Minute and second of arc

For the SI units of angle, see radian and milliradian.
"Arcsec" redirects here. For the arcsecant function, see Inverse trigonometric functions.
This article is about divisions of a degree of angle. For divisions of an hour of angle, see hour angle.

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
Symbol′, arcmin
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 minute of arc, arcminute (arcmin), arc minute, or minute arc, denoted by the symbol ′, is a unit of angular measurement equal to ⁠1/60⁠ of one 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 (arcsec), or arc second, denoted by the symbol ″,[2] is ⁠1/60⁠ of an arcminute, ⁠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 three-dimensional area such as on a sphere, square arcminutes or seconds may be used.

  1. ^ a b Weisstein, Eric W. "Arc Second". mathworld.wolfram.com. Retrieved 31 August 2020.
  2. ^ "Minutes of Arc to Degree Conversion". Inch Calculator. Retrieved 25 July 2021.