International System of Units
SI stands for Système International d’Unités, i.e. French for “the International System of Units.” The letters SI are used in all languages to designate this system. The SI system became an international standard at a congress in 1960 and is used in large parts of the world.
The SI system is built from units belonging to two different classes: seven base units, which are defined physically, and a number of derived units, which are formed by combining the base units according to simple geometric and physical laws.
Additional information about the SI system is provided (in English or French) by the Bureau International des Poids et Mesures (BIPM), from which the brochure “Le Système International d’Unités” can be downloaded in PDF format.
Definition of the Seven Base Units of the SI System
Below are the definitions of the seven base units of the SI system:
meter (m)
The meter is the base unit of length.
1 m is defined as the distance light travels in a vacuum during 1/299,792,458 of a second.
kilogram (kg)
The kilogram is the base unit of mass.
1 kg is the mass of a prototype in the form of a platinum–iridium cylinder kept in Sèvres, France. It is currently the only base unit defined by a physical object and also the only base unit with a prefix.
second (s)
The second is the base unit of time.
1 s is defined as 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)
The ampere is the base unit of electric current.
1 A is the magnitude of a constant electric current which, when flowing through two straight, parallel conductors of infinite length and negligible circular cross-section placed one meter apart in a vacuum, produces a force of 2 × 10⁻⁷ newtons per meter of conductor length between them.
kelvin (K)
The kelvin is the base unit of temperature.
1 K is defined as 1/273.16 of the thermodynamic temperature of the triple point of water. The base unit of temperature is named after the Scottish mathematician and physicist William Thomson, 1st Lord Kelvin (1824–1907).
mole (mol)
The mole is the base unit of amount of substance.
1 mol is defined as the amount of substance that contains as many elementary entities as there are atoms in 0.012 kilograms of carbon-12. The entities may be atoms, ions, electrons, molecules, other particles, or specified groups of particles.
candela (cd)
The candela is the base unit of luminous intensity.
1 cd is the luminous intensity, 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.
Derived SI Units
From the seven base units of the SI system, other units can be derived for various purposes. Below are some common derived SI units; many more exist:
farad (F)
The farad is the SI unit of capacitance in an electrical system, i.e. its ability to store electric charge.
1 F is defined as the capacitance of a capacitor that has equal and opposite charges of 1 coulomb on each plate and a potential difference of 1 volt between the plates. The farad is a very large unit and is most often used with the prefix micro (µF). It is named after the English chemist and physicist Michael Faraday (1791–1867).
hertz (Hz)
The hertz is the SI unit of frequency.
1 Hz is defined as one cycle per second. In most cases, frequencies much higher than 1 Hz are used. In acoustics, kilohertz (kHz) is most common, and in radio contexts megahertz (MHz) is used. The unit is named after the German physicist Heinrich Rudolf Hertz (1857–1894).
joule (J)
The joule is the SI unit of work or energy.
1 J is defined as the amount of work done when a force of 1 newton moves an object a distance of one meter in the direction of the force. The unit is named after the English physicist James Prescott Joule (1818–1889).
newton (N)
The newton is the SI unit of force.
1 N is defined as the force required to give a mass of 1 kg an acceleration of 1 meter per second squared. The unit is named after the English mathematician and physicist Sir Isaac Newton (1642–1727).
ohm (Ω)
The ohm is the SI unit of electrical resistance. Its symbol is the Greek letter omega (Ω).
1 Ω is defined as the resistance between two points of a conductor when a potential difference of one volt between those points produces a current of one ampere. The unit is named after the German physicist Georg Simon Ohm (1789–1854).
pascal (Pa)
The pascal is the SI unit of pressure.
1 Pa is the pressure generated when a force of 1 newton is distributed over an area of 1 square meter. The pascal is a rather small unit and is most often used with the prefix kilo (kPa). It is named after the French mathematician, physicist, and philosopher Blaise Pascal (1623–1662).
volt (V)
The volt is the SI unit of electric potential difference.
