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Definition of units in the metric system (SI)
Here we give definitions and some explanation of metric units. They are divided into what are know as the base units, derived units and those which are approved for use with SI but not part of the core system.
Contents of this page
Metric prefixes
Here we explain the metric prefixes in two parts. First we concentrate on those in common use for everyday purposes and then give a comprehensive list for the whole range.
What is a metric prefix?
A metric prefix is a convenient way of expressing mulitiples and subdivisions (larger and smaller) of any defined unit. In metric that means multiplying or dividing by 10, 100, 1000 etc. It consists of a partial word like "kilo" , "centi" etc.
The prefix is placed before the name or symbol for the unit to indicate a multiple or subdivision. For example:
"kilo" means 1000, so kilometre means 1000 metres.
"centi" means one hundredth, so centimetre means one hundreth of a metre, or in other words 100 centimetre = 1 metre.
In symbols these two examples are written km (symbol for kilo = k, symbol for metre = m) and cm (symbol for centi = c) respectively.
These rules apply to all units and their symbols. So for example:
1 kW = 1000 W, 1 kg = 1000 g, 1 km = 1000 m, and so on.
| name | symbol | value of multiple or subdivision | example |
|---|---|---|---|
| nano | n | billionth (0.000 000 001) | 1000 000 000 nanometre = 1 metre (1000 000 000 nm = 1 m) Wavelength of green light = 550 nm |
| micro | µ | millionth (0.000 001) | 1000 000 microgram = 1 gram (1000 000 µg = 1 g) Often seen in drug doses |
| milli | m | thousandth (0.001) | 1000 millimetre = 1 metre (1000 mm = 1 m) Very handy for small or precision measurements. |
| centi | c | hundredth (0.01) | 100 centilitre = 1 litre (100 cL = 1 L) Common for wine and spririts |
| deci | d | tenth (0.1) | 1 dm = 0.1 m Not seen a great deal but can be useful (note 1 dm3 = 1 L) |
| deca | da | 10 | 1 decagram = 10 gram Seldom used but shown for completeness |
| hecto | h | 100 | 1 hectolitre = 100 litre (1 hL = 100 L) See hectare for another example below. |
| kilo | k | 1000 | See examples above. Very common. |
| mega | M | 1000 000 | 1 megawatt = 1000 000 watt = 1000 kilowatt (1 MW = 1000 000 W = 1000 kW) |
| giga | G | 1000 000 000 | 1 gigahertz = 1000 000 000 hertz (1 GHz = 1000 000 000 Hz) Seen in PC specs, e.g. 2.7 GHz processor. |
The remainder of the prefixes are shown here. They cover a very wide range and are not generally encountered outside science and engineering applications. Note that scientific notation is used for convenience.
| name | symbol | value | name | symbol | value |
|---|---|---|---|---|---|
| yotta | Y | 1024 | pico | p | 10-12 |
| zetta | Z | 1021 | femto | f | 10-15 |
| exa | E | 1018 | atto | a | 10-18 |
| peta | P | 1015 | zepto | z | 10-21 |
| tera | T | 1012 | yocto | y | 10-24 |
Base units
We include all of the 7 base units at the core of the SI. They are so called because each one introduces an independant physical quantity not contained in any other unit in the system. The formal definitions are given along with a laypersons guide as to what they measure (note that the formal definitions may be simplified for clarity).
