In firearms speak, an MOA (minute of angle) is defined as: the change of distance from the point of aim equivalent to 1/60th of 1 degree of angle.

The distance covered by a minute of angle is dependent upon the distance to the target. However, the change is linear. If you know what an MOA is at one distance, you can use the ratio of the distances to calculate the MOA of a different distance.

As an example, an MOA at 100 yards is just over an inch, as shown in the calculations below. Most people round it off to an inch, for simplicity of calculation. Therefore, at 50 yards, an MOA equals half an inch.  At 200 yards, an MOA equals two inches.

The triangle below depicts the definition of a MOA:

The ‘X’ side of the triangle is the distance to the target.

The ‘Y’ side is one minute of angle when angle A equals 1/60th of 1 degree (1/60 = 0.016666667).

Using trigonometry, we find that the tangent of angle A, multiplied by the distance X, equals Y.

In the case of 100 yards, the calculation is :

tan 0.016666667 (degrees) * 100 (yards) = 1 MOA

0.000290888222688 * 100 (yards) = 1 MOA

0.029088822268808 (yards) = 1 MOA

0.029088822268808 (yards) * 36 (inches/yard) = 1.04719760167709

1 MOA = 1.04719760167709 inches