What is minute of angle?


February 26, 2009, 11:01 PM
Can someone help me better understand exactly what MOA is? Is sub-MOA simply within an inch? (or some other measurement) at a certain distance?


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February 26, 2009, 11:07 PM
Someone will give a more in depth answer but it basicaly equates to 1" per hundred yards; 100 yds= 1", 200 yards =2", 250 yards=2.5 " 1000 yards= 10" or think of minute of angle as a long cone that has a taper of 1" per 100 yards. if my rifle shoots MOA that menas it will keep it's shots in a 1" diameter circle of "group" at 100 yards. 2" group at 200 yards etc. Some will argue three shots per group, some will say 10. Sub MOA would mean it shoots a grop in under an inch, like .5 moa, .75 moa etc.. Some folks will argue how to measure teh groups whether outside to outside or center to center.

I do my groups in 3 shots and I measure then outside to outside.

February 26, 2009, 11:11 PM
360 degrees in a circle

each degree is further subdivided into 60 minutes

(and each minute has 60 seconds)

so one "minute of angle" is an angular measure that equals 1/60th of a degree

February 26, 2009, 11:16 PM
This question is asked regularly.
A Minute Of Angle is a minute of degree. 360 degrees in a circle. 60 minutes in a degree. (60 seconds in a minute.)
If your sights are off one minute of a degree, your gun will shoot it's group at an angle to that error by that amount. That amount equates to about an inch (1.021" as I recall, and someone here will certainly chime in if my memory has failed) at 100yds. (Do the [algebra] math ). 2" at 200 yds and 4" at 400yd and so on.
So yes, MOA is 1" at 100 yds. (+/-)

Hungry Seagull
February 26, 2009, 11:17 PM
Dont confuse it with "Mils" where there is 3600 mils in a complete 360 degree compass.

February 26, 2009, 11:22 PM
MOA is Minute of Angle. 1/60th of 1 degree angle is a Minute of angle. 2 100 yard lines at a minute of angle result in points 1.047" apart. We round off to 1.0" for convenience.

4 MOA is:
1" at 25 yds
2" at 50 yds
3" at 75 yds
4" at 100 yds
8" at 200 yds
16" at 400 yds
24" at 600 yds (Actually 25.128)

It is a way to convert an angular difference to a linear difference at a given range. For ultimate accuracy at long range use 1.047 and round off after all calculations are done as seen in the 600 yd example above.

February 27, 2009, 12:00 AM
double post

February 27, 2009, 12:01 AM
A diagram form FM 23-10 (us army sniper handbook)

February 27, 2009, 12:34 AM
excellent diagram there... couldn't explain it better.

Zak Smith
February 27, 2009, 12:48 AM
[non-sense deleted because I wasn't paying attention]

It's 1.0472" per 100 yards not 1" per 100 yards. 1" per 100 is commonly referred to as IPHY or Shooters' MOA.

This is important because if you compute drop based on IPHY but your scope is true MOA, or vice versa, the approx 5% error is enough to miss a 30" plate at 1000 yards, using a common 308 load.

February 27, 2009, 12:53 AM
i am glad that i am not a long range shooter, and that this is something that i don't have to worry about, because though your post is very imformative, and dumbed down real well, i am lost in the sauce.

February 27, 2009, 01:25 AM
i still don't get it completely but am getting there.

February 27, 2009, 01:36 AM
The simple answer is if you shoot a group at 100 yards that measures 1.05" center-to-center between the two widest shots, you've just shot a 1 MOA group. Your "group" can be 2, 3, 5 or as many shots as you please. Most people consider 3 shots to be the minimum number for a "group" and 5 to be the most, practically speaking. For hunting rifles, 3 shot groups are normal as it's unlikely you'll get even that many off at an animal.

February 27, 2009, 03:04 AM
Alright. This really doesn't matter much for us casual people, it's only if you're curious why people say 1.047 inches is MOA at 100 yards instead of 1. It's all new to me, I thought 1 inch was the true minute of angle measurement at 100 yards. In reality, it's a small wedge-like division of a circle, so it keeps getting larger the bigger your circle is. Anyway, it's not too bad, here's eschewing all the trigonometry.

1 yard = 3 feet
1 foot = 12 inches
So, 36 inches = 1 yard
3600 inches = 100 yards

Now, there are 360 degrees in a circle, and 60 little "minutes" in each degree. Multiplying these two will give us how many minutes are in a circle.

MOA in a circle = 360 x 60
MOA in a circle = 21600

Now, to get the exact MOA for a certain circle, we hafta know the exact circumference (total length of the circle's edge) of the circle that has, in this case, a 100 yard radius (distance from center to outer edge). This way we can cut the circle into exact little slices of cake. Think of standing on a football goal line, and then spinning the point on the opposite goal line around you in a circle, that's the size of this circle.

Circumference = 2 x Pi x r

Pi is that 3.14(etc) number, look it up if you don't remember the symbol for it.
r is radius. We want radius in inches, instead of 100 yards, because that's what we'll measure our MOA in.

C = 2 x 3.14(etc) x 3600 inches
C = 22619.46711 inches

So we have roughly 22619 inches of circumference for our 100 yard circle, and we divide it by 21600, which is how many minutes are in a circle.

MOA at 100 yds = 22619.46711/21600 inches
MOA at 100 yds = 1.047197551 inch

That's why it's not really just 1 inch, and makes a difference at longer distances. (Or, just say screw it and divide pi by 3. But then you don't understand much.) Hope this helps someone, just a way to sorta understand it in layman's numbers.

