Main Page | See live article | Alphabetical index

Minute of arc

A minute of arc, arcminute, or MOA is a unit of angular measurement which comprises one-sixtieth of a degree. The symbol for one arcminute is 1'.

The minute of arc is a measurement of angle or arc, equal to one sixtieth (1/60) of one degree. Since one degree is defined as one three hundred and sixtieth (1/360) of a circle, 1 MOA is 1/21600 of the amount of arc in a closed circle, or 10800*pi radians. Its usage is limited to those fields which require a handy unit for the expression of very small amounts of arc.

This unit is commonly found in the firearms industry and literature, particularly that concerning high-powered rifles. It is popular because 1 MOA almost exactly subtends one inch at 100 yards, a traditional distance on target ranges. A shooter can easily readjust his or her rifle scope simply by measuring the distance in inches the bullet hole is from the desired impact point, and adjusting the scope that many MOA in the opposite direction. Most target scopes designed for long distances are adjustable in quarter (1/4) or eighth (1/8) MOA 'clicks.' One eighth MOA is equal to approximately an eighth of an inch at 100 yards or one inch at 800 yards.

Sometimes, a firearm will be 'measured' in MOA. This simply means that under ideal conditions, the gun is capable of repeatedly producing a group of shots that 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 and when locked into a vise, of shooting a 1-inch group at 100 yards.) However, ideal performance in a ballistics lab is often very different from real-world results.

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 equals about 1.15 miles or 1.86 km, approximately one nautical mile (approximately, because the Earth is slightly 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, are sufficient to give a position as accurately as with degrees-minutes-seconds.

The subdivision of the minute of arc is the arcsecond.