Unit of length

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.

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

History

Before the establishment of the decimal metric system in France during the French Revolution in the late 18th century, many units of length were based on parts of the human body.

The Nippur cubit was one of the oldest known units of length. The oldest known metal standard for length corresponds to this Sumerian unit and dates from 2650 BCE. This copper bar was discovered in Nippur, on the banks of the Euphrates, and is kept in the Istanbul Archaeological Museum. Archaeologists consider that this 51.85 centimetres long unit was the origin of the Roman foot. Indeed, the Egyptians divided the Sumerian cubit into 28 fingers and 16 of these fingers gave a Roman foot of 29.633 cm.

Metric system

SI

The base unit in the International System of Units (SI) is the meter, defined as "the length of the path travelled by light in vacuum during a time interval of 1⁄299792458 seconds." It is approximately equal to 1.0936 yd. Other SI units are derived from the meter by adding prefixes, as in millimeter or kilometer, thus producing systematic decimal multiples and submultiples of the base unit that span many orders of magnitude. For example, a kilometer is 1000 m.

Non-SI

In the centimeter–gram–second system of units, the basic unit of length is the centimeter, or 1⁄100 of a meter. Other non-SI units are derived from decimal multiples of the meter.

Name	Symbol	SI value
fermi	fm	1 femtometer
ångström	Å	100 picometers
micron	μm	1 micrometer
Norwegian/Swedish mil or myriameter		10,000 meters
x unit	xu	0.1 picometer

Imperial/U.S.

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.

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

thou or mil (1⁄1000 of an inch)
inch (25.4 mm)
foot (12 inches, 0.3048 m)
yard (3 feet, 0.9144 m)
(terrestrial) mile (5280 feet, or 1760 yards 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, 51⁄2 yards, or 5.0292 m)

Australian building trades

The Australian building trades adopted the metric system in 1966 and the units used for measurement of length are meters (m) and millimeters (mm). Centimeters (cm) are avoided as they cause confusion when reading plans. For example, the length two and a half meters is usually recorded as 2500 mm or 2.5 m; it would be considered non-standard to record this length as 250 cm.

Surveyor's trade

American surveyors use a decimal-based system of measurement devised by Edmund Gunter in 1620. The base unit is Gunter's chain of 66 feet (20 m) which is subdivided into 4 rods, each of 16.5 ft or 100 links of 0.66 feet. A link is abbreviated "lk", and links "lks", in old deeds and land surveys done for the government.

Science

Astronomy

Astronomical measure uses:

Earth radius R_🜨 ≈ 6,371 km
Lunar distance LD ≈ 384402 km. Average distance between the center of Earth and the center of the Moon.
astronomical unit au. Defined as 149597870700 m. 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.
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 meters
The classical electron radius	r_e	2.817940285(31)×10⁻¹⁵
The Compton wavelength of the electron	λ_C	2.426310215(18)×10⁻¹²
The reduced Compton wavelength of the electron	λ_C	3.8615926764(18)×10⁻¹³
The Compton wavelength (or reduced Compton wavelength) of any fundamental particle	λ_x
The Bohr radius of the hydrogen atom (Atomic unit of length)	a₀	5.291772083(19)×10⁻¹¹
The reduced wavelength of hydrogen radiation	1 / R_∞	9.112670505509(83)×10⁻⁸
The Planck length	𝓁_P	1.616199(97)×10⁻³⁵
Stoney unit of length	l_S	1.381×10⁻³⁵
Quantum chromodynamics (QCD) unit of length	l_QCD	2.103×10⁻¹⁶
Natural units based on the electronvolt	1 eV⁻¹	1.97×10⁻⁷

Archaic

Archaic units of distance include:

cana
cubit
rope
league
li (China)
pace (the "double pace" of about 5 feet used in Ancient Rome)
verst (Russia)

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:

Double-decker bus (9.5–11 meters in length)
American football field (100 yards in length)
Thickness of a human hair (around 80 micrometers)

Other

Horse racing and other equestrian activities keep alive:

furlong = 1⁄8 mile (201.168 m)
horse length ≈ 8 feet (2.4 m)

References

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