Measurement Systems
SI Derived Units SI Prefixes
SI - Système International
The 11th CGPM (1960) adopted a first series of prefixes and symbols of prefixes to form the names and symbols of decimal multiples and sub-multiples of SI units. Over the years the list has been extended to the following: SI Prefixes
SI stands for Système International d’Unités, or the International System of Units. SI is the abbreviation used in all languages to indicate this system.
SI - Principles of the system
The SI is constructed from seven Base Units, which are defined in physical terms. By combining these units in accordance with simple geometrical and physical laws, we can arrive at the Derived Units. For practical reasons, 21 of the derived units have their own names.
In principle, the SI covers all application areas, although certain units outside SI are so useful that they are accepted for general use together with the SI. These units are referred to as additional units, of which the most common are: degree, minute and second for plane angle, litre for volume, minute, hour and day for time and tonne for mass.
Further information on the SI system can be obtained from the book Le Système International d’Unités, published by the Bureau International des Poids et Mesures, BIPM, Pavillon de Breteuil, F-92319 Sèvres, Cedex, France. Information on SI can also be obtained from standards in the ISO 31 series.
SI - Base Units
The International System (SI) of comprised of seven base units: physical units defined by an operational definition. All but one of these is independently reproducible through experiment. The kilogram is the only base unit still tied to a physical artifact.
All other physical units can be derived from these base units: these are known as the SI derived units. Derivation is by dimensional analysis. SI prefixes are used to abbreviate long positive and negative numbers.
The following are the base units from which all others are derived; they are dimensionally independent.
-
"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 caesium-133 atom"
(13th CGPM, 1967, Resolution 1) -
"The metre is the
length of the path travelled by light in vacuum during a time
interval of 1/299 792 458 of a second"
(17th CGPM, 1983, Resolution 1) -
"The kilogram is
the unit of mass: it is equal to the mass of the international
prototype of the kilogram"
(1st CGPM, 19989 & 3rd CGPM, 1901) -
"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."
(14th CGPM 1971) -
"The kelvin, unit
of thermodynamic temperature, is the fraction 1/273,16 of the
thermodynamic temperature of the triple point of water"
(13th CGPM, 1967, Resolution 4) -
"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"
(16th CGPM, 1979, Resolution 3) -
"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 metre apart in vacuum, would produce
between theses conductors a force equal to 2 x 10-7
newton per metre of length"
(9th CGPM 1948)
SI - Derived Units
The SI is constructed from seven Base Units, which are defined in physical terms. By combining these units in accordance with simple geometrical and physical laws, we can arrive at the Derived Units. For practical reasons, the derived units have their own names. There are 20 derived units as well as two special derived units which are dimensionless. These dimensionless units are ratios formed by dividing two SI units.
| Quantity | SI dimensionless unit | |||
| Name | Definition | |||
| plane angle | radian | rad | m·m-1 = 1 | |
| 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 2π radians in a circle. | ||||
| solid angle | steradian | sr | m2·m-2 = 1 | |
| 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 4π steradians on a sphere. (m2·m-2 = 1) | ||||
| Quantity | SI derived unit | |||
Name |
in terms of other units... | Expression in terms of SI base units | ||
| frequency | hertz | Hz | s-1 | |
| force | newton | N | m·kg·s-2 | |
| pressure, stress | pascal | Pa | N/m2 | m-1·kg·s-2 |
| energy, work, quantity of heat | joule | J | N·m | m2·kg·s-2 |
| power, radiant flux | watt | W | J/s | m2·kg·s-3 |
| electric charge, quantity of electricity | coulomb | C | s·A | |
| electric potential difference, electromotive force | volt | V | W/A | m2·kg·s-3·A-1 |
| capacitance | farad | F | C/V | m-2·kg-1·s4·A2 |
| electric resistance | ohm | W | V/A | m2·kg·s-3·A-2 |
| electric conductance | siemens | S | A/V | m-2·kg-1·s3·A2 |
| magnetic flux | weber | Wb | V·s | m2· kg·s-2·A-1 |
| magnetic flux density | tesla | T | Wb/m2 | kg·s-2·A-1 |
| inductance | henry | H | Wb/A | m2· kg·s-2·A-2 |
| Celsius temperature | degree Celsius | °C | °C = K-273.15 | K |
| luminous flux | lumen | lm | cd·sr | m2·m-2·cd = cd |
| illuminance | lux | lx | lm/m2 | m2·m-4·cd = m-2·cd |
| radioactivity (decay/time) | becquerel | Bq | s-1 | |
| absorbed dose (kerma), (ionizing radiation) | gray | Gy | J/kg | m2·s-2 |
| dose equivalent, (ionizing radiation) | sievert | Sv | J/kg | m2·s-2 |
| Catalytic Activity | katal | kat | mol/s | s-1·mol |
SI - Prefixes
A prefix combined with a unit indicates that the unit is multiplied by a particular power of ten. The new unit is referred to as a multiple unit. There are 20 standardised prefixes. The choice of prefix depends on purely practical considerations: in practice, it should be chosen such that the resulting numeral lies between 0.1 and 1000. Prefixes that indicate multiplication by 1000 or 1/1000 should preferably be chosen.
The 11th CGPM (1960) adopted a first series of prefixes and symbols of prefixes to form the names and symbols of decimal multiples and sub-multiples of SI units. Over the years the list has been extended to the following:
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