{{refimprove|date=December 2006}}
A '''minute of arc''', '''arcminute''', or '''MOA''' is a unit of [[angle|angular measurement]], equal to one sixtieth (1/60) of one [[degree (angle)|degree]]. <ref>http://wordnet.princeton.edu/perl/webwn?s=minute%20of%20arc</ref> Since one degree is defined as one three hundred sixtieth (1/360) of a circle, 1 MOA is 1/21600 of the amount of arc in a closed circle, measured in [[degree (angle)|degree]]s. It is used in those fields which require a unit for the expression of small angles, such as [[astronomy]] or [[marksmanship]].
==Symbols, abbreviations and subdivisions==
The standard symbol for marking the arcminute is the [[prime (symbol)|prime]] (′) (U+2032), though a single quote (') (U+0027) is commonly used where only [[ASCII]] characters are permitted. One arcminute is written 1′ (or 1'''''). It is also abbreviated as '''arcmin''' or '''amin''' or, less commonly, the prime with a [[circumflex]] over it (<math>\hat{'}</math>).
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 1/1296000 of a circle, or (π/648000) [[radian]]s, which is approximately 1/206265 [[radian]]. The symbol for the arcsecond is the double prime (″) (<code>U+2033</code>). To express even smaller angles, standard [[SI prefix]]es can be employed; in particular, the '''milliarcsecond''', abbreviated '''mas''', is sometimes used in [[astronomy]].
{|align=center cellpadding=1 cellspacing=0 border=1
|+ '''The [[sexagesimal]] system of [[Angle|angular measurement]]'''
|-
! unit !! value !! symbol !! abbreviations !!conversion
|-
| degree || 1/360 circle || [[degree symbol|°]] || deg||align="right"|17.4532925 mrad
|-
| arcminute || 1/60 degree || ′ ([[prime (symbol)|prime]]) || arcmin, amin, <math>\hat{'}</math>, MOA||align="right"|290.8882087 µrad
|-
| arcsecond || 1/60 arcminute || ″ (double prime) || arcsec||align="right"| 4.8481368 µrad
|-
| milliarcsecond || 1/1000 arcsecond || || mas||align="right"|4.8481368 nrad
|}
==Uses==
===Firearms===
This unit is commonly found in the [[firearms]] industry and literature, particularly that concerning the accuracy of [[rifle]]s. The industry tends to refer to it as ''minute of angle'' rather than ''minute of arc''. It is popular because 1 MOA [[subtend]]s approximately one [[inch]] at 100 [[yard]]s, a traditional distance on [[Shooting range|target ranges]]. A shooter can easily readjust his rifle [[telescopic sight|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.
Calculating the physical equivalent group size equal to one minute of arc can be done using the equation: equivalent group size = tan(MOA ∕ 60)*distance. In the example previously given and substituting 3600 inches for 100 yards, tan(1 MOA ∕ 60)∙ 3600 inches = 1.0471975511966 inches.
In [[metric units]] 1 MOA at 100 meters = 2.90888208665722 centimeters.
Sometimes, a firearm's accuracy will be measured in MOA. This simply means that under ideal conditions, the gun is capable of repeatedly producing a group of shots whose center points (center-to-center) fit into a circle, the diameter of which can be subtended by that amount of arc. (E.g.: a "1 MOA rifle" should be capable, under ideal conditions, of shooting a 1-inch group at 100 yards, a "2 MOA rifle" a 2-inch group at 100 yards, etc.) Some manufacturers such as [[Weatherby]] and [[Cooper Firearms of Montana|Cooper]] offer actual guarantees of real-world MOA performance.
