What is moa???


October 30, 2003, 06:15 PM
Can someone tell me what "moa" stands for, relating to rifle accuracy? Thanks!

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October 30, 2003, 06:19 PM
1moa = 1 minute of angle its a engineering term I think.
It means 1 inch at 100 yards.

October 30, 2003, 06:20 PM
minute of angle.


October 30, 2003, 06:32 PM
If my math is right, it's 1.044 inches at 100 yards.

Personally, I prefer mills.

Bill Hook
October 30, 2003, 06:44 PM
1/21600th of a circle. If you know your circumference (=2Pi*r), then divide that by 21600.

October 30, 2003, 07:25 PM
Easier to just do a trig function with the base in inches(or 100 yards remembering that the output will be in yards and needs to be converted to inches) or whatever distance you're shooting.

One minute being 1/60th of a degree, 100 yards in inches being (100x12x3) or 3600 inches, using the tangent function of 1/60 of a degree and multiplying by 3600 winds up with MOA equalling right about 1.047 inches at 100 yards.

Moving over to the Mil-Dot system for range estimation, it's a similar but easier system. The mil-dot system is based off of a system of radian measure, from what I can gather the "mil" doesn't stand for military but rather it is a metric unit description where "mil" means 1/1000. A radian is an arc about the circumfrence of a circle that is equal in length to the radius. At 100 yards a radian would also be equal to 100 yards. A "mil-radian" would be equal to 1/1000 of a radian at whatever the distance, say we're looking for a mil-radian at 100 yards then we're going to be dealing with 1/1000 of our 100 yard value. Remembering back to what our inch value is for 100 yards we have 3600 inches per 100 yards, to figure out the mil-radian in inches we simply take 1/1000 of 3600 inches and it is a simple 3.6 inches at 100 yards. The Mil-Dot reticle is based on this concept of mil-radians and has dot spacing to reflect those values and works wonderfully in calculating/esimating range.

Shooting sports can be a fun and practical application of math, usually it doesn't get too terribly much more complex than just using some simple trig. Now calculating hit probability at a specific distance given the best possible accuracy out of shooter/rifle combo as well as target size, that enters into the realm of statistics and probability which I'm not all that comfortable with.

Jim K
October 30, 2003, 07:54 PM
Great responses. But for all practical purposes, one MOA is one inch at 100 yards. This is pure coincidence, of course, but is useful shorthand for discussing accuracy.

So 1 minute of Angle is about 2 inches at 200 yards, 3 inches at 300 yards, and so on, though that .047 adds up. So a rifle that shoots into one inch at 100 yards, will shoot into 10 inches at 1000? Probably not, since too many other factors enter in, such as the effects of wind, bullet shape, drift, etc.


October 30, 2003, 08:54 PM
Think of it this way: a circle (no matter how big or how small) is divided up into 360 degrees, and each of those degrees is further divided up into 60 minutes (and past that, each of those minutes is divided up into 60 seconds). If you're standing at the center of a circle with a radius of 100 yards, and you fire your rifle at a target on the edge of that circle, and all of your shots hit within 1.044", they've all hit within one "minute of angle" or 1 MOA.

October 30, 2003, 10:04 PM
As long as we're being pedantic, a mill isn't 1000th of a radian, it's 1/6400th of a circle. There are 2*pi*1000, or 6223.2 millirads in a circle. The military rounds that to 6400, for reaons I have never quite understood.

October 31, 2003, 05:05 PM
It probably isn't a coincidence that they went with rounding up to 6400, would have to push numbers a bit but it may very well wind up having something to do with the swept area of a radian being devisible by 1000 for a mil-radian.

Care to show the math for calculating the swept area of a mil-rad at 100 yards using the unit circle and radian measure?

Not that I don't believe you, I know that radian measure and milrads have their uses for artillery and many other aspects but I think it's just too clean and simple that for range finding with a mil-dot reticle that 1 radian is devisible by 1000 and will output a proper answer.

Going out and looking around, it seems there are multiple answers to what a defintion of a "mil-radian" is depending on where you are and what your specialty is. Artillery shell chuckers will expect one thing while a nut behind the butt of a rifle is gonna expect something else. Lookin around I found these two sights, the snipercountry.com site is in keeping with how I've done it for as long as I've been shooting and how I came to understand the system being used.

First to explain some of the military changing of the mil-radian system as based on a 2PI-radian circle and the second which explains radians as a function of swept area being equal to that of the radius.



Simply stated, it looks like we are both right. :)

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