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. Its subdivision arcsecond comprises one sixtieth of an arcminute.

Since one degree is defined as one three hundred and sixtieth (1/360) of a circle, 1 arcminute is 1/21600 of the amount of arc in a closed circle, or (π/10800) radians. Its usage is limited to those fields which require a handy unit for the expression of very small amounts of arc, such as astronomy.

The symbol for marking the arcminute is the prime (′) (U+2032, ′); the symbol for the arcsecond is the double prime (″) (U+2033, ″). One and a half arcminutes would be 1′30″. The abbreviations arcmin and arcsec, or less commonly the (double) prime with an arch over it ( $\hat {'}$ and $\hat {$ }), or amin and asec, are also used. The phrase arcsec'' in this context should not be confused with the inverse trigonometric function arc secant, which has the same abbreviation.

1 complete circle = 360° = 21,600′ = 1,296,000″
1″ = 1/60 ′ = 1/3600 ° = 1/1296000 of a complete circle

Uses

Firearms

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. 100 yards or multiples thereof are traditional distances on target ranges. (The precisely-calculated value to five digits is 1.0472 inches, which is within experimental error variation from simply assuming 1 inch.) 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 on the target, 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.

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 equals about 1.15 miles or 1.86 km, approximately one nautical mile (approximately, because the Earth is slightly oblate). In humans, the ability to resolve a spatial pattern separated by a visual angle of one minute of arc is considered normal visual acuity. 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 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, give almost as much accuracy as degrees-minutes-seconds.

In right ascension and longitude, the linear size of the degree (and therefore arcmin and arcsec) changes with how far you are from the equator. As opposed to a degree of latitude, which always corresponds to about 111 km (69 mi), a degree of longitude corresponds to a distance from 0 to 111 km: it is 111 km times the cosine of the latitude, when the distance is laid out on a circle of constant latitude; if the shortest distance, on a great circle were used, the distance would be even a little less.

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

Similarly to cartography above, astronomy also uses the arcminute and arcsecond. Also the arcsecond is used to give values of seeing, sizes of objects on the sky, field of view of telescopes, or practically any angular distance.

In the equatorial coordinate system, astronomers typically measure Declination in degrees, arcminutes and arcseconds. The other coordinate, Right Ascension (RA), is usually measured in units of time: one circle comprises 24 hours, or $24 \times 60$ minutes or $24 \times 3600$ seconds. RA minutes and seconds are not to be confused with Declination arcminutes and arcseconds, as they are of a different size. Angular sizes are measured in degrees (and its subtensions) regardless of whether measuring in an East-West, North-South, or other direction.

Units of angle

Gourt Home::Gourt :: Minute of arc

Uses

Firearms

Cartography

Property Surveying

Astronomy