Non-SI units mentioned in the SI

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While the International System of Units (SI) is used throughout the world in all fields, many non-SI units continue to be used in the scientific, technical, and commercial literature. Some units are deeply embedded in history and culture, and their use has not been entirely replaced by their SI alternatives. The authority behind the SI system, the General Conference on Weights and Measures, recognised and acknowledged such traditions by compiling a list of non-SI units accepted for use with SI. [1]


While not an SI-unit, the litre may be used with SI units. It is equivalent to (10 cm) = (1 dm) = 10 m. CubeLitre.svg
While not an SI-unit, the litre may be used with SI units. It is equivalent to (10 cm) = (1 dm) = 10 m.

Some units of time, angle, and legacy non-SI units have a long history of use. Most societies have used the solar day and its non-decimal subdivisions as a basis of time and, unlike the foot or the pound, these were the same regardless of where they were being measured. The radian, being 1/2π of a revolution, has mathematical advantages but is rarely used for navigation. Further, the units used in navigation around the world are similar. The tonne, litre, and hectare were adopted by the CGPM in 1879 and have been retained as units that may be used alongside SI units, having been given unique symbols. The catalogued units are given below. [2]

Most of these, in order to be converted to the corresponding SI unit, require conversion factors that are not powers of ten. Some common examples of such units are the customary units of time, namely the minute (conversion factor of 60 s/min, since 1 min = 60 s), the hour (3600 s), and the day (86400 s); the degree (for measuring plane angles, = π180rad); and the electronvolt (a unit of energy, 1 eV = 1.602176634×10−19 J). [2]

This is a list of units that are not defined as part of the International System of Units (SI) but are otherwise mentioned in the SI Brochure, [2] listed as being accepted for use alongside SI-units, or for explanatory purposes.

Units officially accepted for use with the SI

Name Symbol Quantity Value in SI units
minute min time 1 min = 60  s
hour h time 1 h = 60 min = 3600 s
day d time 1 d = 24 h = 1440 min = 86400 s
astronomical unit au length 1 au = 149597870700 m
degree ° plane angle and phase angle = (π180) rad
arcminute plane angle and phase angle 1′ = (160 = (π10800) rad
arcsecond plane angle and phase angle 1″ = (160)′ = (13600 = (π648000) rad
hectare ha area 1 ha = 1 hm2 = 10000  m2
litre l, L volume 1 L = 1 dm3 = 1000  cm3 = 0.001  m3
tonne t mass 1 t = 1 Mg = 1000  kg
dalton Da mass 1 Da = 1.66053906660(50)×10−27 kg [3] [note 1]
electronvolt eV energy 1 eV = 1.602176634×10−19 J [4]
neper Np logarithmic ratio quantity 1 Np = 1
bel, decibel B, dB logarithmic ratio quantity

The SI prefixes can be used with several of these units, but not, for example, with the non-SI units of time.

Other units defined but not officially sanctioned

The following table lists units that are effectively defined in sidenotes and footnotes in the 9th SI brochure. Units that are mentioned without a definition or that occur in historical material recorded in the appendices are not included.

Name Symbol Quantity Equivalent official unit
gal [note 2] Gal acceleration 1 Gal = 1 cm/s2 = 0.01  m/s2
unified atomic mass unit [note 3] u mass 1 u = 1  Da
volt-ampere reactive var reactive power 1 var = 1  VA

Changes to units mentioned in the SI

With the publication of each edition of the SI brochure, the list of non-SI units listed in tables changed compared to the preceding SI brochures. [5] The table below compares the status of each unit for which the status has changed between editions of the SI Brochure.

