The International System of Units, abbreviated SI from its French language name, Le Système International d'Unités, is a comprehensive set of units of measurement. Aside from its dominance in science, the United States Omnibus Trade and Comptetitiveness Act of 1988 states "the metric system of measurement is the preferred system of weights and measures for United States trade and commerce".[1]
The SI is based on the original metric system developed in France in the 1790s. In October 1960 the 11th international "General Conference on Weights and Measures" met in Paris and renamed the Metric System (MKSA) of units (based on the six base units: meter, kilogram, second, ampere, kelvin and candela—in 1971 mole was added as seventh base unit) to the "International System of Units." The 11th Conference also established the abbreviation "SI" as the official abbreviation, to be used in all languages. Adoption of the abbreviation SI, especially outside scientific circles, is slow. The terms "metric system" or "MKSA units" are still frequently being used.
For more background and a bibliography for the SI units see the SI units page on the NIST website.[2]
The SI is founded on seven SI base units for seven base quantities assumed to be mutually independent:
SI base units | |||
---|---|---|---|
Name | Symbol | Quantity | Definition |
metre | m | length | The meter is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second. |
kilogram | kg | mass | The kilogram is equal to the mass of the international prototype of the kilogram. |
second | s | time | The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom. |
ampere | A | electrical current | The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 meter apart in vacuum, would produce between these conductors a force equal to 2 x 10-7 newton per meter of length. |
kelvin | K | temperature | The kelvin, unit of thermodynamic temperature, is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water. |
mole | mol | amount of substance | The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12 |
candela | cd | luminous intensity | The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 x 1012 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian. |
To allow for ease of discussion of quantities orders of magnitude different from the base units, prefixes may be used to form decimal multiples and submultiples of units. The SI prefixes with their meanings and symbols are:
SI Prefixes | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Name | quetta- | ronna- | yotta- | zetta- | exa- | peta- | tera- | giga- | mega- | kilo- | hecto- | deca- |
Symbol | Q | R | Y | Z | E | P | T | G | M | k | h | da |
Factor | 1030 | 1027 | 1024 | 1021 | 1018 | 1015 | 1012 | 109 | 106 | 103 | 102 | 101 |
Name | deci- | centi- | milli- | micro- | nano- | pico- | femto- | atto- | zepto- | yocto- | ronto- | quecto- |
Symbol | d | c | m | µ | n | p | f | a | z | y | r | q |
Factor | 10-1 | 10-2 | 10-3 | 10-6 | 10-9 | 10-12 | 10-15 | 10-18 | 10-21 | 10-24 | 10-27 | 10-30 |
It is important to note that the kilogram is the only SI unit with a prefix as part of its name and symbol. Because multiple prefixes may not be used, in the case of the kilogram the prefix names are used with the unit name "gram" and the prefix symbols are used with the unit symbol "g." With this exception, any SI prefix may be used with any SI unit, including the degree Celsius and its symbol °C. [3]
Other quantities, called derived quantities, are defined in terms of the seven base quantities via a system of quantity equations. The SI derived units for these derived quantities are obtained from these equations and the seven SI base units.
There are two dimensionless derived units, for plane angle and solid angle:
Name | Symbol | Quantity | Definition |
---|---|---|---|
radian | rad | angle | The unit of angle is the angle subtended at the centre of a circle by an arc of the circumference equal in length to the radius of the circle. There are radians in a circle. |
steradian | sr | solid angle | The unit of solid angle is the solid angle subtended at the centre of a sphere of radius r by a portion of the surface of the sphere having an area r2. There are steradians on a sphere. |
Twenty other derived units have specific names; most are named after pioneering researchers in the fields in which they are used. These are:
Name | Symbol | Quantity | Expression in terms of other units | Expression in terms of SI base units |
---|---|---|---|---|
hertz | Hz | Frequency | 1/s | s−1 |
newton | N | Force, Weight | m∙kg/s2 | m∙kg∙s−2 |
joule | J | Energy, Work, Heat | N∙m | m2∙kg∙s−2 |
watt | W | Power, Radiant flux | J/s | m2∙kg∙s−3 |
pascal | Pa | Pressure, Stress | N/m2 | m−1∙kg∙s−2 |
lumen | lm | Luminous flux | cd∙sr | cd |
lux | lx | Illuminance | lm/m2 | m−2∙cd |
coulomb | C | Electric charge or flux | s∙A | s∙A |
