MOA math made easy


January 30, 2014, 09:44 PM
This is as easy as it gets. A radian = 57.295646 but for this application 57.3 is close enough.

100 yards divided by 57.3 = 1.745201 yards in one degree of angle at 100 yards. To convert the yards to inches in one minute of angle (moa) multiply 1.745201 by (.6 a constant) .6 * 1.745201 yd = 1.04712 inches, rounded to 1.047”

Two steps …… how ever many yards divided by 57.3 then that sum multiplied by .6 gives you the inches in one moa at that yardage.

Examples to the nearest 100th

1. 25 yards/57.3 = .4363 * .6 = .26” moa
2. 600 yards/57.3 = 10.4712 * .6 = 6.28” moa
3. 1000 yards/57.3 = 17.45201 *.6 = 10.47” moa

For the scope’s click value divide inches by the number of clicks the scope has in one moa. Divide by 4 if it is ¼ moa scope or by 8 if it is a 1/8th moa scope. At 1000 yards ¼ moa each click is 2.6” a 1/8th moa click is 1.3"

4. 400yards/57.3 = 6.98 * .6 = 4.18” moa
Lets say the bullet drop is 17” at 400 yds.
17/4.18 = 4.05” moa
Round to 4 moa……..To move up 4 moa - 17 clicks on a ¼ moa scope, or 33 clicks on a 1/8 moa scope.

Okay you made the 4 moa adjustment and you are still 1 inch low. Each click of a ¼ moa scope is 4.18 divided by 4 = 1.047 inch so you would adjust up 1 click with a ¼ moa scope. Each click of a 1/8 moa scope is .52 inch so you would adjust up 2 clicks.

Say you are 1-1/2 inch low. With ¼ moa scope you either adjust up 1 click and be ½” low or 2 clicks up and be ½” high. 3 clicks on 1/8 moa scope is 1.56” so you are right on.

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Jim Watson
January 30, 2014, 10:22 PM
Way more complicated than it needs to be.
A minute of angle is so close to one inch per hundred yards of range as to make no matter. It works out to less than half an inch at 1000 yards difference between an inch per hundred and a trigonometric minute.

If you like radians, a milliradian is one meter per 1000 meters of range. Ten centimeters at 100 meters.

Mixing the measures just makes for extra thought when you ought to be concentrating on setting up the shot. US snipers have to study hard to use a milliradian reticle and minute scope adjustments. But now we can get mil-mil scopes... or minute reticles.

January 31, 2014, 09:31 AM
Yep, don't make it harder than it needs to be.

January 31, 2014, 09:59 AM
I have always opted for the trigonometric approach to finding MOA. A minute is 1/60 degree so you put it into the formula tan(1/60)=MOA/D(inches to target) (make sure the calculator is in degrees). 3600*tan(1/60)=1.047 inches at 100 yards


January 31, 2014, 10:28 AM
It's easier for me to figure 1 degree per 100 yds and add 1/20 extra.

1000 yds = 10 degrees plus .5
200 yds = 2 degrees plus .1
50 yds = .5 degree plus 0 (not worth the calculation)


EDIT: Frankly, I'll never be good enough to ever worry about adding the 1/20 extra.

Jim Watson
January 31, 2014, 10:36 AM
I just ignore the 4.7% differential. I do not have good enough gun and ammo to detect it, nor enough shooting skill.

January 31, 2014, 11:02 AM
Pi*2*36*Range(yds)/(360*60) = Pi*Range(yds)/300 = 1 moa

Arkansas Paul
January 31, 2014, 11:54 AM
I shoot the target at 100 yds, and adjust until the point of impact is where I want it.

You guys think too damn much. :)

January 31, 2014, 05:50 PM
Somebody said it earlier - you're being waaaayyy to complicated. If you're shooting at 600 yards, you estimate the impact needs to go up 12 inches, divide the 6 into the 12 inches it has to move and it comes up 2 MOA.

The .047 part of the equation is small enough to not worry about it.

If at 500 yards, need to drop 11 inches, 11 divided by 5 is 2.2, close enough to 2 MOA and one click or 2 and a quarter MOA.

It will be more than accurate enough for most situations.

January 31, 2014, 07:03 PM
by the way - for the math challenged that can't do things like Pi and square roots in their heads - There is a kinda cool smart phone app called 'MyScript Calculator' you can write equations in with your fingertip and it will do the calcs for you - instead of trying to key them in on the too small virtual keyboards.

ole farmerbuck
January 31, 2014, 07:20 PM
I shoot the target at 100 yds, and adjust until the point of impact is where I want it.

