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Non-SI units mentioned in the SI

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While not an SI-unit, the litre may be used with SI units. It is equivalent to (10 cm)3 = (1 dm)3 = 10−3 m3.

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⁄180 rad); and the electronvolt (a unit of energy, 1 eV = 1.602176634×10−19 J).[2]

Units officially accepted for use with the SI

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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.

Other units defined but not officially sanctioned

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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

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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:

  • "accepted": The unit is accepted for use with the SI.
  • "temporary": The unit is accepted for use with the SI, but is planned to be phased out.
  • "listed": The unit is defined in a table of units in the brochure but not accepted for use with the SI.
  • "footnote": The unit is defined in a footnote or side note, without any mention in the main text.
  • "omitted": There is no mention of the unit in the brochure, excluding historical appendices.

See also

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Notes and references

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Notes

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  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.

References

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  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. ^ a b c 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. ^ "2022 CODATA Value: atomic mass constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. May 2024. Retrieved 2024-05-18.
  4. ^ "2022 CODATA Value: electron volt". The NIST Reference on Constants, Units, and Uncertainty. NIST. May 2024. Retrieved 2024-05-18.
  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.
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