Name Symbol 1st–3rd SI Brochures 4–6th SI Brochures 7th SI Brochure 8th SI Brochure 9th SI Brochure
astronomical unit au [note 4] acceptedomittedacceptedacceptedaccepted
parsec pc acceptedomittedomittedomittedomitted
neper Np omittedomittedacceptedlistedaccepted
bel B omittedomittedacceptedlistedaccepted
decibel dB omittedomittedomittedlistedaccepted
unified atomic mass unit u acceptedacceptedacceptedacceptedfootnote
dalton Da omittedomittedfootnoteacceptedaccepted
natural unit (n.u.) of speedc0omittedomittedomittedlistedomitted
n.u. of actionħomittedomittedomittedlistedomitted
n.u. of massmeomittedomittedomittedlistedomitted
n.u. of timeħ(mec02)omittedomittedomittedlistedomitted
atomic unit (a.u.) of chargeeomittedomittedomittedlistedomitted
a.u. of massmeomittedomittedomittedlistedomitted
a.u. of actionħomittedomittedomittedlistedomitted
a.u. of lengtha0omittedomittedomittedlistedomitted
a.u. of energyEhomittedomittedomittedlistedomitted
a.u. of timeħEhomittedomittedomittedlistedomitted
nautical mile M temporarytemporarytemporarylistedomitted
knot kn temporarytemporarytemporarylistedomitted
ångström Å temporary temporary temporary listed omitted
are a temporary temporary temporary omitted omitted
hectare ha temporary temporary temporary accepted accepted
barn b temporary temporary temporary listed omitted
bar bar temporary temporary temporary listed omitted
standard atmosphere atm temporary listed listed omitted omitted
gal Gal temporary temporary listed listed footnote
curie Ci temporary temporary listed omitted omitted
roentgen R temporary temporary listed omitted omitted
rad rad temporary temporary listed omitted omitted
rem rem omitted temporary listed omitted omitted
erg erg listedlistedlistedlistedomitted
dyne dyn listedlistedlistedlistedomitted
poise P listedlistedlistedlistedomitted
stokes st listedlistedlistedlistedomitted
maxwell Mx listedlistedlistedlistedomitted
gauss G listedlistedlistedlistedomitted
ørsted Oe listedlistedlistedlistedomitted
phot ph listedlistedlistedlistedomitted
fermi listedlistedlistedomittedomitted
metric carat listedlistedlistedomittedomitted
torr Torr listedlistedlistedomittedomitted
kilogram-force kgf listedlistedomittedomittedomitted
calorie cal listedlistedlistedomittedomitted
micron μ listedlistedlistedomittedomitted
x-unit xu listedlistedomittedomittedomitted
stilb sb listedlistedomittedomittedomitted
gamma (Mass) γ listedlistedlistedomittedomitted
γ (magnetic flux density) γ listedlistedomittedomittedomitted
lambda λ listedlistedomittedomittedomitted
jansky Jy omittedomittedlistedomittedomitted
millimetre of mercury mmHg omittedomittedomittedlistedomitted

In this table, the status descriptions have the following meanings:

See also

Notes and references


  1. A footnote in the 9th SI Brochure gives an exact definition of the dalton.
  2. This is a unit employed in geodesy and geophysics to express acceleration due to gravity.
  3. The unified mass unit (u) is a synonym of the dalton (Da). In edition 9 (2019) of the SI Brochure, the unified mass unit is no longer listed as being accepted for use with SI units, though it notes its equivalence with the dalton in a footnote. In edition 8 (2006), both names were mentioned in parallel. In edition 7 (1998), position was the reverse of that in edition 9. Earlier editions mentioned only u.
  4. The symbol given for the astronomical unit changed from ua in the 8th to au in the 9th SI Brochure.

Related Research Articles

The General Conference on Weights and Measures is the supreme authority of the International Bureau of Weights and Measures (BIPM), the intergovernmental organization established in 1875 under the terms of the Metre Convention through which member states act together on matters related to measurement science and measurement standards. The CGPM is made up of delegates of the governments of the member states and observers from the Associates of the CGPM. It elects the International Committee for Weights and Measures as the supervisory board of the BIPM to direct and supervise it.

<span class="mw-page-title-main">Kilogram</span> Metric unit of mass

The kilogram is the base unit of mass in the International System of Units (SI), having the unit symbol kg. It is a widely used measure in science, engineering and commerce worldwide, and is often simply called a kilo colloquially. It means 'one thousand grams'.