1 V is defined as the potential difference between two points in an electric conductor when a current of 1 ampere between those points generates a power of 1 watt. The unit is named after the Italian physicist Count Alessandro Giuseppe Anastasio Volta (1745–1827).
watt (W)
The watt is the SI unit of power.
1 W is defined as the power produced when one joule of energy is transferred per second. The unit is named after the Scottish engineer James Watt (1736–1819).
Supplementary SI Units
The supplementary units are dimensionless units. The following supplementary units are permitted:
- Plane angle: radian (rad)
1 rad = 1 m / m - Solid angle: steradian (sr)
1 sr = 1 m² / m²
The unit of plane angle, the radian, is the plane angle that subtends an arc equal in length to the radius.
The unit of solid angle, the steradian, is the angle of a cone with its vertex at the center of a sphere that cuts off an area on the surface of the sphere equal to the area of a square whose side length equals the radius of the sphere.
Additional Units Defined on the Basis of SI Units
The following additional units, defined on the basis of SI units, are permitted even though they are not decimal multiples according to the SI system:
Time
- minute (min): 1 min = 60 s
- hour (h): 1 h = 60 min
- day (d): 1 d = 24 h
Plane angle
- revolution (rev): 1 rev = 2π rad
- degree (°): 1° = (π/180) rad
- minute (′): 1′ = (1/60)°
- second (″): 1″ = (1/60)′
- gon (gon): 1 gon = (π/200) rad
Of the units listed above, only gon may be used with prefixes.
Multiples of Units
The SI system allows unit sizes to be increased or decreased using prefixes. For example, it is impractical to use the meter when measuring large distances such as the distance between two cities. In such cases, distances are better measured in thousands of meters. The prefix for 1,000 is kilo, making the kilometer (km) a more suitable unit.
For very small dimensions, such as the diameter of a human hair, the prefix micro (µ), meaning 0.000001, is used in front of the meter, yielding micrometers (µm).
Below is the complete scale of prefixes and their multipliers:
| Name | Symbol | Factor |
|---|---|---|
| yotta | Y | 10²⁴ |
| zetta | Z | 10²¹ |
| exa | E | 10¹⁸ |
| peta | P | 10¹⁵ |
| tera | T | 10¹² |
| giga | G | 10⁹ |
| mega | M | 10⁶ |
| kilo | k | 10³ |
| hecto | h | 10² |
| deka | da | 10¹ |
| — | — | 1 |
| deci | d | 10⁻¹ |
| centi | c | 10⁻² |
| milli | m | 10⁻³ |
| micro | µ | 10⁻⁶ |
| nano | n | 10⁻⁹ |
| pico | p | 10⁻¹² |
| femto | f | 10⁻¹⁵ |
| atto | a | 10⁻¹⁸ |
| zepto | z | 10⁻²¹ |
| yocto | y | 10⁻²⁴ |
SI Multiples with Special Names
Some SI multiples have special names and symbols:
- Volume: liter (l or L), 1 l = 1 dm³
- Mass: tonne (t), 1 t = 1,000 kg
- Pressure: bar (bar), 1 bar = 10⁵ Pa
Rules for Using SI Units
There are several rules governing the use of the SI system and its units:
- A unit may have only one prefix. For example, “millimillimeter” is not allowed; instead, “micrometer” should be used.
- Most prefixes that make a unit larger are written with uppercase letters (M, G, T, etc.). Exceptions are kilo (k), hecto (h), and deka (da). Prefixes that make a unit smaller are written in lowercase (m, n, p, etc.).
- Many units are eponymous, meaning they are named after people. Such unit names are written in lowercase when spelled out (newton, volt, pascal, etc.) but with an uppercase letter when abbreviated (N, V, Pa, etc.). An exception is the liter, where “L” is allowed to avoid confusion with the number 1.
- Abbreviated units are never pluralized.
- Unit symbols (J, N, g, Pa, etc.) are never followed by a period, unless at the end of a sentence.
- Numbers may be grouped in sets of three digits separated by spaces (not commas) to improve readability.
- The SI system recommends using a comma as the decimal separator (3,14159). Using a decimal point, common in English-speaking countries, is acceptable provided the dot is aligned with the bottom of the digits (3.14159) and not centered.