This is a great article that I found online about MOA:
MOA, or Minute of Angle, is a common measurement for describing various characteristics in rifle scopes. It is most generally used to illustrate the click value for windage and elevation turrets on rifle scopes. The click worth is how much the reticle moves per one click on the turret. Values from 1/8 to 1 MOA are generally experienced. For dot sights, MOA is usually used to describe the dot size and, within the instance of the circledot 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 a couple of inches at 200 yards, 3 inches at 300 yards, etc. The smaller the click worth, the a lot more precise the windage and elevation modifications will be on your rifle scope. This precision could be essential during competitive shooting and for longrange shots. Furthermore, understanding the circle size in circle dot reticles helps make rifle scopes useful for rangefinding.
In our information of MOA, we'll start having a circle. Naturally, a circle is a geometric figure where all points are equidistant from a single point, known as the center. The distance from the center to the circle may be the radius and a segment of the entire circle is called an arc. The circle is divided into 360 degrees and every degree is divided into 60 minutes. Returning to our rifle scopes for a moment, one MOA is 1/60th of one degree.
For our illustration, we'll use a circle having 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 known as a Unit Circle. Utilizing a unit circle makes all the math easy. The circumference of the circle is decided by the formula, a couple of(pi)r, exactly where r is the radius and pi may be the constant worth 3.14. Pi is really one of those infinite decimals that keeps going on and on but we'll stop it at decimal a couple of points for our exercise.
So, our circumference is 2 times 3.14 times 1 or 6.28. Now we wish to determine the length of an arc determined by 1 MOA. So, 6.28/360 degrees is .0174 and we'll divide that by an additional 60 minutes to get .000291. Of course, we don't require 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 .000291 times 100 to get .0291. Easy math right? Now, to convert that to inches we'll multiply it by 36 since you can find 36 inches in a yard. So, .0291 * 36 = 1.0476
When peering through a rifle scope or red dot sight at a target 100 yards away, .0476 is a pretty insignificant amount so we merely rely on our rule of thumb that 1 MOA equals 1 inch at 100 yards.
Source: http://ezinearticles.com/?MOAandAdjustingYourRifleScopes&id=3315444

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