Minute and second of arc

A minute of arc, arcminute (arcmin), arc minute, or minute arc, denoted by the symbol ,[1] is a unit of angular measurement equal to 1/60 of one degree.[2] Since one degree is 1/360 of a turn (or complete rotation), one minute of arc is 1/21600 of a turn. The nautical mile (nmi) was originally defined as a minute of latitude on a spherical Earth, so the actual Earth circumference is very near 21600 nmi. A minute of arc is π/10800 of a radian.

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 systemNon-SI units mentioned in the SI
Unit ofAngle
Symbolorarcmin
In unitsDimensionless 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   π·1000/10800 ≈ 0.2909 mrad
   gons   9/600g = 0.015g
   turns   1/21600

A second of arc, arcsecond (arcsec), or arc second, denoted by the symbol ,[3] is 1/60 of an arcminute, 1/3600 of a degree,[2] 1/1296000 of a turn, and π/648000 (about 1/206181.8) of a radian.

These units originated in Babylonian astronomy as sexagesimal 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 three-dimensional area such as on a sphere, square arcminutes or seconds may be used.