Minute of Angle (MOA)


September 4, 2003, 06:28 PM
Ok I hear about 1 MOA... or our rifle is guaranteed 1/2 MOA...

WHAT does MOA (Minute of Accuracy) mean for me? Cuz' right now it does not mean ANYTHING to me.

Thanks, RTFM.

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September 4, 2003, 06:37 PM
Acutually....MOA means Minute Of Angle.

A good explination can be found here:


Mal H
September 4, 2003, 06:42 PM
Here's another good thread on the subject: http://www.thehighroad.org/showthread.php?s=&threadid=18353

Almost everytime that subject comes up, the thread takes a header into either nonsense or Math 702. It never fails. :D

September 4, 2003, 08:11 PM
Both good links.
Quicky is an inch at 100 yds. That works just fine.


September 5, 2003, 07:51 AM
Ok starting to make a dent in my head.

Thanks for the links.

September 5, 2003, 12:02 PM
I always thought it stood for "Minute of ATM" or "Minute of Alley" as in accuracy of my J Frame at 2 meters at 10pm... :)

or in reference to my 10/22.. minute of squirrel :)

now for the math

Minute of angle (MOA) refers loosely by shooters as an inch at 100 yards. It is more accurately, the distance of a line that is made from point A to point B of an angle of one minute of one degree at a distance of 100 yards. Sounds confusing? It really isn't. Take a circle whose radius is 100 yards around your shooting bench. This is also the distance at which you are shooting, muzzle to target. Now that we have found out the circle's diameter by multiplying the radius (100 yards) by 2, this gives us 200 yards. Next, we multiply the diameter (200 yards) by (3.14159 26536) and this is equal to the circumference of the circle in yards (628.31853072 yards). Multiply the circle in yards by 3 to get the circumference of the circle in feet (1884.95559216 ft.) and multiply the circle in feet by 12 to get the circumference of the circle in inches (22619.4671058465).

circumference (in inches) = 2 * r * * (3 * 12)
circumference (in inches) = 2 * 100 yards * 3.14159 26536 * (3' * 12")
circumference (in inches) = 200 yards * 3.14159 26536 * (3' * 12")
circumference (in inches) = 628.31853072 yards * (3' * 12")
circumference (in inches) = 1884.95559216 feet * 12"
circumference (in inches) = 22619.46710592 inches

A circle is divided into 360 evenly spaced marks called degrees, each degree is divided into 60 evenly spaced marks called minutes, and each minute is divided into 60 evenly spaced marks called seconds. To get the total minutes in a circle multiply 360 by 60 and that gives us 21600 minutes.

Now we divide the circumference of the circle in inches (22619.4671058465) by the minutes of a circle (21600) and we get the inches in each minute of angle at a distance of 100 yards and it is 1.0471975511966 or rounding off 1.0472 inches. The equation for this is:

MOA = * (yardage * 2 * 3 * 12) ÷ (360 * 60)
MOA = * (yardage * 2 * 3 * 12) ÷ 21600
MOA = * (yardage * 72) ÷ 21600
MOA = yardage * 226.194671058465 ÷ 21600
MOA = yardage * 0.010471975511966

Replacing the yardage with 100, we have 1.0471975512 inches at 100 yards or more commonly called 1 inch at 100 yards or MOA.By replacing the distance of 100 yards with whatever distance you are shooting at will give you the MOA at that yardage. If you prefer it to be in meters the equation will be * (meters * 2 * multiplier (100)) ÷ 21600 and the multiplier of 100 turns the answer from meters into centimeters. If we wanted the answer to be in millimeters the multiplier would be 1000. Remember that one inch is equal to 2.54 centimeters and there is 12 inches per foot and 3 feet per yard and there are 100 centimeters in a meter. So, 100 ÷ 2.54 will equal 39.3700787401575 inches per meter and that is 3.28083989501312 feet per meter and that make a 100 meters to be 328.083989501312 feet and that comes out to be 109.361329833771 yards in a 100 meters. Now, lets work a problem out in centimeters:

MOA = 3.14159 26536 * (100m * 2 *100) ÷ 21600 = 3.14159 26536 * (20000cm) ÷ 21600
MOA = 62831.8530717959cm ÷ 21600
MOA = 2.90888208665722...cm.

For a millimeter you can work this one out but the answer should be 29.0888208665722...mm. If you got that answer you understand MOA and the metric system.

September 5, 2003, 03:20 PM
heh...i'm gonna paste the above post into something i can print out and review later.
i've been meaning to ask this very question, but didnt want to sound like a huge noob. but now it makes sense.

Steve Smith
September 5, 2003, 04:14 PM
You guys have got to start using the search feature!

September 5, 2003, 05:04 PM
SpaceManSpiff, that's what I thought too, but you know what.
A) I'm flame retardant
B) I believe folks around here are good people. That's why I come her soooooooo much. I learn, and I am not afraid to ask even the noob questions. We all had to learn it some time. Might as well be here.

Steve, I tried the server was sooooo slow and the return was marginal.


Steve Smith
September 5, 2003, 05:11 PM
Steve, I tried the server was sooooo slow and the return was marginal.

An acceptable excuse. ;) We're working on it.

Dave R
September 5, 2003, 06:04 PM
I prefer the definition "2-inch groups at 200 yards".

Sounds the same as 1" groups at 100 yards, but pratical experience says its a more difficult standard. More wind variation? Minute variation in the earth's gravity?

I dunno. But 2 at 200 seems a little tricker than 1 at 100.

One o' these days I'll start working on 3" at 300 yards.

September 6, 2003, 01:15 AM
Okay, here's my question. Ignore the little tiny details, and just assume that one MOA equals one inch at 100 yards. If you place your one-MOA rifle in a perfect Ransom rest, and perfectly aim it at a tiny dot 100-yards away, will your groups be: (1) no more than 1/2 inch from the dot, or (2) no more than 1 inch from the dot? I assume it's the former (i.e., no more than 1/2 inch from the dot), but I've never heard the question answered this way.

September 6, 2003, 01:28 AM
Former. Sorta.
If your group centers on the dot.
One MOA group will have centers of the widest spread holes one inch apart.


Mal H
September 6, 2003, 10:16 AM
Sam's right.

To further clarify a bit - the MOA accuracy of a firearm has little to nothing to do with the sights on it. In your example, the group will be centered around the dot somewhere within a 1/2" radius circle if and only if the sights are perfectly sighted for that rifle with that ammo at that precise distance. An MOA is much easier to 'guarantee' than where the actual group will fall. IOW, a group could be 2 feet from the target and still be within one MOA.

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