Minute of arc
A minute of arc, arcminute, or MOA is a unit of angular measurement, equal to one sixtieth (1/60) of one degree. [1] 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. It is used in those fields which require a unit for the expression of small angles, such as marksmanship.
Contents |
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 written 1′ (or 1'). It is also abbreviated as arcmin or amin or, less commonly, the prime with a circumflex over it ( î ).
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) 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.
| unit | value | symbol | abbreviations | conversion |
|---|---|---|---|---|
| degree | 1/360 circle | ° | deg | 17.4532925 mrad |
| arcminute | 1/60 degree | ′ (prime) | arcmin, amin, î, MOA | 290.8882087 µrad |
| arcsecond | 1/60 arcminute | ″ (double prime) | arcsec | 4.8481368 µrad |
| milliarcsecond | 1/1000 arcsecond | mas | 4.8481368 nrad |
Practical uses
Firearms
This unit is commonly found in the firearms industry and literature, particularly that concerning the accuracy of rifles. The industry tends to refer to it as minute of angle rather than minute of arc. It is popular because 1 MOA subtends approximately one inch at 100 yards, a traditional distance on target ranges. A shooter can easily readjust his 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.
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 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. [2]
Vision
In humans, 20/20 vision is the ability to resolve a spatial pattern separated by a visual angle of one minute of arc.
Minute of angle
Minute of angle (MOA) is the common term for a ballistic round's deviation from its initial heading due to gravity and/or the effect of air resistance on velocity. Informally known as a "Bullet's Trajectory" or "the rainbow effect". Long range weapons must account for this effect because a fired round falls at an exponential rate Weapons such as large caliber rifles use scopes with adjustments for distance and windage.
