Please explain MOA


March 21, 2003, 02:00 PM
Could somebody explain what MOA means, in simple english. For example, when someone says that a rifle is guaranteed "sub 1-MOA at 100 yards" what does that translate to.

Thanks for your patience... rifles are new to me.

If you enjoyed reading about "Please explain MOA" here in archive, you'll LOVE our community. Come join today for the full version!
March 21, 2003, 02:10 PM
Sven, I'm no expert but in navigation you go by the divisions of a circle. There are 360 degrees in a circle, 60 minutes in a degree, and 60 seconds in a minute. So what you are measuring is a fraction of a circle. A minute would be a pie-shaped slice that started as nothing in the center of the circle where the bullet exits your bbl and keeps growing wider the further it goes away from the center. It all goes back to the Babylonians and their base 60 arithmetic, IIRC.

Anyway, at a distance of 100 yards a degree works out to be ~60 inches, a minute ~1 inch. HTH

Mal H
March 21, 2003, 02:24 PM
Sven - MOA is simply a convenient method of describing or assessing the accuracy of a rifle. At 100 yds you could just as easily say that the rifle is guaranteed to make 3 shot groups of 1 inch or less. But, what makes the MOA method better is that it can be translated to different yardages if you know the MOA accuracy at, say, 100 yds. At 200 yds, that same rifle should keep groups in a 2 inch circle, 4 inches at 400 yds, etc. This is not to say that accuracy is a linear concept due to the many variables that enter into it: bullet stability, wind, and the rifle itself. With some rifles which are accurate at up to 300 yds, the accuracy can fall off after that whereas other rifles will hold their accuracy out to 1000 or more yds. The subtle differences in the rifles make the difference.

A mathematical note: There are several methods to determine the actual size of a MOA at any distance. You can use trig functions, but the simplest is to take the circumference of a circle whose radius is the target distance and divide by the numbr of minutes in a circle as BigG noted. 100 yds * 36 inches/yd *2 * PI / 360 deg * 60 min/deg = 3600 * 2 * 3.14159 / 21600 = 1.05 inches in a MOA at 100 yds.

March 21, 2003, 02:26 PM
If you take a circle with a radius of 100 yards and cut a slice of it 1 minute (or 1/60th of a degree) wide, the arc length will be 1.024 inches, which is close enough to round to 1 inch. Hence, a rifle capable of 1 minute-of-angle accuracy will not throw any shots farther than 1" from each other at 100 yards.

The geometry is linear, so you can extrapolate groups at other ranges easily. 1 MOA at 100 yards is 1", so 1 MOA at 200 yards is 2", at 500 yards is 5", at 25 yards is 1/4th in, and so on.

March 21, 2003, 02:58 PM
Adding to what the others have said, MOA Accuracy is the "Mother Of All Accuracy". That's a good thing. :D

March 21, 2003, 09:56 PM
I see from the above that we've got MOA pretty well covered.

I've a good friend in the 1st Marine Expeditionary Unit in the big sandbox right now (Told him if he gets shot... I'll kill him. God bless you Eric) and we were talking about the Barrett M82A1 that his unit were trained on; he said that the M82A1 was more than capable of 'minute of jeep':D

March 21, 2003, 10:00 PM
And for rifles of lesser accuracy:

MOT = Minute Of Torso
MOM = Minute Of Man


March 22, 2003, 12:39 AM
1 MOA (inches) = Distance (yards) / 95.5
1 MOA (inches) = Distance (meters) / 87.3
1 MOA (centimeters) = Distance (yards) / 37.6
1 MOA (centimeters) = Distance (meters) / 34.4

Group size (inches) * 95.5 / Distance (yards) = Size of group in MOA

Group size (inches) * 87.3/ Distance (meters) = Size of group in MOA

Group size (centimeters) * 37.6/Distance (yards) = Size of group in MOA

Group size (centimeters) * 34.4/Distance (meters) = Size of group in MOA

So, 1 MOA is actually:
1.047" at 100 yards.
1.146" at 100 meters.
2.66 cm at 100 yards.
2.91 cm at 100 meters.

A half inch group at 100 yards would be a 0.478 MOA group.
The same size group at 125 meters would be a 0.35 MOA group.

March 22, 2003, 12:46 AM
In most technical fields that use fractions of degrees instead of radians (such as astronomy), the more common term is "arc minute." Minute of Angle/MOA is the way it is more commonly phrased in the shooting world, however.

Since there are pi radians in 180 degrees, one arcminute/MOA equals about 0.03 milliradians.

BTW, one arcminute is the angle that the HOUR hand of a conventional (12-hour) clock moves in two seconds, or the angle the earth spins in 4 seconds. Very small angle!


March 22, 2003, 06:57 PM
here's the formula I use in MS Excel to determine MOA of a given group:


In the case of this exact formula, the group size goes in A4 and the distance in yards goes in B4. Just change the A4 and B4 to whatever cells you want. Copy it & paste it in and it'll start working for you right away. You may have to change the cell references if you have the "R1C1 reference style" set in Excel.


For the technically minded, you can use the trig functions for a right triangle if you take the isoceles triangle formed by the bore and the group size and split it in half longwise to get two right triangles. Do the trig on one to get 1/2 the MOA, and double it. The tangent of the 1/2 grouping angle is opposite (1/2 the group size) over the adjacent (distance in yards). Use arctangent to get the angle, then do the stuff excel requires to convert from radians to minutes of angle, and bam!, there you are.


If you enjoyed reading about "Please explain MOA" here in archive, you'll LOVE our community. Come join today for the full version!