# The International System of Units

The International System of Units (French: Système International d'Unités, SI) is the modern form of the metric system and is the world's most widely used system of measurement, used in both commerce and science. It comprises a coherent system of units of measurement built on seven base units. It defines twenty-two named units, and includes many more unnamed coherent derived units. The system also establishes a set of twenty prefixes to the unit names and unit symbols that may be used when specifying multiples and fractions of the units.

## SI units and prefixes

The International System of Units (SI) defines seven units of measure as a basic set from which all other SI units are derived.

Quantity name Common quantity symbols SI unit name SI unit symbol Dimension symbol
Length l, x, r, etc. metre m [L]
Mass m kilogram kg [M]
Time t second s [T]
Temperature T, θ kelvin K [Θ]
Amount of substance n mole mol [N]
Electric current i, I ampere A [I]
Luminous intensity Iv candela cd [J]

A physical quantity (or "physical magnitude") is a physical property of a phenomenon, body, or substance, that can be quantified by measurement. Most physical quantities include a unit, but not all - some are dimensionless. Neither the name of a physical quantity, nor the symbol used to denote it, implies a particular choice of unit, though SI units are usually preferred and assumed today due to their ease of use and all-round applicability. For example, a quantity of mass might be represented by the symbol m, and could be expressed in the units kilograms (kg), pounds (lb), or daltons (Da). By convention, physical quantities are organized in a dimensional system built upon base quantities, each of which is regarded as having its own dimension.

Prefixes are added to unit names to produce multiple and sub-multiples of the original unit. All multiples are integer powers of ten, and above a hundred or below a hundredth all are integer powers of a thousand. Multiples of the kilogram are named as if the gram were the base unit, so a millionth of a kilogram is a milligram, not a microkilogram.

Fractions
Multiples
Prefix name
Prefix symbol
Factor
Prefix name
Prefix symbol
Factor
deci d 10-1 deca da 101
centi c 10-2 hecto h 102
milli m 10-3 kilo k 103
micro µ 10-6 mega M 106
nano n 10-9 giga G 109
pico p 10-12 tera T 1012
femto f 10-15 peta P 1015
atto a 10-18 exa E 1018

## Writing unit symbols and the values of quantities

In 1948, the ninth CGPM approved the first formal recommendation for the writing of symbols in the metric system when the basis of the rules as they are now known was laid down. These rules were subsequently extended by International Organization for Standardization (ISO) and the International Electrotechnical Commission (IEC) and now cover unit symbols and names, prefix symbols and names, how quantity symbols should be written and used and how the values of quantities should be expressed. Both ISO and the IEC have published rules for the presentation of SI units that are generally compatible with those published in the SI Brochure.

The value of a quantity is written as a number followed by a space (representing a multiplication sign) and a unit symbol; e.g., 2.21 kg, 7.3×102 m2, 22 K. This rule explicitly includes the percent sign (%) and the symbol for degrees of temperature (°C). Exceptions are the symbols for plane angular degrees, minutes, and seconds (°, ′, and ″), which are placed immediately after the number with no intervening space.

Unit symbols are written in upright (Roman) type (m for metres), whereas quantity symbols are written in italic type (m for mass).

Symbols are treated as mathematical entities, which means that the rules of algebra apply to them. For example, the equation T = 293 K can also be written T/K = 293. It is often convenient to write the quotient of a quantity and a unit in graphs and tables, so that the labels or entries are simply numbers.

## References

• International Bureau of Weights and Measures, 2006. International System of Units (SI) 205–208. doi:10.1201/9780849382994.axc
• Thompson, A., Taylor, B.N., 2008b. Guide for the Use of the International System of Units (SI) (Special publication 811). National Institute of Standards and Technology, Gaithersburg, MD.