Minute and second of arc

A minute of arc (MOA), arcminute (arcmin) or minute arc is a unit of angular measurement equal to one-sixtieth (1/60) of one degree. As one degree is 1/360 of a circle, one minute of arc is 1/21600 of a circle (or, in radians, π/10800). It is used in fields that involve very small angles, such as astronomy, optometry, ophthalmology, optics, navigation, land surveying and marksmanship.

The number of square arcminutes in a complete sphere is approximately 148,510,660 square arcminutes.

A second of arc (arcsecond, arcsec) is 1/60 of an arcminute, 1/3,600 of a degree, 1/1,296,000 of a circle, and π/648,000 (about 1/206,265) of a radian. This is approximately the angle subtended by a U.S. dime coin (18mm) at a distance of 4 kilometres (about 2.5 mi).

To express even smaller angles, standard SI prefixes can be employed; the milliarcsecond (mas), for instance, is commonly used in astronomy.

Symbols and abbreviations

The standard symbol for marking the arcminute is the prime (′) (U+2032), though a single quote (') (U+0027) is commonly used where only ASCII characters are permitted. One arcminute is thus written 1′. It is also abbreviated as arcmin or amin or, less commonly, the prime with a circumflex over it ().