temperature Θ kelvin (K)
      degree Celsius (°C)
      centigrade (°C) [K] = [°C] + 273.15
      Luminous intensity J candela (cd) international candle 0.982
      Amount of substance N mole (mol) No legacy unit n/a
      Area L2 square metre (m2) are (are) 100
      Acceleration LT−2 (m·s−2) gal (gal) 10−2
      Frequency T−1 hertz (Hz) cycles per second 1
      Energy L2MT−2 joule (J) erg (erg) 10−7
      Power L2MT−3 watt (W) (erg/s)
      horsepower (HP)
      Pferdestärke (PS)
      Force LMT−2 newton (N) dyne (dyn)
      sthene (sn)
      kilopond (kp)
      Pressure L−1MT−2 pascal (Pa) barye (Ba)
      pieze (pz)
      atmosphere (at)
      Electric charge IT coulomb (C) abcoulomb
      statcoulomb or franklin
      Potential difference L2MT−3I−1 volt (V) international volt
      Capacitance L−2M−1T4I2 farad (F) abfarad
      Inductance L2MT−2I−2 henry (H) abhenry
      Electric resistance L2MT−3I−2 ohm (Ω) international ohm
      Electric conductance L−2M−1T3I2 siemens (S) international mho (℧)
      Magnetic flux L2MT−2I−1 weber (Wb) maxwell (Mx) 10−8
      Magnetic flux density MT−2I−1 tesla (T) gauss (G) 10−4
      Magnetic field strength IL−1 (A/m) oersted (Oe) 1034π = 79.57747
      Dynamic viscosity ML−1T−1 (Pa·s) poise (P) 0.1
      Kinematic viscosity L2T−1 (m2·s−1) stokes (St) 10−4
      Luminous flux J lumen (lm) stilb (sb) 104
      Illuminance JL−2 lux (lx) phot (ph) 104
      [Radioactive] activity T−1 becquerel (Bq) curie (Ci) 3.70×1010
      Absorbed [radiation] dose L2T−2 gray (Gy) roentgen (R)
      rad (rad)
      Radiation dose equivalent L2T−2 sievert roentgen equivalent man (rem) 0.01
      Catalytic activity NT−1 katal (kat) No legacy unit n/a
      Quantity Dimension Unit and symbol Equivalence
      Mass M tonne (t) 1000 kg
      Area L2 hectare (ha) 0.01 km2
      104 m2
      Volume L3 litre (L or l) 0.001 m3
      Time T minute (min)
      hour (h)
      day (d)
      60 s
      3600 s
      86400 s
      Pressure L−1MT−2 bar 100 kPa
      Plane angle none degree (°)
      minute (ʹ)
      second (″)
      (π180) rad
      (π10800) rad
      (π648000) rad

      1 mg = 0.001 g
      1 km = 1000 m
      1 mm2 (square millimetre) = (1 mm)2  = (0.001 m)2  = 0.000001 m2
      1 km2 (square kilometre = (1 km)2 = (1000 m)2 = 1000000 m2
      1 mm3 (cubic millimetre) = (1 mm)3 = (0.001 m)3 = 0.000000001 m3
      1 km3 (cubic kilometre) = (1 km)3 = (1000 m)3 = 1000000000 m3
      force = mass × acceleration
      energy  = force × distance
      power = energy  ÷ time
      length, height, etc.
      (d, x, l, h, etc.)
      • The mètre for length
      • The are (100 m2) for area [of land]
      • The stère (1 m3) for volume of stacked firewood
      • The litre (1 dm3) for volumes of liquid
      • The gramme for mass.
      • 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.
      • Flying an overloaded American International Airways aircraft from Miami, Florida to Maiquetia, Venezuela on 26 May 1994. The degree of overloading was consistent with ground crew reading the kilogram markings on the cargo as pounds.
      • In 1999 the Institute for Safe Medication Practices reported that confusion between grains and grams led to a patient receiving phenobarbital 0.5 grams instead of 0.5 grains (0.03 grams) after the practitioner misread the prescription.
      • The Canadian "Gimli Glider" accident in 1983, when a Boeing 767 jet ran out of fuel in mid-flight because of two mistakes made when calculating the fuel supply of Air Canada's first aircraft to use metric measurements: mechanics miscalculated the amount of fuel required by the aircraft as a result of their unfamiliarity with metric units.
      • The root cause of the loss in 1999 of NASA's US$125 million Mars Climate Orbiter was a mismatch of units – the spacecraft engineers calculated the thrust forces required for velocity changes using US customary units (lbf·s) whereas the team who built the thrusters were expecting a value in metric units (N·s) as per the agreed specification.
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    • Metric System