| Unit name | symbol | What it measures and its definition |
|---|---|---|
| metre | m | Space. The metre is a unit of distance and is the basis for measuring length, area and volume. The metre was originally derived from one ten millionth of the distance from Earth's pole the equator but has been refined several times to tie it to more precisely measured physical constants. It is now defined in terms of the distance travelled at the speed of light during a very precisely defined fraction of a second. Definition: The length of the path travelled by light in a vacuum during a time interval 1/ 299 792 458 of a second. |
| kilogram | kg | Mass. In ordinary language the kilogram measures what most regard as weight. Stricly speaking mass is the amount of matter in an object, whereas weight is to do with the pull of gravity (how heavy it is). It was originally just 1000 grams where 1 gram was the mass of 1 cubic centimetre of water (making the kilogram equal to the mass of 1 litre of water). Nowadays it is defined in terms of a more stable reference in the form of a piece of platinum iridium known as the international prototype. Scientists have for many years been trying to find a better way of defining and measuring it in terms of natural constants in a manner similar to that of the metre and second. Definition: A unit of mass equal to the mass of the international prototype of the kilogram. |
| second | s | Time. It is the familiar unit of time that we count with our watches and clocks. It is now defined by the natural beats of a highly stable caesium atomic clock. Definition: The duration of 9 192 631 770 periods of the radiation corresponding to the transistions between the two hyperfine levels of the ground state of the caesium 133 atom. |
| ampere | A | Electric current. This is the familiar 'amp' we associate with things like fuses and electric cable. It is the fundamental base unit for electricity and magnetism. It is now defined in terms of the magnetic force (induced by the current) exerted between a pair of wires one metre apart. Definition: A constant current between (negligibly thin) parallel conductors 1 m apart, of infinite length, that would produce a force of 2 x 10-7 newtons per metre of length (see section on derived units for a description of the newton). |
| kelvin | K | Thermodynamic temperature. It measures temperature in the way we normally understand it, i.e. how hot something is. It is closely linked to the Celsius scale except that zero kelvin (0 K) is when there is literally no heat at all (absolute zero) and everything freezes (-273.15 °C). Definition: The fraction 1/273.16 of the thermodynamic temperature of the triple point of water (freezing point of water). |
| mole | mol | Amount of a substance. Used in chemistry and physics. It represents a fixed number of "elementary entities" of a substance. Those entities may be molecules, atoms, ions or any groups of particles so long as they are all the same. definition: The amount of substance containing as many elementary entities as there are atoms in 0.012 kilograms of carbon 12. |
| candela | cd | Luminous intensity. Essentially this measures the 'brightness' of radiation. It's defined in terms of the intensity of a very pure yellow-green light source with a strength measured by its power spread over a cone shaped beam. Definition: The luminous intensity, in a given direction, of a source that emits monochromatic radiation at a frequency of 540 x 1012 hertz and has a radiant intensity in that direction of 1/682 watt per steradian. |
Derived units
These are derived from the base units as some meaningful combination. Some have special names whereas others are known by the elements that make them up and their mathematical relationship. Only a select few are listed here.
| Symbol | Unit name | What it measures |
|---|---|---|
| m2 | area (square metre) See the list of approved units for others. | |
| m3 | volume (cubic metre) See the list of approved units for others. | |
| m/s | Speed or velocity (metre per second) | |
| m/s2 | Acceleration (metre per second squared) i.e the rate of change of speed in m/s per second. | |
| kg/m3 | Density (kilogram per cubic metre) | |
| N | newton | Force. The force which will accelerate a mass of 1 kg at a rate of 1 m/s2 |
| Pa | pascal | Pressure = 1 N/m2 See approved units for others |
| J | joule | Energy. The energy required to accelerate a mass of 1 kg at a rate of 1 m/s2 over a distance of a metre (= 1 N m) Also tied to electrical units (see below). The kJ is that used in nutrition data. |
| W | watt | Power = 1 J/s The familiar unit for electrical appliances. Note the mechanical origin. |
| V | volt | Electrical potential difference or electromotive force = 1 W/A This is the familiar unit associated with batteries and electricity supplies. |
| °C | Celsius | Temperature, 0 °C = 273.16 K Based on water which freezes at zero and boils at 100 °C The same as used in weather forecasts and oven temps etc. |
| Hz | hertz | Frequency. (1/s) Same as the cycle per second. The unit used for radio frequencies, sound and computer processor speeds and so on. |
For a more comprehensive list of these units see our reference page for appropriate sources. Also see a chart to illustrate the above relationships.
Units approved for use with SI
They are given this status because they are useful in many practical everyday applications but are not strictly necessary for pure scientific and engineering work. They are however highly compatible and so do not detract from the advantages of metric, in fact they are very handy and user friendly. Again only select few are shown.
| Unit name | Symbol | Definition and what is measured |
|---|---|---|
| minute | min | Time = 60 s |
| hour | h | Time = 60 min = 3 600 s |
| day | d | Time = 24 h = 86 400 s |
| are (pronounced air) |
a | Area = 100 m2 A little known unit but still in use in some countries. Also forms the basis of hectare (hecto are) |
| hectare | ha | Area = 100 a = 10 000 m2 Used for land areas |
| litre | l or L | Volume = 1000 cm3 = 0.001 m3 = dm3 (decimetre cube) The familiar litre in which we buy petrol etc. Note that (for all practical everyday purposes) 1 litre of pure liquid water weighs 1 kg |
| tonne | t | Mass = 1000 kg Used in Transport, Vehicle masses and weight limits etc Also the approximate weight of a cubic metre of water (see litre above) |
| bar | bar | Pressure = 100 kPa Used in weather mapping (mbar) |