Minute and second of arc

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. Since one degree is 1/360 of a turn (or complete rotation), one arcminute is 1/21,600 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 circumference is very near 21,600nmi. A minute of arc is pi/10,800 of a radian. A second of arc, arcsecond (arcsec), or arc second, denoted by the symbol , is 1/60 of an arcminute, 1/3,600 of a degree, 1/1,296,000 of a turn, and pi/648,000 (about 1/206,264.8) 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. The prime symbol () designates the arcminute, though a single quote (U+0027) is commonly used where only ASCII characters are permitted. One arcminute is thus written as 1′. It is also abbreviated as arcmin or amin. Similarly, double prime (U+2033) designates the arcsecond, though a double quote (U+0022) is commonly used where only ASCII characters are permitted. One arcsecond is thus written as 1′′. It is also abbreviated as arcsec or asec. In celestial navigation, seconds of arc are rarely used in calculations, the preference usually being for degrees, minutes, and decimals of a minute, for example, written as 42° 25.32′ or 42° 25.322′. This notation has been carried over into marine GPS receivers, which normally display latitude and longitude in the latter format by default. The average apparent diameter of the full Moon is about 31 arcminutes, or 0.52°.