Minute and second of arc

This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. Find sources: "Minute and second of arc" – news · newspapers · books · scholar · JSTOR (March 2022) (Learn how and when to remove this message)

Arcminute
An illustration of the size of an arcminute (not to scale). A standard association football (soccer) ball (with a diameter of 22 cm or 8.7 in) subtends an angle of 1 arcminute at a distance of approximately 756 m (827 yd).
General information
Unit system	Non-SI units mentioned in the SI
Unit of	Angle
Symbol	′, arcmin
In units	Dimensionless with an arc length of approx. ≈ ⁠0.2909/1000⁠ of the radius, i.e. 0.2909 ⁠mm/m⁠
Conversions
1 ′ in ...	... is equal to ...
degrees	⁠1/60⁠° = 0.016°
arcseconds	60″
radians	⁠π/10800⁠ ≈ 0.000290888 rad
milliradians	⁠5π/54⁠ ≈ 0.2909 mrad
gradians	⁠3/200⁠g = 0.015g
turns	⁠1/21600⁠ turn

A minute of arc, arcminute (abbreviated as arcmin), arc minute, or minute arc, denoted by the symbol ′, is a unit of angular measurement equal to ⁠1/60⁠ of a degree.^[1] Since one degree is ⁠1/360⁠ of a turn, or complete rotation, one arcminute is ⁠1/21600⁠ of a turn. The nautical mile (nmi) was originally defined as the arc length of a minute of latitude on a spherical Earth, so the actual Earth's circumference is very near 21600 nmi. A minute of arc is ⁠π/10800⁠ of a radian.

A second of arc, arcsecond (abbreviated as arcsec), or arc second, denoted by the symbol ″,^[2] is a unit of angular measurement equal to ⁠1/60⁠ of a minute of arc, ⁠1/3600⁠ of a degree,^[1] ⁠1/1296000⁠ of a turn, and ⁠π/648000⁠ (about ⁠1/206264.8⁠) of a radian.

These units originated in Babylonian astronomy as sexagesimal (base 60) subdivisions of the degree; they are used in fields that involve very small angles, such as astronomy, optometry, ophthalmology, optics, navigation, land surveying, and marksmanship.

To express even smaller angles, standard SI prefixes can be employed; the milliarcsecond (mas) and microarcsecond (μas), for instance, are commonly used in astronomy. For a two-dimensional area such as on (the surface of) a sphere, square arcminutes or seconds may be used.