You guys think too damn much. :)

January 31, 2014, 08:53 PM
+1, or +3, or whatever it is by now?

To me, a MOA = 1" at 100 yards, 2" at 200 yards, etc.

I use a 12" ruler to measure targets, and do mental math to change 1/8" to 1/8 MOA.
But only if the scope adjustments are in MOA.

All of them I ever owned are not in mil-dots.
They are in fractions of an inch.

And we used to do pretty good shooting at 1,000+ with military supplied scopes back in the day.
Course that was well before anyone told us we couldn't without mil-dot scopes!

I guess we were just too ignorant to know it wouldn't work back then?


January 31, 2014, 08:54 PM
1 inch is pretty darn near 1 MOA at 100 yards.

ole farmerbuck
January 31, 2014, 08:57 PM
I dont really measure most of my shots. I just know where they are and where they are suppose to be and adjust from there.;)

January 31, 2014, 09:20 PM
As an old deerhunter,if I get three holes inside a 2 inch dia. circle at 100 yards I am extremely happy.Three deer were not so happy this fall.

January 31, 2014, 10:26 PM
If you like radians, a milliradian is one meter per 1000 meters of range. Ten centimeters at 100 meters.

A radian is not a unit of linear or metric measurement. It can be used with any measurement system.

A radian is an angular measurement. It is the radius distance measured along the arc of the circle circumference and then a line from the end of that distance along the circumference back to the center making a pie shaped section with an angular measurement of 57.3 degrees. There are 6.28 (2 PI) radians in a circle.

A milliradian is simply 1/1000 of a radian and can be used with either the English standard measurement system or metric. A milliradian used with standard measurement with a scope is 3.6 inches at 100 yards and 36 inches at 1,000 yards.

MILRAD scope clicks are usually 0.1 milliradian per click or 0.36 inches at 100 yards or 3.6 inches at 1,000 yards.

The nice thing about milliradians is you can easily use a scope with a MRAD reticle to estimate distance.

A 6-foot tall person is 2 yards tall. If you looked at them through a scope and they were 4 milliradian dots or marks tall you would calculate the distance:

2 (yards) / 4 (reticle mil marks) x 1,000 = 500. So the person is 500 yards away.

January 31, 2014, 10:40 PM
I can figure minute of deer. Shoot and retrieve. ;)

Jim Watson
January 31, 2014, 11:29 PM
Yes, buckhorn, I understand that a radian is an angle.
I would have been correct to say that a milliradian SUBTENDS one meter at a thousand meters, also one yard at 1000 yards. Ever hear of the Thousand Inch range the Army used to use for reduced range practice? Same deal.
But it just works out so nice in SI.
A tenth of a yard at 100 yards is just awkward to work with. You need a cheat sheet to use mixed units of feet, inches, and yards.

And you can go back in history and compare the Infantry Mil and the Artillery Mil, neither is exactly a geometric milliradian. The Infantry Mil is a lot closer to geometry, 6280 per revolution vs trig of 2000 Pi (6283.2) The artillery settled for 6400.

January 31, 2014, 11:43 PM
good grief people. in the immortal words of burt gummer, "find something simple and complicate it!"

February 1, 2014, 12:07 AM
All this MOA math made easy makes my head hurt!


February 1, 2014, 12:21 AM
It's all easy math, but if that extra .047 makes a difference to your shooting you're one h*ll of a lot better than me.

February 1, 2014, 01:10 AM
This is simple and easy to remember.

Dividing the distance in yards by 95.5 will give the value of 1 MOA in inches at that distance.

It's an approximation, but it's a good one. The approximation differs from the exact value by less than 0.0075%

February 1, 2014, 03:06 PM
I used to go hunting/shooting after school to forget about math class.

February 2, 2014, 10:28 PM
Looks like we are ready for estimating range to the nearest inch made easy using scope subtension. :D

February 3, 2014, 01:20 PM
JohnSKa Now that is as easy as it gets. Thanks

February 3, 2014, 07:27 PM
I just flip the lever on my rifle to "SEMI-AUTO" and adjust my "Point of Impact" on the deer I'm shooting at, accordingly.

Double Naught Spy
February 3, 2014, 08:19 PM
JohnSKa Now that is as easy as it gets. Thanks

I think I will just stick to 1" per 100 yards. My turrets won't adjust in 0.047" increments anyway.

