MOA Calculator — Minute of Angle

A Minute of Angle is an angular measurement equal to 1/60th of a degree. In practical terms, one MOA creates a spread that increases proportionally with distance. The fundamental mathematical formula used is:

Spread = MOA × (pi / 10800) × Distance

Because the ratio of an arc to its radius depends on radians, dividing pi by 10800 converts the minute of angle into a linear scale factor. As a result, once you know two variables—such as your target distance and group spread—you can easily compute the exact MOA value.

Imagine you are at a shooting range testing a new rifle setup. You fire a 3-shot group at a target placed 200 yards away, resulting in a physical spread measuring 4.188 inches. To find out what MOA your group represents, we apply our formula:

4.188 = MOA × (3.14159 / 10800) × 200

First, compute the angular coefficient: (3.14159 / 10800) × 200 ≈ 0.058178. Next, divide your spread by this coefficient: MOA = 4.188 / 0.058178 ≈ 2.0 MOA. This means your rifle group spans exactly 2 minutes of angle at that distance.

Always ensure your distance and spread measurements use the same unit system (such as inches or centimeters) before running the calculation to avoid scaling errors. Remember that MOA scales linearly; an adjustment that moves your point of impact by 1 inch at 100 yards will move it by 2 inches at 200 yards, and 5 inches at 500 yards. When measuring physical groups on paper, always measure from the center of the bullet holes for maximum accuracy.