Minute of arc

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A minute of arc, or arcminute or minute of angle (MOA), is a unit of angular measurement, equal to one sixtieth (1/60) of one degree.[1] This conversion is recognised for calculations involving SI Units.[2] Since one degree is defined as one three hundred and sixtieth (1/360) of a circle, 1 minute of arc is 1/21,600 of the same. It is used in those fields which require a unit for the expression of small angles, such as astronomy, navigation and marksmanship. One arcsecond =1/3600 of a degree.

The number of square arcminutes in a complete sphere is

or approximately 148,510,660.498 square arcminutes.


Symbols, abbreviations and subdivisions

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 (\hat{'}).

The subdivision of the minute of arc is the second of arc, or arcsecond. There are 60 arcseconds in an arcminute. Therefore, the arcsecond is 1/3600 of a degree, or 1/1296000 of a circle, or (π/648000) radians, which is approximately 1/206265 radian. The symbol for the arcsecond is the double prime (″) (U+2033). To express even smaller angles, standard SI prefixes can be employed; in particular, the milliarcsecond, abbreviated mas, is sometimes used in astronomy.

In celestial navigation, seconds of arc are rarely used in calculations, the preference usually being for degrees, minutes and decimals of a minute, written for example as 42° 25′.32 or 42° 25′.322.[3][4] This notation has been carried over into marine GPS receivers, which normally display latitude and longitude in the latter format by default.[5]



The arcminute is commonly found in the firearms industry and literature, particularly that concerning the accuracy of rifles, though the industry tends to refer to it as minute of angle. It is popular because 1 MOA subtends approximately one inch at 100 yards, a traditional distance on target ranges. A shooter can easily readjust their rifle scope by measuring the distance in inches the bullet hole is from the desired impact point, and adjusting the scope that many MOA in the same direction. Most target scopes designed for long distances are adjustable in quarter (¼) or eighth (⅛) MOA "clicks". One eighth MOA is equal to approximately an eighth of an inch at 100 yards or one inch at 800 yards.

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