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]
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, 1° = π⁄180rad); 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.
Name | Symbol | Quantity | Value in SI units |
---|---|---|---|
minute | min | time | 1 min = 60 s |
hour | h | 1 h = 60 min = 3600 s | |
day | d | 1 d = 24 h = 1440 min = 86400 s | |
astronomical unit | au | length | 1 au = 149597870700 m |
degree | ° | plane angle and phase angle | 1° = (π⁄180) rad |
arcminute | ′ | 1′ = (1⁄60)° = (π⁄10800) rad | |
arcsecond | ″ | 1″ = (1⁄60)′ = (1⁄3600)° = (π⁄648000) 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 | 1 Da = 1.66053906892(52)×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 | — | |
The SI prefixes can be used with several of these units, but not, for example, with the non-SI units of time.
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 |
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] | accepted | omitted | accepted | accepted | accepted |
parsec | pc | accepted | omitted | omitted | omitted | omitted |
neper | Np | omitted | omitted | accepted | listed | accepted |
bel | B | omitted | omitted | accepted | listed | accepted |
decibel | dB | omitted | omitted | omitted | listed | accepted |
unified atomic mass unit | u | accepted | accepted | accepted | accepted | footnote |
dalton | Da | omitted | omitted | footnote | accepted | accepted |
natural unit (n.u.) of speed | c0 | omitted | omitted | omitted | listed | omitted |
n.u. of action | ħ | omitted | omitted | omitted | listed | omitted |
n.u. of mass | me | omitted | omitted | omitted | listed | omitted |
n.u. of time | ħ⁄(mec02) | omitted | omitted | omitted | listed | omitted |
atomic unit (a.u.) of charge | e | omitted | omitted | omitted | listed | omitted |
a.u. of mass | me | omitted | omitted | omitted | listed | omitted |
a.u. of action | ħ | omitted | omitted | omitted | listed | omitted |
a.u. of length | a0 | omitted | omitted | omitted | listed | omitted |
a.u. of energy | Eh | omitted | omitted | omitted | listed | omitted |
a.u. of time | ħ⁄Eh | omitted | omitted | omitted | listed | omitted |
nautical mile | M | temporary | temporary | temporary | listed | omitted |
knot | kn | temporary | temporary | temporary | listed | omitted |
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 | listed | listed | listed | listed | omitted |
dyne | dyn | listed | listed | listed | listed | omitted |
poise | P | listed | listed | listed | listed | omitted |
stokes | st | listed | listed | listed | listed | omitted |
maxwell | Mx | listed | listed | listed | listed | omitted |
gauss | G | listed | listed | listed | listed | omitted |
ørsted | Oe | listed | listed | listed | listed | omitted |
phot | ph | listed | listed | listed | listed | omitted |
fermi | listed | listed | listed | omitted | omitted | |
metric carat | listed | listed | listed | omitted | omitted | |
torr | Torr | listed | listed | listed | omitted | omitted |
kilogram-force | kgf | listed | listed | omitted | omitted | omitted |
calorie | cal | listed | listed | listed | omitted | omitted |
micron | μ | listed | listed | listed | omitted | omitted |
x-unit | xu | listed | listed | omitted | omitted | omitted |
stilb | sb | listed | listed | omitted | omitted | omitted |
gamma (Mass) | γ | listed | listed | listed | omitted | omitted |
γ (magnetic flux density) | γ | listed | listed | omitted | omitted | omitted |
lambda | λ | listed | listed | omitted | omitted | omitted |
jansky | Jy | omitted | omitted | listed | omitted | omitted |
millimetre of mercury | mmHg | omitted | omitted | omitted | listed | omitted |
In this table, the status descriptions have the following meanings:
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.
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 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.
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.
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 official status in nearly every country in the world, employed in science, technology, industry, and everyday commerce.
The SI base units are the standard units of measurement defined by the International System of Units (SI) for the seven base quantities of what is now known as the International System of Quantities: they are notably a basic set from which all other SI units can be derived. The units and their physical quantities are the second for time, the metre for length or distance, the kilogram for mass, the ampere for electric current, the kelvin for thermodynamic temperature, the mole for amount of substance, and the candela for luminous intensity. The SI base units are a fundamental part of modern metrology, and thus part of the foundation of modern science and technology.
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, ions, or ion pairs) per mole (SI unit) and used as a normalization factor in the amount of substance in a sample. In the SI dimensional analysis of measurement units, the dimension of the Avogadro constant is the reciprocal of amount of substance, denoted N−1. The Avogadro number, sometimes denoted N0, is the numeric value of the Avogadro constant (i.e., without a unit), namely the dimensionless number 6.02214076×1023; the value chosen based on the number of atoms in 12 grams of carbon-12 in alignment with the historical definition of a mole. The constant is named after the Italian physicist and chemist Amedeo Avogadro (1776–1856).
The dalton or unified atomic mass unit is a 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. It is a non-SI unit accepted for use with SI. The atomic mass constant, denoted mu, is defined identically, giving mu = 1/12m(12C) = 1 Da.
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 squared.
The gram is a unit of mass in the International System of Units (SI) equal to one thousandth of a kilogram.
The joule-second is the unit of action and of angular momentum in the International System of Units (SI) equal to the product of an SI derived unit, the joule (J), and an SI base unit, the second (s). The joule-second is a unit of action or of angular momentum. The joule-second also appears in quantum mechanics within the definition of the Planck constant. Angular momentum is the product of an object's moment of inertia, in units of kg⋅m2 and its angular velocity in units of rad⋅s−1. This product of moment of inertia and angular velocity yields kg⋅m2⋅s−1 or the joule-second. The Planck constant represents the energy of a wave, in units of joule, divided by the frequency of that wave, in units of s−1. This quotient of energy and frequency also yields the joule-second (J⋅s).
The vacuum magnetic permeability is the magnetic permeability in a classical vacuum. It is a physical constant, conventionally written as μ0. It quantifies the strength of the magnetic field induced by an electric current. Expressed in terms of SI base units, it has the unit kg⋅m⋅s−2·A−2. It can be also expressed in terms of SI derived units, N·A−2.
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 an element or compound is its relative atomic mass or relative molecular mass multiplied by the molar mass constant.
The kelvin is the base unit for temperature in the International System of Units (SI). The Kelvin scale is an absolute temperature scale that starts at the lowest possible temperature, taken to be 0 K. By definition, the Celsius scale and the Kelvin scale have the exact same magnitude; that is, a rise of 1 K is equal to a rise of 1 °C and vice versa, and any temperature in degrees Celsius can be converted to kelvin by adding 273.15.
The hectare is a non-SI metric unit of area equal to a square with 100-metre sides (1 hm2), that is, 10,000 square metres, and is primarily used in the measurement of land. There are 100 hectares in one square kilometre. An acre is about 0.405 hectares and one hectare contains about 2.47 acres.
The angstrom is a unit of length equal to 10−10 m; that is, one ten-billionth of a metre, a hundred-millionth of a centimetre, 0.1 nanometre, or 100 picometres. The unit is named after the Swedish physicist Anders Jonas Ångström (1814–1874) It was originally spelled with Swedish letters, as Ångström and later as ångström. The latter spelling is still listed in some dictionaries, but is now rare in English texts. Some popular US dictionaries list only the spelling angstrom.
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.
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, 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.