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International System of Units

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The International System of Units is a decimal system of weights and measures which is based on and extends the metric system. It is abbreviated as SI in all languages.

SI includes seven basic units (see table 1). The metre, defined to be 1,650,763.73 wavelengths in vacuum of the red-orange line of the krypton-86 spectrum, is the SI unit for length. The kilogram, which is approximately 2.2 pounds avoirdupois and equals 1,000 grams (as defined by the platinum-iridium prototype kilogram held by the International Bureau of Weights and Measures in Sèvres, France), is the SI unit for mass. It is the sole base unit that remains defined by an artefact. It is also the only SI unit with a prefix as part of its name and symbol. The second, or the duration of 9,192,631,770 cycles of the radiation corresponding to a specified transition of the caesium-133 atom, is the SI unit for time. The ampere is the SI unit for electric current. It is the constant current produced by one volt which, when maintained in two parallel conductors separated by one metre in vacuum, generates an electromagnetic force of 2 x 10-7 N m-1. The kelvin, which is equal to 1/273.16 of the thermodynamic temperature at the triple point of water, is the SI unit for thermodynamic temperature. The kelvin’s magnitude equals that of the degree Celsius; however, a temperature expressed in degrees Celsius is the numerical equivalent of the temperature in kelvins less 273.15. The mole is the SI unit for amount of substance; it contains as many elementary units of substance as there are atoms in 0.012 kg of carbon-12. Elementary units must be specified, as they may be atoms, electrons, ions, molecules, radicals, etc. The candela is the SI unit for luminous intensity. It equals the luminous intensity of the black-body radiation, in the perpendicular direction, from an area of 1/600,000 square metres at platinum’s freezing temperature (2,042 kelvins) under 101,325 pascals of pressure, which approximates the intensity of a single paraffin candle.

Table 1. SI base units

 Quantity SI unit name Symbol Length Metre m Mass1 Kilogram kg Time Second s Electric current Ampere A Thermodynamic temperature Kelvin2 K Amount of substance Mole mol Luminous intensity Candela cd

1 "Weight” is often used to mean “mass”.
2 The name “degree kelvin” and the symbol “degK” were declared obsolete
at a 1967 international conference.

SI also includes two supplementary units (see table 2). Radian and steradian are the dimensionless units for the dimensionless quantities plane angle and solid angle, respectively. Units for other quantities are derived from the seven basic and two supplementary units.

Table 2. SI supplementary units

 Quantity SI unit name Symbol Expression in terms of SI base units Plane angle Radian rad m·m– 1 =1 Solid angle Steradian sr m2 ·m– 2 =1

Table 3 lists selected SI derived units expressed in terms of base units. Derived units with special names and symbols are listed in table 4. These may be used to express other derived units (see table 5). The two supplementary units may also be used to express derived units (see table 6).

The 16 prefixes used to create multiples and submultiples of SI units are listed in table 7. Since multiple prefixes cannot be used, these prefixes are used with gram (g), but not with kilogram (kg).

A number of units that are not part of SI are widely used, especially in the United States. Those which are considered acceptable for use with SI in the US are listed in table 8. A conversion table for SI units is provided in table 9.

Table 3. Selected SI derived units expressed in terms of base units

 Quantity SI unit name Symbol Area Square metre m2 Volume Cubic metre m3 Speed, velocity Metre per second m/s Acceleration Metre per second squared m/s2 Wave number Reciprocal metre m– 1 Density, mass density Kilogram per cubic metre kg/m3 Specific volume Cubic metre per kilogram m3/kg Current density Ampere per square metre A/m2 Magnetic field strength Ampere per metre A/m Concentration (of amount of substance) mole per cubic metre mol/m3 Luminance Candela per square metre cd/m2

Table 4. SI derived units with special names

 Quantity SI unit name Symbol Expression in terms of other units Frequency Hertz Hz s– 1 Force Newton N m·kg/s2 Pressure, stress Pascal Pa N/m2 Energy, work, quantity of heat Joule J N·m Power, radiant flux Watt W J/s Electric charge, quantity of electricity Coulumb C s·A Electric potential, potential difference, electromotive force Volt V W/A Capacitance Farad F C/V Electric resistance Ohm Omega V/A Electric conductance Siemens S A/V Magnetic flux Weber Wb V·s Magnetic flux density Tesla T Wb/m2 Inductance Henry H Wb/A Celsius temperature1 Degree Celsius C K Luminous flux Lumen lm cd·sr Activity (of a radionuclide) Becquerel Bq s– 1 Absorbed dose, specific energy imparted, kerma, absorbed dose index Gray Gy J/kg Dose equivalent, dose equivalent index Sievert Sv J/kg

1 In addition to the thermodynamic temperature (T) expressed in kelvins (see table 105.1), Celsius
temperature (t) is also used and is defined by the equation t = T – T0 where T0 = 273.15 K by
definition. The unit “degree Celsius”, which is equal to the unit “kelvin”, is used to express Celsius
temperature.  Here, the term “degree Celsius” is a special name substituted for “kelvin”.
However, a difference or interval of Celsius temperature can be expressed in either kelvins
or degrees Celsius.

