International System of Units

The International System of Units is the international standard form of the metric system today. SI is the short name for this from the French language phrase Système International d'unités.

The metric system is a system of measuring based on the metre for length, distance or displacement, kilogram for mass, and second for time.

The metre, kilogram and second can be used in combination with each other. This will make different units of measurement to mean other amounts, such as volume, energy, pressure, and velocity.

Sometimes we want to talk about larger or smaller measurements. Then we add a prefix. A prefix is adding something to the beginning of a word to make a new word. The prefix kilo- means "1000" and the prefix milli- means "0.001". So one kilometre is 1000 metres and one milligram is a 1000th of a gram. These prefixes are shown in the table on the right side.

Metric System (SI) prefixes

yotta-	Y	1 000 000 000 000 000 000 000 000
zetta-	Z	1 000 000 000 000 000 000 000
exa-	E	1 000 000 000 000 000 000
peta-	P	1 000 000 000 000 000
tera-	T	1 000 000 000 000
giga-	G	1 000 000 000
mega-	M	1 000 000
kilo-	k	1 000
hecto-	h	100
deca-	da	10
		1
deci-	d	1/10
centi-	c	1/ 100
milli-	m	1/ 1 000
micro-	µ	1/ 1 000 000
nano-	n	1/ 1 000 000 000
pico-	p	1/ 1 000 000 000 000
femto-	f	1/ 1 000 000 000 000 000
atto-	a	1/ 1 000 000 000 000 000 000
zepto-	z	1/ 1 000 000 000 000 000 000 000
yocto-	y	1/ 1 000 000 000 000 000 000 000 000

History and use

These were created in France after the French Revolution. They are now used almost everywhere in the world, except for the United States, Liberia and Myanmar, where the older imperial units are still widely used. Other countries, most of them historically related to the British Empire, are slowly replacing the old imperial system with the metric system.

Even the United Kingdom, which created the old US units of measurement, is now using the metric system and the imperial system at the same time. There is pressure to become more metric, both from UK government plans written before Britain's entry into the European Union and because of EU rules about common systems of measurement.

Base units of measurement

The SI base units are measurements used by scientists and other people around the world. All the other units can be written by combining these seven base units in different ways. These other units are called "derived units".

Length (l)

Unit: metre or meter (m)

One metre is defined as the distance light travels in a vacuum in 1/299,792,458 second. It is also 1/10000000 (one ten-millionth) of the distance from the North Pole to the Equator. This standard was adopted in 1983 when the speed of light in vacuum was defined to be precisely 299,792,458 m/s.

Mass (m)

Unit: kilogram (kg)

One kilogram is defined to be the mass of a specific cylinder of platinum-iridium alloy. It is kept at the International Bureau of Weights and Measures near Paris. There is an ongoing effort to introduce a definition using other basic or atomic constants.

Time (t)

Unit: second (s)

One second is defined as the time required for 9,192,631,770 periods of the radiation between to two specific energy levels of the element caesium-133. This definition was adopted in 1967.

Electrical current flow (I)

Unit: ampere (A)

The ampere is that constant electrical current (or flow) which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed one metre apart in vacuum, would produce between these conductors a force equal to 2 × 10^-7 newton per metre of length.

The ampere is one of two base units (the other being the candela) that uses derived units in its definition, not just base units. One newton is 1 kg m s^-2.

Temperature (T)

Unit: kelvin (K)

The kelvin, unit of temperature, is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water. It is named after Lord Kelvin.

Amount of substance (n)

Unit: mole (mol)

1. 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; its symbol is "mol".
2. When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles.

Luminous intensity (brightness of light) (I)

Unit: candela (cd)

The candela is the luminous intensity (brightness), in a given direction, of a source that emits monochromatic radiation of frequency 540 × 10¹² hertz and that has a radiant intensity in that direction of 1/683 watt per steradian.

The candela is one of two base units (the other being the ampere) that uses derived units in its definition, not just base units. One hertz is 1 s^-1, one watt is 1 J s^-1 = 1 kg m² s^-3 and the steradian 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.

Derived units of measurement

Plane angle

Unit: radian (rad)

A Radian is the angle between one radius of a circle and another whose endpoint is the same distance around the circle as they are from the center of the circle

Solid angle

Unit: steradian (sr)

Frequency

Unit: hertz (Hz)
The unit hertz is used to tell how many times something happens in one second. It is equivalent to one per second (1/s or s⁻¹)

Force

Unit: newton (N)
Newtons measure force, which is how strong something pushes or pulls something else. This also describes weight, which is the earth (or any planet) pulling on an object. A newton is the force required to accelerate one kilogram to one Metre per second in one second. It is the same as one kilogram meter per second squared (kg∙m/s² or kg∙m∙s⁻²).

Pressure

Unit: pascal (Pa)
One Pascal is the pressure applied when one newton of force is applied to an area of one squared meter. It is the same as one N/m² or N∙m⁻².

Energy

Unit: joule (J)
A Joule is used to describe the energy an object has. It also describes work, which is adding or taking energy from an object. One Joule is the work done when one newton of force is applied to an object over one meter. It is the same as one newton metre (N∙m).

Power

Unit: watt (W) Watts measure how quickly work is done. They are a measure of how many Joules of work are done each second. One watt is the same as one joule per second (J/s or J∙s^-1).

Electric charge

Unit: coulomb (C) Coulombs measure electric charge. They tell how strongly charged an object is, and whether it is positively or negatively charged. A coulomb is defined as the amount of charge that passes through a point with a current of one ampere for one second. It is the same as one ampere second (A∙s).

Electrical potential

Unit: volt (V)

Capacitance

Unit: farad (F)

Electrical resistance

Unit: ohm (Ω)

Derived units with special names

There are also derived units which have special names. Usually these were made to make calculating simpler.

Named units derived from SI base units

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
pascal	Pa	pressure, stress	N/m2	m−1∙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
coulomb	C	electric charge or electric flux	s∙A	s∙A
volt	V	voltage, electrical potential difference, electromotive force	W/A = J/C	m2∙kg∙s−3∙A−1
farad	F	electrical capacitance	C/V	m−2∙kg−1∙s4∙A2
ohm	Ω	electrical resistance, impedance, reactance	V/A	m2∙kg∙s−3∙A−2
siemens	S	electrical conductance	1/Ω	m−2∙kg−1∙s3∙A2
weber	Wb	magnetic flux	J/A	m2∙kg∙s−2∙A−1
tesla	T	magnetic field	V∙s/m2 = Wb/m2 = N/A∙m	kg∙s−2∙A−1
henry	H	inductance	V∙s/A = Wb/A	m2∙kg∙s−2∙A−2
Celsius	°C	Celsius Temperature	T°C = TK − 273.15	K
lumen	lm	luminous flux	cd∙sr	cd
lux	lx	illuminance	lm/m2	m−2∙cd
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