Minute of Arc/Angle (MOA)

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 (1⁄8) 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, 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 1 inch or more. In competitive target shooting, this might mean the difference between a hit and a miss.

The physical group size equivalent to m minutes of arc can be calculated as follows: group size = tan(m⁄60) × distance. In the example previously given, for 1 minute of arc, and substituting 3,600 inches for 100 yards, 3,600 tan(1⁄60) = 1.047 inches. In metric units 1 MOA at 100 meters = 2.908 centimeters.

Use in Firearms Training
When comparing various shooting styles/stances, and a shooter's level of proficiency, it behooves shooters to use MOA as a measure of their accuracy, since it provides both an understanding of distance and grouping in a very small, easily abbreviated format. It's much easier to write 15~MOA (where ~ is an approximation) than "8 inch group at 50 yards." When training with firearms, it is always important to try to keep MOA as low as possible; as this is an indicator of the actual accuracy of a shooter's aim; regardless of range.

An Easy MOA Calculator

Use in Determining a Weapons Inherent Accuracy
Most shooters will refer to the group size of a gun, with all other variable removed (ie; on a  bench, secured) as the inherent accuracy of a firearm.

A shooter will fire a group at a particular Point Of Aim (POA), and the resulting group center or mean Point Of Impact (POI) will usually be offset somewhat from the intended POI or the POA. This offset is an indicator of the accuracy of the rifle, since it is this bias that must either be removed using the scope adjustments, or by applying an offset “hold” when firing a shot. Assuming that the scope can be adjusted appropriately, or the shooter can consistently hold off the POA by the necessary amount, then this will be the most probable POI for any given shot. This accuracy can be affected by many variables, such as variations in the charge weight, ignition and burning rate, bullet consistency, barrel and action heating, and wind. We will ignore these effects for the remainder of this article.

Once a given POI is established, a group of shots will be distributed around the mean POI in a (usually) random fashion. The size of this distribution is the repeatability of the rifle. This is what has been described above as the group size. An important assumption here is that we are ignoring many real-world effects such as shot-to-shot velocity variations (causing a vertical dispersion which is added to the random distribution), and that of wind (causing a horizontal dispersion which is added to the random distribution), as well as many others.

A truly accurate rifle will have a precise and repeatable POI and a small distribution of shot impacts around that point.