Minute of angle (MOA) is a unit of angular measurement, like degree or radian. It is a subdivision of a degree, 1/60th. Just as there are 60 minutes in 1 hour, there are 60 minutes in 1 degree. Minutes of angle are used as a common unit to describe sight corrections in long range shooting.

Caveat: I’m not writing from a position of authority. I picked up a new hobby, and writing short articles is a way to document my learning, and encourage further study.

The rule of thumb is, 1MOA equates to 1 inch per 100 yards. So if you were shooting at 300 yards, and the bullet impact was 3 inches to the right of centre, you would compensate by adjusting your sight by 1MOA to the left, and take another shot anticipating a more accurate impact.

Dusting off some trigonometry from high school, we can generate a slightly more precise table of MOA conversions for common shooting distances. If we assume:

  • the line of aim is at the target centre
  • the target is perpendicular to the line of aim

then we can represent the scenario with a diagram.

TrigonometryTriangle

  • the shooter’s eye is at A
  • bullet impact is at B
  • the target centre is at C
  • the line of aim is AC
  • the distance to target is b
  • we suppose the angle BAC is equal to 1MOA
  • solve for a

Trigonometry tells us

      tan(Ø) = opposite / adjacent
    tan(BAC) = a / b
tan(BAC) * b = a

Converting as needed to ensure suitable units.

1MOA distance conversions
Distance (yd) 1MOA @ distance (in) 1MOA @ distance (mm)
100 1.0 27
200 2.1 53
300 3.1 80
400 4.2 106
500 5.2 133
600 6.3 160
700 7.3 186
800 8.4 213
900 9.4 239
1000 10.5 266

So the rule of thumb is pretty good, but the further you are from your target, a larger error starts to appear.

For competition long range shooting the targets have codified dimensions - see chapter 13 of the Standard Shooting Rules published by the National Rifle Association of Australia. If you know how big the target rings are, given a point of impact, you can estimate the vertical and horizontal sight adjustments required to produce more accurate shots. Sights on precision rifles often adjust by fractions of a minute - third, quarter, even eighth-minute increments, to enable very fine adjustments at long range.