Firearms

The arcminute is commonly found in the firearms industry and literature, particularly concerning the accuracy of rifles, though the industry refers to it as minute of angle. It is especially popular with shooters familiar with the Imperial measurement system because 1 MOA subtends approximately one inch at 100 yards, a traditional distance on target ranges. Since most modern rifle scopes are adjustable in half (1⁄2), quarter (1⁄4), or eighth (1⁄

MOA increments, also known as clicks, this makes zeroing and adjustments much easier. For example, if the point of impact is 3" high and 1.5" left of the point of aim at 100 yards, the scope needs to be adjusted 3 MOA down, and 1.5 MOA right. Such adjustments are trivial when the scope's adjustment dials have an MOA scale printed on them, and even figuring the right number of clicks is relatively easy on scopes that click in fractions of MOA.

One thing to be aware of is that some scopes, including some higher-end models, are calibrated such that an adjustment of 1 MOA corresponds to exactly 1 inch, rather than 1.047". This is commonly known as the Shooter's MOA (SMOA) or Inches Per Hundred Yards (IPHY). While the difference between one true MOA and one SMOA is less than half of an inch even at 1000 yards,[4] this error compounds significantly on longer range shots that may require adjustment upwards of 20-30 MOA to compensate for the bullet drop. If a shot requires an adjustment of 20 MOA or more, the difference between true MOA and SMOA will add up to 10 inches or more. In varmint hunting or competitive target shooting, this can easily mean the difference between a hit and a miss.

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 3,600 inches for 100 yards, 3,600 tan(1 MOA⁄60) inches = 1.047 inches.

In metric units 1 MOA at 100 meters = 2.908 centimeters.

Sometimes, a precision firearm's accuracy will be measured in MOA. This simply means that under ideal conditions i.e. no wind, match-grade ammo, clean barrel, and a vise or a benchrest used to eliminate shooter error, the gun is capable of producing a group of shots whose center points (center-to-center) fit into a circle, the average diameter of circles in several groups can be subtended by that amount of arc. For example, a 1 MOA rifle should be capable, under ideal conditions, of shooting an average 1-inch groups at 100 yards. Most higher-end rifles are warrantied by their manufacturer to shoot under a given MOA threshold (typically 1 MOA or better) with specific ammunition and no error on the shooter's part. For example, Remington's M24 Sniper Weapon System is required to shoot 0.8 MOA or better, or be rejected.

Rifle manufacturers and gun magazines often refer to this capability as sub-MOA, meaning it shoots under 1 MOA. This means that a single group of 3 to 5 shots at 100 yards, or the average of several groups, will measure less than 1 MOA between the two furthest shots in the group, i.e. all shots fall within 1 MOA. If larger samples are taken (i.e., more shots per group) then group size typically increases, however this will ultimately average out. If a rifle was truly a 1 MOA rifle, it would be just as likely that two consecutive shots land exactly on top of each other as that they land 1 MOA apart. For 5 shot groups, based on 95% confidence a rifle that normally shoots 1 MOA can be expected to shoot groups between 0.58 MOA and 1.47 MOA, although the majority of these groups will be under 1 MOA. What this means in practice is if a rifle that shoots 1" groups on average at 100 yards shoots a group measuring .7" followed by a group that is 1.3" this is not statistically abnormal.[5][6]

[edit]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 along the equator or a meridian equals about 1.86 kilometres / 1.16 miles, approximately one nautical mile. A second of angle, one sixtieth of this amount, is about 30 meters or roughly 100 feet. The exact distance varies along meridians because the shape of the Earth is slightly oblate.

Positions are traditionally given using degrees, minutes, and seconds of angles for latitude, the angle north or south of the equator, and for longitude, the angle east or west of the Prime Meridian. Any position on or above the Earth's reference ellipsoid can be precisely given with this method. However, because of the somewhat clumsy base-60 nature of minutes and seconds, positions are frequently expressed in fractional degrees only, expressed in decimal form to an equal amount of precision. Degrees given to three decimal places (1⁄1,000 of a degree) have about 1⁄4 the precision of degrees-minutes-seconds (1⁄3,600 of a degree) and specify locations within about 120 meters or 400 feet.