Topic summary
Minute and second of arc
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. 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; therefore, the actual Earth's circumference is approximately 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 ″, is a unit of angular measurement equal to 1/60 of a minute of arc, 1/3600 of a degree, 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.