February 3, 2014, 11:29 PM
My turrets won't adjust in 0.047" increments anyway.You've been cheated! You must have one of those high-falutin' Yurpeen scopes. Get you some good Chineez optics and they'll adjust in all kinds of increments--usually two or three different increments in just one shootin' session.

Double Naught Spy
February 4, 2014, 08:16 AM
I already had that issue with a Lithuanian scope, LOL.

February 4, 2014, 12:03 PM
I just use the OnTarget software. Does all the calculations for me, and makes a pretty picture that I can post online when I have a worthy group. ;) (

February 4, 2014, 11:48 PM
Everyone develops a comfort zone in ranging and ballistics be it minute of deer, minute of PD or MOA. I do all this in my head because I am a math whizz. Not.easy even with a calculator for some. Pile the trigonometry approach for windage and elevation and it gets pretty three dimensional PDQ.

I taught this stuff for years to M/O's and the quick and dirty one inch rule was achievable for most guys. Like someone pointed out if a guy could shoot that 0.047 consistently he is one heck of a shot.


February 4, 2014, 11:57 PM
honestly, in all the sniper/field/practical rifle matches i've shot, i can't recall needing to do much math.

you make a cheat sheet like this:

you take your inputs like wind speed, distance and it gives you the hold. or target size and mil reading and it gives you the distance.

if you're doing MOA or MIL math in the field before you shoot, you're just not prepared.

about the only time i use the formula at all is if i get stage descriptions several hours before i shoot, with target sizes, and i know i will need to mil them, i will calculate the target size in order to estimate safe holds so i can shoot in a bracket.

February 5, 2014, 02:53 PM
Assuming your scope has 8 clicks per MOA, the tiny excess would be one more click for 3". If you have 4 clicks per MOA (the most I've seen), the tiny excess would only span 1 click for a 6" adjustment.

I don't see this every being practical for sighting in.


February 5, 2014, 03:21 PM
try one of these sometime for 1/10th MOA clicks, i guess for when shooting a groundhog in the eye isn't good enough and you need to hit inside the pupil.

(joking aside, i had one and it was a great scope)

February 5, 2014, 06:45 PM
As a surveyor, I'd just get out my $7000 total station and measure the distance to the nearest 0.01 foot, then calculate the MOA on my HP-50G calculator; MUCH simpler...


I like JohnKSa's method, that is one of the simplest I've seen.

ole farmerbuck
February 5, 2014, 07:04 PM
I thought scopes used to be 1/4" or 1/8" (inch) per click and not MOA.

February 5, 2014, 08:56 PM
I thought scopes used to be 1/4" or 1/8" (inch) per click and not MOA.They are 1/4" or 1/8" ONLY at 100 yards. And that's because 1/4" is about 1/4MOA at 100 yards and 1/8" is aobut 1/8MOA at 100 yards.

Scope adjustments have always been made in terms of angular measurements--that's the only way to make a scope work. However, sometimes they are stated in terms of linear distances/measurements on a target at a given distance (most commonly 100 yards).

February 5, 2014, 09:08 PM
farmer, some are certainly labeled that way. some, it's anybody's guess what they actually are. some are clearly IPHY and others are clearly MOA or MIL.

February 6, 2014, 12:40 AM
An aircraft is much like a bullet. A 1 degree course deviation results in a 1nm deviation at 60nm. 60 to 1 rule. (rounding a nautical mile to 6000 ft)

A bullet does the same. :D

1911 guy
February 11, 2014, 10:32 AM
Unless you have a Mil-Dot scope, ignore mils and learn minutes of angle. As stated, 1.047" at 100 yards. If you're not shooting F-class or tiny varmints at big ranges, call it 1"

As range increases, so does the subtended value of one MOA. Ex: at 200 yards, 1 MOA equals (technically subtends) 2.094 inches.

"Inches, Minutes, Clicks". How far off was my shot, how many MOA is that at range and how many clicks do I move? A scope that moves 1/4 MOA at 100 yards will also move 1/4 MOA at 200. You've got to watch the ones that are incremented in 1/4 inch, as this begins to deviate from MOA and you'll be one click off at 500 yards and stack up from there. Like I said, it only matters if you shoot longer distances than the average 200 yard deer.

Truth is, the average shooter is far more likely to miss an animal due to unfamiliarity with elevation issues than forgetting to click off that extra 1/4 MOA.

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