Sevres.science / The SI

The International System of Units

Constants, base units, everything else

The rulebook of the SI is the SI Brochure, published by the International Bureau of Weights and Measures (BIPM) in Sèvres. Its current, ninth edition describes the system as it has stood since 20 May 2019, when all units were redefined in terms of constants.

The seven defining constants include the speed of light, the Planck constant and the charge of a single proton. Their values are exact by agreement. The seven base units follow from them: the second, metre, kilogram, ampere, kelvin, mole and candela.

Derived units: 22 with names of their own

Every other unit is a combination of base units. Speed is metres per second; density is kilograms per cubic metre. Some combinations are used so often that they have their own name and symbol. The SI recognises 22 of them.

They are the radian and steradian (angles), hertz (frequency), newton (force), pascal (pressure), joule (energy), watt (power), coulomb (electric charge), volt, farad, ohm, siemens, weber, tesla and henry (electricity and magnetism), degree Celsius (temperature), lumen and lux (light), becquerel, gray and sievert (radioactivity and radiation dose) and katal (catalytic activity).

A name is a shortcut, not a new idea. One newton is simply 1 kg m s⁻²: the force that speeds up one kilogram by one metre per second, every second.

Prefixes: from quecto to quetta

Prefixes scale a unit by powers of ten, so that the same unit can describe a virus and a galaxy. A kilometre is 10³ m; a nanosecond is 10⁻⁹ s. There are 24 SI prefixes, running from quecto (10⁻³⁰) to quetta (10³⁰).

The newest four arrived in November 2022, when the 27th General Conference on Weights and Measures adopted ronna (R, 10²⁷) and quetta (Q, 10³⁰), with ronto (r, 10⁻²⁷) and quecto (q, 10⁻³⁰) as their small counterparts. The BIPM expects the large ones to be used for quantities of digital information.

SI prefixes are always powers of ten. The binary prefixes used in computing, such as kibi (2¹⁰) and mebi (2²⁰), are separate and not part of the SI. The rules for writing prefixes are on the Writing units page.

Units that live alongside the SI

Some familiar units are not SI units but are officially accepted for use with the SI, because they are too useful to drop. They include the minute, hour and day; the degree of angle; the hectare; the litre; the tonne; the electronvolt; the decibel; and the astronomical unit.

Who looks after the SI

The SI rests on a treaty, the Metre Convention of 1875. Its member states meet in the General Conference on Weights and Measures (CGPM), which takes the decisions about the system. Under the Convention it meets at least once every six years.

Between meetings the work is steered by the International Committee for Weights and Measures (CIPM), eighteen metrologists from different countries, supported by consultative committees for individual fields. The BIPM in Sèvres is the permanent laboratory and secretariat of the whole structure.

Each country has its own national metrology institute that brings the SI to its laboratories, industry and markets. In Poland this is the Główny Urząd Miar (Central Office of Measures); Poland joined the Metre Convention in 1925.

Why the system is called coherent

The SI is a coherent system: its derived units are made from the base units with no extra numerical factor. One newton is one kilogram times one metre per second squared, and one joule is one newton times one metre, with the number 1 every time. That is why formulas in physics work directly in SI units, without conversion factors.

Units outside the SI break this pattern. An hour is 3600 seconds and a litre is a thousandth of a cubic metre, so calculations with them need a factor. They are accepted for everyday use, but science is usually written in coherent units.

How the SI reaches your kitchen scale

A measurement is only as good as the chain that connects it to the definition of the unit. National metrology institutes realise the units or hold standards calibrated against them. Accredited calibration laboratories calibrate their reference instruments against those standards, and manufacturers and users calibrate their own instruments against the laboratories. Each link is documented with its uncertainty. This unbroken chain is called traceability.

For the kilogram, for example, any institute that realises the definition can pass the unit on from its own primary mass standards, and the BIPM passes it on from the average of its own set of one-kilogram reference standards.

One certificate, accepted everywhere

Since 1999 the CIPM Mutual Recognition Arrangement has allowed national metrology institutes to recognise one another’s measurement standards and calibration certificates. It rests on key comparisons, in which institutes measure the same travelling standard and publish how far their results agree, and on lists of the calibration and measurement capabilities each institute offers.

The results are public. The BIPM maintains the key comparison database, the KCDB, where anyone can look up the comparisons and the capabilities of each institute.