The katal is that catalytic activity that will raise the rate of conversion by one mole per second in a specified assay system. It is a unit of the International System of Units (SI) used for quantifying the catalytic activity of enzymes and other catalysts.

<span class="mw-page-title-main">Litre</span> Unit of volume

The litre or liter is a metric unit of volume. It is equal to 1 cubic decimetre (dm3), 1000 cubic centimetres (cm3) or 0.001 cubic metres (m3). A cubic decimetre occupies a volume of 10 cm × 10 cm × 10 cm and is thus equal to one-thousandth of a cubic metre.

<span class="mw-page-title-main">Metre Convention</span> 1875 international treaty

The Metre Convention, also known as the Treaty of the Metre, is an international treaty that was signed in Paris on 20 May 1875 by representatives of 17 nations: Argentina, Austria-Hungary, Belgium, Brazil, Denmark, France, Germany, Italy, Peru, Portugal, Russia, Spain, Sweden and Norway, Switzerland, Ottoman Empire, United States of America, and Venezuela.

<span class="mw-page-title-main">International System of Units</span> Modern form of the metric system

The International System of Units, internationally known by the abbreviation SI, is the modern form of the metric system and the world's most widely used system of measurement. Coordinated by the International Bureau of Weights and Measures it is the only system of measurement with an official status in nearly every country in the world, employed in science, technology, industry, and everyday commerce.

A metric prefix is a unit prefix that precedes a basic unit of measure to indicate a multiple or submultiple of the unit. All metric prefixes used today are decadic. Each prefix has a unique symbol that is prepended to any unit symbol. The prefix kilo-, for example, may be added to gram to indicate multiplication by one thousand: one kilogram is equal to one thousand grams. The prefix milli-, likewise, may be added to metre to indicate division by one thousand; one millimetre is equal to one thousandth of a metre.

<span class="mw-page-title-main">Avogadro constant</span> Fundamental metric system constant defined as the number of particles per mole

The Avogadro constant, commonly denoted NA or L, is an SI defining constant with an exact value of 6.02214076×1023 mol-1 (reciprocal moles). It is defined as the number of constituent particles (usually molecules, atoms, or ions) per mole (SI unit) and used as a normalization factor in the amount of substance in a sample. In practice, its value is often approximated as 6.02×1023 mol-1 or 6.022×1023 mol-1. The constant is named after the physicist and chemist Amedeo Avogadro (1776–1856).

The dalton or unified atomic mass unit is a non-SI unit of mass defined as 1/12 of the mass of an unbound neutral atom of carbon-12 in its nuclear and electronic ground state and at rest. The atomic mass constant, denoted mu, is defined identically, giving mu = 1/12m(12C) = 1 Da.

<span class="mw-page-title-main">Metrology</span> Science of measurement and its application

Metrology is the scientific study of measurement. It establishes a common understanding of units, crucial in linking human activities. Modern metrology has its roots in the French Revolution's political motivation to standardise units in France when a length standard taken from a natural source was proposed. This led to the creation of the decimal-based metric system in 1795, establishing a set of standards for other types of measurements. Several other countries adopted the metric system between 1795 and 1875; to ensure conformity between the countries, the Bureau International des Poids et Mesures (BIPM) was established by the Metre Convention. This has evolved into the International System of Units (SI) as a result of a resolution at the 11th General Conference on Weights and Measures (CGPM) in 1960.

<span class="mw-page-title-main">Newton (unit)</span> Unit of force in physics

The newton is the unit of force in the International System of Units (SI). It is defined as , the force which gives a mass of 1 kilogram an acceleration of 1 metre per second per second. It is named after Isaac Newton in recognition of his work on classical mechanics, specifically his second law of motion.

<span class="mw-page-title-main">Bar (unit)</span> Unit of pressure equal to 100,000 Pa

The bar is a metric unit of pressure defined as 100,000 Pa (100 kPa), though not part of the International System of Units (SI). A pressure of 1 bar is slightly less than the current average atmospheric pressure on Earth at sea level. By the barometric formula, 1 bar is roughly the atmospheric pressure on Earth at an altitude of 111 metres at 15 °C.