Rifle manufacturers and gun magazines often refer to this capability as "Sub-MOA", meaning it shoots under 1 MOA. This is typically a single group of 3 to 5 shots at 100 yards, or the average of several groups. If larger samples are taken, i.e. more shots per group, then group size typically increases. <ref>[http://www.bobwheeler.com/guns/GroupStat.pdf Statistical notes on rifle group patterns by Robert E. Wheeler]</ref>
===Cartography===
Minutes of angle (and its subunit, seconds of angle or SOA—equal to a sixtieth of a MOA) are also used in [[cartography]] and [[navigation]]. At [[sea level]], one minute of angle (around a [[great circle]] such as the equator or a [[Meridian (geography)|meridian]]) equals about 1.15 [[mile]]s or 1.86 [[kilometre|km]], approximately one [[nautical mile]] (approximately, because the [[Earth]] is slightly [[Oblate spheroid|oblate]]).
Traditionally positions are given using degrees, minutes, and seconds of angles in two measurements: one for [[latitude]], the angle north or south of the [[equator]]; and one for [[longitude]], the angle east or west of the [[Prime Meridian]]. Using this method, any position on or above the face of the Earth can be precisely given. However, because of the somewhat clumsy base-60 nature of MOA and SOA, many people now prefer to give positions using degrees only, expressed in decimal form to an equal amount of precision. Degrees, given to three decimal places (1/1000 of a degree), give almost as much precision as degrees-minutes-seconds (1/3600 of a degree).
===Property surveying===
Related to cartography, property boundary [[surveying]] using the [[metes and bounds]] system relies on fractions of a degree to describe property lines' angles in reference to [[cardinal directions]]. A boundary is described with a beginning reference point, a cardinal direction followed by an angle and a second cardinal direction, and a linear distance. The boundary runs the specified linear distance from the beginning point, the direction of the distance being determined by rotating the first cardinal direction the specified angle toward the second cardinal direction. For example, "''North 65° 39’ 18” West 85.69 feet''" would describe a property line running from the starting point 85.69 feet in a direction 65° 39’ 18” (or 65.655°) away from north toward the west.
===Astronomy===
The arcminute and arcsecond are also used in [[astronomy]]. Degrees (and therefore arcminutes) are used to measure [[declination]], or angular distance north or south of the [[celestial equator]]. The arcsecond is also often used to describe [[parallax]], due to very small parallax angles, and tiny angular diameters (e.g. Venus varies between 10″ and 60″). The parallax, [[proper motion]] and angular diameter of a star may also be written in milliarcseconds (mas), or thousandths of an arcsecond. The [[parsec]] gets its name from "parallax second", for those arcseconds.
From the Earth the star with the largest [[angular diameter]] (apart from the Sun) is 0.05 arcsecond and this is a red super giant. Due to the effects of atmospheric [[seeing]], ground-based [[telescope]]s will smear the image of a star to an angular diameter of about 0.5 arcsecond; in poor seeing conditions this increases to 1.5 arcseconds or even more.
Space telescopes are not affected by the Earth's atmosphere, but are [[Diffraction limit#Diffraction limit of telescopes|diffraction limited]]; for example the [[Hubble space telescope]] can reach an angular size of stars down to about 0.1". Techniques exist for improving seeing on the ground, for example [[adaptive optics]], which can give images around 0.05 arcsecond on a 10 m class telescope.
===Human vision===
In humans, [[Visual acuity#.22Normal.22 vision|20/20 vision]] is the ability to resolve a spatial pattern separated by a visual angle of one minute of arc.
==References==
{{reflist}}
[[Category:Units of angle|Arcminute]]
[[Category:Firearms]]
[[ast:Minutu sexaxesimal]]
[[da:Bueminut]]
[[de:Bogenminute]]
[[et:Minut (geomeetria)]]
[[es:Minuto de arco]]
[[eu:Minutu sexagesimal]]
[[fr:Sous-unités du degré]]
[[ko:분 (각도)]]
[[it:Primo (geometria)]]
[[he:דקת קשת]]
[[lb:Bouminutt]]
[[nl:Boogminuut]]
[[ja:分 (角度)]]
[[no:Bueminutt]]
[[pl:Minuta kątowa]]
[[pt:Minuto de arco]]
[[sr:Лучни минут]]
[[sv:Bågminut]]
[[ta:பாகைத்துளி]]
[[uk:Мінута]]
[[zh:角分]]