volt | V | Electrical potential difference, Electromotive force | W/A = J/C | m2∙kg∙s−3∙A−1 |
ohm | Ω | Electric resistance, Impedance, Reactance | V/A | m2∙kg∙s−3∙A−2 |
farad | F | Electric capacitance | C/V | m−2∙kg−1∙s4∙A2 |
weber | Wb | Magnetic flux | J/A | m2∙kg∙s−2∙A−1 |
tesla | T | Magnetic flux density, magnetic induction | V∙s/m2 = Wb/m2 | kg∙s−2∙A−1 |
henry | H | Inductance | V∙s/A = Wb/A | m2∙kg∙s−2∙A−2 |
siemens | S | Electric conductance | 1/Ω | m−2∙kg−1∙s3∙A2 |
becquerel | Bq | Radioactivity (decays per unit time) | 1/s | s−1 |
gray | Gy | Absorbed dose (of ionizing radiation) | J/kg | m2∙s−2 |
sievert | Sv | Equivalent dose (of ionizing radiation) | J/kg | m2∙s−2 |
katal | kat | Catalytic activity | mol/s | s−1∙mol |
degree Celsius | °C | Thermodynamic temperature | T°C = TK − 273.15 |
Some derived units are named after the basic units from which they are derived, sometimes including the dimension. Other derived units have names which are a mix of base unit names and derived unit names. Some are listed below:
Compound units derived from basic SI units | ||||
---|---|---|---|---|
Name | Symbol | Quantity | Expression in terms of SI base units | |
square metre | m2 | area | m2 | |
cubic metre | m3 | volume | m3 | |
metre per second | m·s−1 | speed, velocity | m·s−1 | |
metre per second squared | m·s−2 | acceleration | m·s−2 | |
metre per second cubed | m·s−3 | jerk | m·s−3 | |
radian per second | rad·s−1 | angular velocity | s−1 | |
reciprocal metre | m−1 | wavenumber | m−1 | |
kilogram metre per second | kg·m·s−1 | momentum | kg·m·s−1 | |
kilogram per cubic metre | kg·m−3 | Density, mass density | kg·m−3 | |
cubic metre per kilogram | kg−1·m3 | specific volume | kg−1·m3 | |
mole per cubic metre | m−3·mol | amount (-of-substance) concentration | m−3·mol | |
cubic metre per mole | m3·mol−1 | molar volume | m3·mol−1 | |
square metre per second | m2·s−1 | kinematic viscosity, diffusion coefficient | m2·s−1 | |
ampere per square metre | A·m−2 | electric current density | A·m−2 | |
ampere per metre | A·m−1 | magnetic field strength | A·m−1 | |
candela per square metre | cd·m−2 | luminance | cd·m−2 |
Compound units derived from SI units | ||||
---|---|---|---|---|
Name | Symbol | Quantity | Expression in terms of SI base units | |
newton second | N·s | momentum, impulse | kg·m·s−1 | |
newton metre second | N·m·s | angular momentum | kg·m2·s−1 | |
newton metre | N·m | torque, moment of force | kg·m2·s−2 | |
joule per kelvin | J·K−1 | heat capacity, entropy | kg·m2·s−2·K−1 | |
joule per kelvin mole | J·K−1·mol−1 | molar heat capacity, molar entropy | kg·m2·s−2·K−1·mol−1 | |
joule per kilogram kelvin | J·K−1·kg−1 | specific heat capacity, specific entropy | m2·s−2·K−1 | |
joule per mole | J·mol−1 | molar energy | kg·m2·s−2·mol−1 | |
joule per kilogram | J·kg−1 | specific energy | m2·s−2 | |
joule per cubic metre | J·m−3 | energy density | kg·m−1·s−2 | |
newton per metre | N·m−1 = J·m−2 | surface tension | kg·s−2 | |
watt per square metre | W·m−2 | heat flux density, irradiance | kg·s−3 | |
watt per metre kelvin | W·m−1·K−1 | thermal conductivity | kg·m·s−3·K−1 | |
pascal second | Pa·s = N·s·m−2 | dynamic viscosity | kg·m−1·s−1 | |
coulomb per cubic metre | C·m−3 | electric charge density | m−3·s·A | |
siemens per metre | S·m−1 | conductivity | kg−1·m−3·s3·A2 | |
siemens square metre per mole | S·m2·mol−1 | molar conductivity | kg-1·s3·mol−1·A2 | |
farad per metre | F·m−1 | permittivity | kg−1·m−3·s4·A2 | |
henry per metre | H·m−1 | permeability | kg·m·s−2·A−2 | |
volt per metre | V·m−1 | electric field strength | kg·m·s−3·A−1 | |
coulomb per kilogram | C·kg−1 | exposure (X and gamma rays) | kg−1·s·A | |
gray per second | Gy·s−1 | absorbed dose rate | m2·s−3 |
The 2006 edition of the International System of Units, published by the International Bureau of Weights and Measures (BIPM) includes non-SI units that are accepted for use with the International System because they are widely used in everyday life.[4] Their use is expected to continue indefinitely, and each has an exact definition in terms of an SI unit. The values in the table below were extracted from Tables 6 and 8 of the 2006 Edition:
Quantity | Name | Symbol | Value in Si units |
---|---|---|---|
time | minute | min | 1 min = 60 s |
hour | h | 1 h = 60 min = 3600 s | |
day | d | 1 d = 24 h = 86400 s | |
area | hectare | ha | 1 ha = 1 hm2 = 104m2 |
volume | litre | L or l | 1 L = 1 dm3 = 103 cm3 = 10−3 m3 |
mass | tonne | t | 1 t = 103 kg |
plane angle | degree | ° | 1 ° = (/180) rad |
minute | ' | 1 ' = (1/60)° = (/10800) rad | |
second | " | 1 " = (1/60)' = (/648000) rad | |
pressure | bar | bar | 1 bar = 0.1 MPa = 100 kPa = 105 Pa |
millimetre of mercury | mmHg | 1 mmHg ≈ 133.322 Pa | |
speed | knot | kn | 1 kn = (1852/3600) m/s |
The numerical values of the principal physical constants can be found in a NIST summary.[7] NIST maintains a web site with the current numerical values of the physical constants in SI units.[8]