# Unit of length

A ruler, depicting two customary units of length, the centimetre and the inch

A unit of length refers to any arbitrarily chosen and accepted reference standard for measurement of length. The most common units in modern use are the metric units, used in every country globally. In the United States the U.S. customary units are also in use. British Imperial units are still used for some purposes in the United Kingdom and some other countries. The metric system is sub-divided into SI and non-SI units.[1][2][3]

## Metric system

### SI

The base unit in the International System of Units (SI) is the metre, defined as "the length of the path travelled by light in vacuum during a time interval of 1299792458 seconds."[4] It is approximately equal to 1.0936 yd. Other SI units are derived from the metre by adding prefixes, as in millimetre or kilometre, thus producing systematic decimal multiples and submultiples of the base unit that span many orders of magnitude. For example, a kilometre is 1000 m.

### Non-SI

In the centimetre–gram–second system of units, the basic unit of length is the centimetre, or 1100 of a metre. Other non-SI units are derived from decimal multiples of the metre.

Name Symbol SI value
fermi fm femtometre
ångström Å 100 picometres
micron μm 1 micrometre
Norwegian/Swedish mil or myriametre 10,000 metres
x unit xu 0.1 picometre

## Imperial/US

The basic unit of length in the imperial and U.S. customary systems is the yard, defined as exactly 0.9144 m by international treaty in 1959.[2][5]

Common imperial units and U.S. customary units of length include:[6]

• thou or mil (11000 of an inch)
• inch (25.4 mm)
• foot (12 inches, 0.3048 m)
• yard (3 feet, 0.9144 m)
• (terrestrial) mile (5280 feet, 1609.344 m)
• (land) league 3 miles (4,800 m)

## Marine

In addition, the following are used by sailors:

• fathom (for depth; only in non-metric countries) (2 yards = 1.8288 m)
• nautical mile (one minute of arc of latitude = 1852 m)

## Aviation

Aviators use feet for altitude worldwide (except in Russia and China) and nautical miles for distance.[citation needed]

## Surveying

Determination of the rod, using the length of the left foot of 16 randomly chosen people coming from church service

Surveyors in the United States continue to use:

• chain (22 yards, or 20.1168 m)
• rod (also called pole or perch) (quarter of a chain, 512 yards, or 5.0292 m)

## Science

### Astronomy

Astronomical measure uses:

• Earth radius REarth ≈ 6,371 km[7]
• Lunar distance LD ≈ 384402 km.[8] Average distance between the center of Earth and the center of the Moon.
• astronomical unit au. Defined as 149597870700 m.[9] Approximately the distance between the Earth and Sun.
• light-year ly ≈ 9460730472580.8 km. The distance that light travels in a vacuum in one Julian year.[10]
• parsec pc ≈ 30856775814671.9 km or about 3.26156 ly
• Hubble length 14.4 billion light-years or 4.55 gigaparsecs

### Physics

In atomic physics, sub-atomic physics, and cosmology, the preferred unit of length is often related to a chosen fundamental physical constant, or combination thereof. This is often a characteristic radius or wavelength of a particle. Some common natural units of length are included in this table:

Atomic property Symbol Length, in metres Reference
The classical electron radius re 2.817940285(31)×10−15 [11]
The Compton wavelength of the electron λC 2.426310215(18)×10−12 [11]
The reduced Compton wavelength of the electron λC 3.8615926764(18)×10−13 [12]
The Compton wavelength (or reduced Compton wavelength) of any fundamental particle λx
The Bohr radius of the hydrogen atom (Atomic unit of length) a0 5.291772083(19)×10−11 [11]
The reduced wavelength of hydrogen radiation 1 / R 9.112670505509(83)×10−8 [11]
The Planck length 𝓁P 1.616199(97)×10−35 [13]
Stoney unit of length lS 1.381×10−35
Quantum chromodynamics (QCD) unit of length lQCD 2.103×10−16
Natural units based on the electronvolt 1 eV−1 1.97×10−7

## Archaic

Archaic units of distance include:

## Informal

In everyday conversation, and in informal literature, it is common to see lengths measured in units of objects of which everyone knows the approximate width. Common examples are:

## Other

Horse racing and other equestrian activities keep alive:

## References

1. ^ Cardarelli, François (2003). Encyclopaedia of Scientific Units, Weights, and Measures: Their SI Equivalences and Origins. Springer. ISBN 9781852336820.
2. ^ a b Hinkelman, Edward G.; Sibylla Putzi (2005). Dictionary Of International Trade: Handbook Of The Global Trade Community. World Trade Press. p. 245. ISBN 9781885073723.
3. ^ Judson, Lewis Van Hagen (1960). Units of Weight and Measure (United States Customary and Metric): Definitions and Tables of Equivalents, Issue,233. U.S. Department of Commerce, National Bureau of Standards. pp. 3–4. Retrieved 16 October 2012.
4. ^ "17th General Conference on Weights and Measures (1983), Resolution 1". Retrieved 2012-09-19.
5. ^ Donald Fenna (2002). A dictionary of weights, measures, and units. Oxford University Press. pp. 130–131. ISBN 978-0198605225. Retrieved 8 January 2012.
6. ^ Cardarelli 2003, pp. 29–30
7. ^ Moritz, H. (March 2000). "Geodetic Reference System 1980". Journal of Geodesy. 74 (1): 128–133. Bibcode:2000JGeod..74..128.. doi:10.1007/s001900050278. S2CID 195290884.
8. ^ Battat, J. B. R.; Murphy, T. W.; Adelberger, E. G. (January 2009). "The Apache Point Observatory Lunar Laser-ranging Operation (APOLLO): Two Years of Millimeter-Precision Measurements of the Earth-Moon Range". Astronomical Society of the Pacific. 121 (875): 29–40. Bibcode:2009PASP..121...29B. doi:10.1086/596748. JSTOR 10.1086/596748.
9. ^ Geoff Brumfiel (14 Sep 2012). "The astronomical unit gets fixed: Earth–Sun distance changes from slippery equation to single number". Retrieved 14 Sep 2012.
10. ^ The IAU and astronomical units, International Astronomical Union, retrieved 2008-07-05
11. ^ a b c d Quinn, T.J.; Leschiutta, S.; Tavella, P. (August 2000). Recent advances in metrology and fundamental constants. Amsterdam ; Washington, DC: IOS Press, 2001. Proceedings of the International School of Physics "Enrico Fermi". pp. 142–143. ISBN 9781586031671.
12. ^ "Compton wavelength over 2 pi". The NIST Reference on Constants, Units, and Uncertainty. NIST. Retrieved 15 October 2012.
13. ^ "Planck length". The NIST Reference on Constants, Units, and Uncertainty. NIST. Retrieved 15 October 2012.