February 27, 2009, 04:03 AM
The first thing to realize is that a full circle has 360 degrees. Each degree is then broken down to 60 minutes. Each minute then has 60 seconds, though in shooting we don't get this precise. When you are given a longitude and latitude the numbers you get are degrees, then minutes, then seconds. This is a way to specify more precisely where you are in the world than just going by the nearest full degree line. Hopefully you see in a circle that a minute is 1/60th of a degree.

The reason you use Minute of angle is that we all shoot at different distances. Just saying my rifle shoots a 1" group doesn't really give the entire picture. Was that group at 25 feet, 25 yards, 250 yards, 2500 yards? Group size isn't a full reflection of the quality of the group. A distance has to be factored in. Minute of angle does that. When you listen to the posts above picture yourself at the middle of the circle. When you shoot at 25 yards your groups should be small. Now look at the diagram above and notice how fairly close to the center the slice of the circle itself is a small distance from left to right(picture with the full circle drawn and a slice darkened). This shows that groups shot close should be small since a bullet traveling on a path different than where you aimed wouldn't have much time to travel away from the point of aim.

At farther distances your groups open up a bit but when you look at the diagram the distance across the slice farther towards the outside edge is bigger than the distance across a section closer to the center. This shows that as you shoot farther away from where you are the groups will naturally get bigger. If a bullet was 1/60th of a degree off from where you aimed it will continue to travel 1/60th of a degree away from the point of aim, which means the farther away you are shooting the farther away that bullet is going to hit from the point of aim. What Minute Of Angle (MOA) does is put a relation to both group size and distance on a group. This way if you shoot a 1 MOA group at 100 yards(roughly 1") you would predict the rifle capable of around 1 MOA at 200 yards (roughly 2") and so on since if in a perfect environment the bullets would always be traveling away from your point of aim at the same angle. Basically it allows you to extrapolate what group sizes would be at different distances. In real life just knowing MOA isn't a full picture as well because wind plays a bigger role in accuracy the further you are shooting so a 1 MOA group at 1000 yards (a little more than 10")is more difficult to produce than a 1 MOA group at 100 yards (a little more than 1") but in a perfect world they would both take the same effort. We don't live in that world though so it is still helpful to know how far a person is shooting to know how good that group really is.

From a sight point of view since we want our sights to be adjustable we need some form of measurement for each click of adjustment. Since a minute of angle is always a minute of angle no matter the distance it is fairly simple to take the amount of change needed divided by the distance you are shooting to get MOA. If you needed to move 1" at 100 yards you would adjust 1 MOA. If you need to adjust 4" at 400 yards you would adjust 1 MOA. If you need to adjust 1" at 400 yards you would adjust 1/4 MOA. If you need to adjust 1" at 25 yards you would adjust 4 MOA. The adjustments on a scope are basically moving point of aim along an arch. Because of this measurements in angles(minutes or fractions of minutes) is fairly common since the adjustments are moving in angles relative to the shooter. If you move your point of aim 1" left at 100 yards it will be 2" left at 200 yards and so on which shows why measuring adjusments in minute of angle(which is really 1/60th of a degree) makes sense.

The above posts before mine summarize how a minute is actually calculated and the math to get there. This was more a why behind it than a how.

February 27, 2009, 04:20 AM
Dont confuse it with "Mils" where there is 3600 mils in a complete 360 degree compass.

A Mil is a miliradian which is 0.001 radians. 360 degrees = 2*PI radians = 6283.19 miliradians.

There are 3600" in 100 yards. Is that what you meant?


Added in edit: 1 Mil = 3.4377 MOA

February 27, 2009, 04:25 AM
if you compute drop based on IPHY but your scope is true MOA, or vice versa,

How do you know if your scope is true MOA or IPHY? I've never heard of IPHY and always assumed that MOA is exactly that ... a measurement of angle equal to 1/60th of one degree.


February 27, 2009, 09:01 AM
many ballistic calculators will even switch between them. for instance, even on my 5.11 HRT watch that has the computer in it, you can change the output from MILS to SMOA to TMOA, where T== True MOA and S== Shooter's MOA

IPHY Inch Per Hundred Yards

and you can call your scope mfg and ask them, and then search on the internet to verify they haven't lied to you, and then measure it yourself. if you're serious about long range shooting, I'd recommend doing the first two things before you buy the scope an the last thing after you receive it. :)

Zak Smith
February 27, 2009, 10:47 AM
[How do you know if your scope is true MOA or IPHY? I've never heard of IPHY and always assumed that MOA is exactly that ... a measurement of angle equal to 1/60th of one degree.

The best way is to measure it by comparing the reticle demarcations and/or click values to known heights at a known distance (ie, the box test - but do it without shooting)

February 27, 2009, 11:23 AM
there aren't 3600 mills in a circle.

mill is short for milliradian. there are 2*pi radians or 6.28 radians. Therefore there are 6280 mills in a circle. The millitary simplified this to 6400.

Hungry Seagull
February 27, 2009, 01:26 PM
Sorry all about the Mils post. And thank you both for the correction. Ive too much artillery.

Throwing in a mils post did not do much I think. I appreciate the other posters for keeping me on track.

February 27, 2009, 10:49 PM
so far 18 additional replies after the question was answered correctly. this makes 19.

February 27, 2009, 11:13 PM
I appreciate all of your responses to my question. The information I can glean from the various responses allows to me consider the answer to the same question from many different angles and levels of expertise.


February 27, 2009, 11:33 PM

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