The molar mass constant, usually denoted by Mu, is a physical constant defined as one twelfth of the molar mass of carbon-12: Mu = M(12C)/12. The molar mass of any element or compound is its relative atomic mass multiplied by the molar mass constant.

<span class="mw-page-title-main">Kelvin</span> SI unit of temperature

The kelvin, symbol K, is a unit of measurement for temperature. The Kelvin scale is an absolute scale, which is defined such that 0 K is absolute zero and a change of thermodynamic temperature T by 1 kelvin corresponds to a change of thermal energy kT by 1.380649×10−23 J. The Boltzmann constant k = 1.380649×10−23 J⋅K−1 was exactly defined in the 2019 redefinition of the SI base units such that the triple point of water is 273.16±0.0001 K. The kelvin is the base unit of temperature in the International System of Units (SI), used alongside its prefixed forms. It is named after the Belfast-born and University of Glasgow-based engineer and physicist William Thomson, 1st Baron Kelvin (1824–1907).

The angstrom or ångström is a metric unit of length equal to 10−10 m; that is, one ten-billionth (US) of a metre, a hundred-millionth of a centimetre, 0.1 nanometre, or 100 picometres. Its symbol is Å, a letter of the Swedish alphabet. The unit is named after the Swedish physicist Anders Jonas Ångström (1814–1874).

<span class="mw-page-title-main">2019 redefinition of the SI base units</span> Definition of the units kg, A, K and mol

In 2019, four of the seven SI base units specified in the International System of Quantities were redefined in terms of natural physical constants, rather than human artifacts such as the standard kilogram. Effective 20 May 2019, the 144th anniversary of the Metre Convention, the kilogram, ampere, kelvin, and mole are now defined by setting exact numerical values, when expressed in SI units, for the Planck constant, the elementary electric charge, the Boltzmann constant, and the Avogadro constant, respectively. The second, metre, and candela had previously been redefined using physical constants. The four new definitions aimed to improve the SI without changing the value of any units, ensuring continuity with existing measurements. In November 2018, the 26th General Conference on Weights and Measures (CGPM) unanimously approved these changes, which the International Committee for Weights and Measures (CIPM) had proposed earlier that year after determining that previously agreed conditions for the change had been met. These conditions were satisfied by a series of experiments that measured the constants to high accuracy relative to the old SI definitions, and were the culmination of decades of research.

<span class="mw-page-title-main">History of the metric system</span> History of the metric system measurement standards

The history of the metric system began during the Age of Enlightenment with measures of length and weight derived from nature, along with their decimal multiples and fractions. The system became the standard of France and Europe within half a century. Other measures with unity ratios were added, and the system went on to be adopted across the world.

In physics, natural units are physical units of measurement in which only universal physical constants are used as defining constants, such that each of these constants acts as a coherent unit of a quantity. For example, the elementary charge e may be used as a natural unit of electric charge, and the speed of light c may be used as a natural unit of speed. A purely natural system of units has all of its units defined such that each of these can be expressed as a product of powers of defining physical constants.

In physics, monochromatic radiation is electromagnetic radiation with a single constant frequency or wavelength. When that frequency is part of the visible spectrum the term monochromatic light is often used. Monochromatic light is perceived by the human eye as a spectral color.


  1. International Bureau of Weights and Measures (2006), The International System of Units (SI) (PDF) (8th ed.), ISBN   92-822-2213-6, archived (PDF) from the original on 2021-06-04, retrieved 2021-12-16
  2. 1 2 3 Bureau international des poids et mesures, "Non-SI units that are accepted for use with the SI", in: Le Système international d'unités (SI) / The International System of Units (SI), 9th ed. (Sèvres: 2019), ISBN   9789282222720, c. 4, pp. 145–146.
  3. "2018 CODATA Value: atomic mass constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
  4. "2018 CODATA Value: electron volt". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
  5. Bureau international des poids et mesures, Le Système international d'unités (SI) / The International System of Units (SI), 8th ed. (Sèvres: Organisation Intergouvernementale de la Convention du Mètre, 2006‑05), ISBN   9282222136.