Table 5. Examples of SI derived units expressed with special names

 Quantity SI unit name Symbol Dynamic viscosity Pascal second Pa·s Moment of force Newton metre N·m Surface tension Newton per metre N/m Heat flux density, irradiance Watt per square metre W/m2 Heat capacity, entropy Joule per kelvin J/K Specific heat capacity, specific entropy Joule per kilogram kelvin J/(kg·K) Specific energy Joule per kilogram J/kg Thermal conductivity Watt per metre kelvin W/(m·K) Energy density Joule per cubic metre J/m3 Electric field strength Volt per metre V/m Electric charge density Coulomb per cubic metre C/m3 Electric flux density Coulomb per square metre C/m2 Permittivity Farad per metre F/m Permeability Henry per metre H/m Molar energy Joule per metre J/mol Molar entropy, molar heat capacity Joule per mole kelvin J/(mol·K) Exposure (x and gamma rays) Coulomb per kilogram C/kg Absorbed dose rate Gray per second Gy/s

Table 6. Examples of SI derived units formed with supplementary units

 Quantity SI unit name Symbol Angular velocity Radian per second rad/s Angular acceleration Radian per second squared rad/s2 Radiant intensity Watt per steradian W/sr Radiance Watt per square metre steradian W/(m2·sr)

Table 7. SI prefixes

 Factor Prefix Symbol 1018 exa E 1015 peta P 1012 tera T 109 giga G 106 mega M 103 kilo k 102 hecto h 101 deka da 10- 1 deci d 10- 2 centi c 10- 3 milli m 10- 6 micro μ 10- 9 nano n 10- 12 pico p 10- 15 femto f 10- 18 atto a

Table 8. Units in use with SI

 Name Symbol Value in SI unit Minute (time) min 1 min = 60 s Hour h 1 h = 60 min = 3,600 s Day d 1 d = 24 h = 86,400 s Degree (angle)  1 = (pi/180) rad Minute (angle)  1  = (1/60) = (pi/10,800) rad Second (angle)  1  = (1/60) = (pi/648,000) rad Litre l1 1 l = 1 dm3 = 10– 3 m3 Tonne2 t 1 t = 103 kg Hectare (land area) ha 1 ha = 1 hm2 = 104 m2 Electronvolt3 eV 1 eV = 1.602 18 x 10– 19 J Unified atomic mass unit3 u 1 u = 1.660 54 x 10– 27 kg

1 Both “l” and “L” are accepted as symbols for litre.
2 In some countries, such as the United States, “metric ton” is used instead of “tonne”.
3 The values of these units in SI units are not known exactly; the values must be obtained
through experiment. The electronvolt is the kinetic energy acquired by an electron passing
through a potential difference of 1 volt in a vacuum.  The unified atomic mass unit equals 1/12 of
the mass of the atom of the nuclide 12C.

Table 9. Conversion of non-SI units to SI units

 From/to To/from Multiply by/divide by Inch (in) m 2.54 x 10– 2 Feet (ft) m 0.3048 Square inch (in2 ) m2 6.4516 x 10– 4 Square foot (ft2 ) m2 9.2903 x 10– 2 Cubic inch (in3 ) m3 1.638 71 x 10– 5 Cubic foot (ft3 ) m3 2.831 68 x 10– 2 Litre (l) m3 10– 3 Gallon (gal) m3 4.546 09 x 10– 3 Mile/hour (mi hr– 1 ) m s– 1 0.477 04 Kilometre/hour (km hr– 1 ) m s– 1 0.277 78 Pound (lb) kg 0.453 592 Gram/cm3 (g cm– 3 ) kg m– 3 103 Pound/in3 kg m– 3 2.767 99 x 104 mmHG Pa 133.322 Atmosphere (atm) Pa 1.013 25 x 105 Horsepower (hp) W 745.7 erg J 10– 7 Electronvolt (eV) J 1.602 10 x 10– 19 Kilowatt-hour (kW hr) J 3.6 x 106 Calorie (cal) J 4.1868 Dyne N 10– 5 kgf N 9.806 65 Poundal N 0.138 255 lbf N 4.448 22

Acknowledgement: The information in the tables is based primarily on data from the US National Institute of Standards and Technology (NIST).

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