Firearms Minute and second of arc

example ballistic table given 7.62×51mm nato load. bullet drop , wind drift shown both in mil , minute of angle.

the arcminute commonly found in firearms industry , literature, particularly concerning accuracy of rifles, though industry refers minute of angle (moa). popular shooters familiar imperial measurement system because 1 moa subtended sphere diameter of 1.047 inches @ 100 yards (2.908 cm @ 100 m), traditional distance on u.s. target ranges. subtension linear distance, example, @ 500 yards, 1 moa subtended sphere diameter of 5.235 inches, , @ 1000 yards 1 moa subtended sphere diameter of 10.47 inches. since many modern telescopic sights adjustable in half (1/2), quarter (1/4), or eighth (1/8) moa increments, known clicks, zeroing , adjustments made counting 2, 4 , 8 clicks per moa respectively.

for example, if point of impact 3 inches high , 1.5 inches left of point of aim @ 100 yards (which instance measured using spotting scope calibrated reticle), scope needs adjusted 3 moa down, , 1.5 moa right. such adjustments trivial when scope s adjustment dials have moa scale printed on them, , figuring right number of clicks relatively easy on scopes click in fractions of moa. makes zeroing , adjustments easier:

to adjust  ⁄2 moa scope 3 moa down , 1.5 moa right, scope needs adjusted 3 × 2 = 6 clicks down , 1.5 x 2 = 3 clicks right
to adjust  ⁄4 moa scope 3 moa down , 1.5 moa right, scope needs adjusted 3 x 4 = 12 clicks down , 1.5 × 4 = 6 clicks right
to adjust  ⁄8 moa scope 3 moa down , 1.5 moa right, scope needs adjusted 3 x 8 = 24 clicks down , 1.5 × 8 = 12 clicks right

another common system of measurement in firearm scopes milliradian. zeroing mil based scope easy users familiar base ten systems. common adjustment value in mil based scopes 1/10 mil (which approximates  ⁄3 moa).

to adjust 1/10 mil scope 0.9 mil down , 0.4 mil right, scope needs adjusted 9 clicks down , 4 clicks right (which equals approximately 3 , 1.5 moa respectively).

one thing aware of moa scopes, including higher-end models, calibrated such adjustment of 1 moa on scope knobs corresponds 1 inch of impact adjustment on target @ 100 yards, rather mathematically correct 1.047 . commonly known shooter s moa (smoa) or inches per hundred yards (iphy). while difference between 1 true moa , 1 smoa less half of inch @ 1000 yards, error compounds on longer range shots may require adjustment upwards of 20-30 moa compensate bullet drop. if shot requires adjustment of 20 moa or more, difference between true moa , smoa add 1 inch or more. in competitive target shooting, might mean difference between hit , miss.

the physical group size equivalent m minutes of arc can calculated follows: group size = tan(m/60) × distance. in example given, 1 minute of arc, , substituting 3,600 inches 100 yards, 3,600 tan(1/60) ≈ 1.047 inches. in metric units 1 moa @ 100 meters ≈ 2.908 centimeters.

sometimes, precision firearm s accuracy measured in moa. means under ideal conditions i.e. no wind, match-grade ammo, clean barrel, , vise or benchrest used eliminate shooter error, gun capable of producing group of shots center points (center-to-center) fit circle, average diameter of circles in several groups can subtended amount of arc. example, 1 moa rifle should capable, under ideal conditions, of shooting average 1-inch groups @ 100 yards. higher-end rifles warrantied manufacturer shoot under given moa threshold (typically 1 moa or better) specific ammunition , no error on shooter s part. example, remington s m24 sniper weapon system required shoot 0.8 moa or better, or rejected.

rifle manufacturers , gun magazines refer capability sub-moa, meaning shoots under 1 moa. means single group of 3 5 shots @ 100 yards, or average of several groups, measure less 1 moa between 2 furthest shots in group, i.e. shots fall within 1 moa. if larger samples taken (i.e., more shots per group) group size typically increases, average out. if rifle 1 moa rifle, 2 consecutive shots land on top of each other land 1 moa apart. 5 shot groups, based on 95% confidence rifle shoots 1 moa can expected shoot groups between 0.58 moa , 1.47 moa, although majority of these groups under 1 moa. means in practice if rifle shoots 1-inch groups on average @ 100 yards shoots group measuring 0.7 inches followed group 1.3 inches not statistically abnormal.

the metric system counterpart of moa milliradian or mil, being equal 1 1000th of target range, laid out on circle has observer centre , target range radius. number of mils on full such circle therefore equal 2 × π × 1000, regardless target range. therefore, 1 moa ≈ 0.2908 mil. means object spans 1 mil on reticle @ range in meters equal object s size in millimeters (e.g. object of 100 mm @ 1 mrad 100 meters away). there no conversion factor required, contrary moa system. reticle markings (hashes or dots) spaced 1 mil apart (or fraction of mil) collectively called mil reticle. if markings round called mil-dots.

in table below conversions mil metric values exact (e.g. 0.1 mil equals 1 cm @ 100 meters), while conversions of minutes of arc both metric , imperial values approximate.

comparison of milliradian (mil) , minute of arc (moa).

(values in bold face exact. mil fractions given in tenths, more convenient practical use.)

1′ @ 100 yards equals 22619/ 21600 = 1.04717593 in ≈ 1.047 inches
1′ ≈ 0.291 mil (or 2.91 cm @ 100 m, approximately 3 cm @ 100 m)
1 mil ≈ 3.44′, 1/10 mil ≈ 1/3′
0.1 mil equals 1 cm @ 100 m, or approximately 0.36 inches @ 100 yards




^ mann, richard (2011-02-18). mil, moa or inches? . shooting illustrated. retrieved 2015-04-13. 
^ wheeler, robert e. statistical notes on rifle group patterns (pdf). archived original (pdf) on 26 september 2006. retrieved 21 may 2009. 
^ bramwell, denton (january 2009). group therapy problem: how accurate rifle? . varmint hunter. 69. retrieved 21 may 2009. 
^ dexadine ballistics software - ballistic data shooting , reloading