Can someone explain MOA to me?

DickWanner

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I had a friend who asked me to explain minute-of-aim to me and honsetly I have no clue what it is. Can someone either explain it to me or direct me to a link that can? Thanks.
 
from Wikipedia:

Firearms

This unit is commonly found in the firearms industry and literature, particularly that concerning the accuracy of rifles. The industry tends to refer to it as minute of angle rather than minute of arc. It is popular because 1 MOA subtends approximately one inch at 100 yards, a traditional distance on target ranges. A shooter can easily readjust his rifle scope by measuring the distance in inches the bullet hole is from the desired impact point, and adjusting the scope that many MOA in the same direction. Most target scopes designed for long distances are adjustable in quarter (¼) or eighth (⅛) MOA "clicks". One eighth MOA is equal to approximately an eighth of an inch at 100 yards or one inch at 800 yards.

Calculating the physical equivalent group size equal to one minute of arc can be done using the equation: equivalent group size = tan(MOA ∕ 60)*distance. In the example previously given and substituting 3600 inches for 100 yards, tan(1 MOA ∕ 60)∙ 3600 inches = 1.0471975511966 inches.

In metric units 1 MOA at 100 meters = 2.90888208665722 centimeters.

Sometimes, a firearm's accuracy will be measured in MOA. This simply means that under ideal conditions, the gun is capable of repeatedly producing a group of shots whose center points (center-to-center) fit into a circle, the diameter of which can be subtended by that amount of arc. (E.g.: a "1 MOA rifle" should be capable, under ideal conditions, of shooting a 1-inch group at 100 yards, a "2 MOA rifle" a 2-inch group at 100 yards, etc.) Some manufacturers such as Weatherby and Cooper offer actual guarantees of real-world MOA performance.

Rifle manufacturers and gun magazines often refer to this capability as "Sub-MOA", meaning it shoots under 1 MOA. This is typically a single group of 3 to 5 shots at 100 yards, or the average of several groups. If larger samples are taken, i.e. more shots per group, then group size typically increases. [2]
 
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In case it's not apparent from the previous two explanations where the term "minute" comes from . . .

If you're familiar with a compass, you know that a complete circle is divided into 360 degrees. So, for example, if you face north and then turn clockwise to face east, you've turned through an arc of 90 degrees (one quarter of 360). Each of those degrees of arc is further divided into 60 minutes (no relation to "minutes" of time), which is where the term minute of arc (or angle - for our purposes the terms are interchangeable and both abbreviate to MOA) comes from. Each of the minutes can be subdivided into 60 seconds, but for purposes of describing the accuracy of sporting firearms that degree of precision isn't necessary.

It's a fortunate coincidence that a movement through an arc of of 1 MOA at the center of a circle happens to translate to approximately 1" of movement at 100 yards, which makes it easy to remember, but it wasn't set up to be that way.
 
Note also that the description of a rifle's accuracy also depends significantly on the number of shots included in a standard group. Since the shots are subject to random influences that affect trajectory, more shots will always mean a larger group size. This is a simple statistical reality and is true even if one ignores or compensates for the effects of heating and (for really hot rounds) erosion on the barrel. More rounds can only make a group larger, never smaller.

Ken
 
More rounds can only make a group larger, never smaller.

Excellent point, one practical application of which is that groups from the so-called one MOA rifle will eventually become larger than 1" as additional shots are fired. Also, 3 and 5-shot groups can't be compared to each other using the group size.

I like to play around with load development for several rifles, and figured out a long time ago that group size is relatively meaningless as a true indicator of accuracy (precision, really, as accuracy is a function of adjusting the scope correctly). I have a little Excel spreadsheet I wrote that allows fair comparisons for any group size. It calculates the geometric center of the group, then the deviation for each shot, and finally the average deviation for the entire group, along with a few other stats.
 
For years the military used Mean Radius but I believe they are now using a slightly different method for some of their more accurate ammunition and are obtaining an average vertical and an average horizontal spread. Alliant Techsystems that runs LC has a product brochure on their website that gives the accuracy of the products they provide the government.

B
 
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