MOA, or Minute of Angle, is a common measurement for describing different attributes in Rifle Scopes and Red Dot Sights. It is most generally used to describe the click value for windage and elevation turrets on rifle scopes. The click value is how much the reticle moves per one click on the turret. Values from 1/8 to 1 MOA are generally encountered. For dot sights, MOA is usually used to describe the dot size and, in the instance of a circle-dot reticle, the circle size as well.
As a general rule of thumb, we say that 1 MOA equals 1 inch at 100 yards. By extension, that would be 2 inches at 200 yards, 3 inches at 300 yards, etc. The smaller the click value, the more precise the windage and elevation adjustments will be on your rifle scope. This precision can be important during competitive shooting and for long-range shots. Additionally, understanding the circle size in circle dot reticles helps make rifle scopes useful for rangefinding.
To understand exactly what MOA is, we'll have to delve into some high school geometry. Ah, so you see. After all these years, there is some practical value to those long hours in geometry class.
In our description of MOA, we'll start with a circle. Of course, a circle is a geometric figure where all points are equidistant from a single point, called the center. The distance from the center to the circle is the radius and a segment of the entire circle is called an arc. The circle is divided into 360 degrees and each degree is divided into 60 minutes. Returning to our rifle scopes for a moment, one MOA is 1 / 60th of one degree.
For our example, we'll use a circle with a radius of one. Let's say it's one yard. If you paid attention in that geometry class, you'll remember that a circle with a radius of one is called a Unit Circle. Using a unit circle makes the math easy. The circumference of a circle is determined by the formula, 2 (pi) r, where r is the radius and pi is the constant value 3.14. Pi is actually one of those infinite decimals that keeps going on and on but we'll stop it at decimal 2 points for our exercise.
So, our circumference is 2 times 3.14 times 1 or 6.28. Now we want to determine the length of an arc determined by one MOA. So, 6.28 / 360 degrees is 0.0174 and we'll divide that by another 60 minutes to get 0.000291. Of course, we do not need rifle scopes to shoot anything one yard away, but we can calculate the length of an arc at 100 yards. To do so, we'll simply multiply the 0.000291 times 100 to get 0.0291. Easy math right? Now, to convert that to inches we'll multiply it by 36 since there are 36 inches in a yard. So, 0.0291 * 36 = 1.0476
When peering through a rifle scope or red dot sight at a target 100 yards away, 0.0476 is a pretty insignificant amount so we simply rely on our rule of thumb that 1 MOA equals 1 inch at 100 yards.