MOA stands for Minute Of Angle. A full circle is divided into 360 degrees and each degree is divided into 60 minutes. Thus, there are 21,600 minutes in a full circle (360 x 60 = 21,600). A minute is a small angle, but it's exactly what's needed for gun sights. A rule of thumb is that changing a sight's elevation setting by 1 minute of angle changes the bullet's impact point by 1 inch at 100 yards. A more exact value and how it's arrived at is shown below:

A circle with a 100 yard radius (distance from the center to the edge) would have a circumference of approximately 628.32 yards or 22,619 inches (100 x 2 x pi = 628.32 {pi is about 3.1416}). Dividing the circumference in inches by the number of minutes in a full circle gives a value of about 1.047 inches (22619 / 21600 = 1.047). Thus, changing a sight's elevation setting by 1 minute of angle changes the bullet's impact point by 1.047 inches at 100 yards.

The size defined by 1 minute of angle increases as range increases. For example, The bullet's impact point would change by 2.094 inches at 200 yards (1.047 x 2) and change by 3.141 inches at 300 yards (1.047 x 3).