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Rifle Scopes MIL and MOA Range Equations Explained & Derived

R

runner

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Minuteman
Jul 18, 2006
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I just revised my paper. Hope it reads better. Warning: For the technical and possibly nerdy. runner

I have written a paper on how they derived the range estimation equations for MILS and MOA. I couldn't find it on the Internet, so I did it myself. It's in simple language and easy math. For anybody interested, go to the link below. If you want, you can skip fwd in the paper to get to the actual derivation parts if you already know some basic stuff. I hope you enjoy it and learn something. I guarantee if you read it thoroughly, you'll never forget the formula's. Thanks, runner

Link

or under the U.S. Optics website at the top of FAQ:

Link

 
Re: MIL and MOA Range Equations Explained & Derived

I read the paper, and it's good information. Nice work, and good drawings. It's probably most interesting to math mavens, but it's a good explanation of the derivation, for those like me who remember things better when they understand how they work.


 
Re: MIL and MOA Range Equations Explained & Derived

Thanks Lindy, I appreciate the kind words.
runner
 
Re: MIL and MOA Range Equations Explained & Derived

Good paper runner. It is interesting to see the math behind it. In my log book it says the conversion from moa to mils is 3.5 but in your work you show it to be 3.6 I wonder why the discrepancy? If you are using 3.5 they should have just put 3.6 becuase most people can't divide by 3.5 or 3.6 in their head so having a more accurate number would be prefered.

PS. I didn't get any virus warnings
 
Re: MIL and MOA Range Equations Explained & Derived

Frei: better go read that paper again.

At 100 yards, one MOA subtends a length of 1.047 inches. At 100 yards, one milliradian subtends a length of 3.6 inches.

3.6/1.047 = 3.438.

Therefore, to convert MOA to milliradians, divide the number of MOA by 3.438.

Diabolus: if you down load the file - right click on the link, and pick "save target as" - you should be able to print the file.
 
Re: MIL and MOA Range Equations Explained & Derived

runner,

Thank you for that, all the detail you'd ever need and presented in a straight forward way.

It might just be me, but I preffer this 'type' of post?

English
 
Re: MIL and MOA Range Equations Explained & Derived

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: Lindy</div><div class="ubbcode-body">Frei: better go read that paper again.

At 100 yards, one MOA subtends a length of 1.047 inches. At 100 yards, one milliradian subtends a length of 3.6 inches.

3.6/1.047 = 3.438.

Therefore, to convert MOA to milliradians, divide the number of MOA by 3.438.

Diabolus: if you down load the file - right click on the link, and pick "save target as" - you should be able to print the file.
</div></div>

Thank you
 
Re: MIL and MOA Range Equations Explained & Derived

runner, thanks for the theory behind the formulas. It is good to know how the applications we employ (i.e. the formulas) really were developed. I was taught in the mil based formulas that rounding up 27.778 to 27.8 makes the math slightly easier and the resulting range difference has no practical impact.

For example: 17" target that reads .9 mils.

17 X 27.8 / .9 = 525 .1111 or 525 yards

17 X 27.78 / .9 = 524.7333 or 525 yards

Are there any negative impacts in using 27.8 in the mil formula?

 
Re: MIL and MOA Range Equations Explained & Derived

DWood,

Good points. No, there is no real negative impact in using "rounded-up" numbers. Heck, in a crunch, you could use just plain old 28 in your example and you would get 17x28/.9=528.8= 529 Close enough even for the best of shooters. My paper is just more of a theoretical thing in general. Thanks,
runner
 
Re: MIL and MOA Range Equations Explained & Derived

runner, thank you for sharing this. gonna put this with my plaster book.
 
Re: MIL and MOA Range Equations Explained & Derived

Wow! Major compliment. Thanks Micronut.

P.S. new edited and improved version coming out shortly.

runner
 
Re: MIL and MOA Range Equations Explained & Derived

I reviewed my paper and made some editing changes to make it a little easier to read and understand. It's a better edition than the first one. The link on my first post has the new and improved version. Any questions or comments to make the paper better are appreciated.
Thanks, runner.
 
Re: MIL and MOA Range Equations Explained & Derived

Hey Runner nice job, I have a question for you. I have a US Optics with the PCMOA reticle which is 1 MOA per line. But it's actually 1 Inch per each line. The guys from USO told me that and I placed a tape measure at 100 yds to verify and it is 1 inch for every line on the reticle. So how would you use your MOA formula if you measure in inches?
 
Re: MIL and MOA Range Equations Explained & Derived

The formula for that is:

<div class="ubbcode-block"><div class="ubbcode-header">Code:</div><div class="ubbcode-body ubbcode-pre" ><pre>
target size(in) * 100
range(yds) = --------------------------
image size

</pre></div></div>
 
Re: MIL and MOA Range Equations Explained & Derived

Roger,

If I tested my MDMOA reticle and it gave me inch readings I would be more than slightly upset.

That being said I can't see .047" at 100 yards any better than the next guy. What I can see is 1/2" at 100 yards. Instead of measuring each line at 100yds, measure 10MOA at 100yds. That will give you a measurement if it's in MOA of 10.47". It the reticle lines up on the 10" mark it would be 1" graduations but if it lines up on the 10.5" mark you DO have an MOA reticle. Similarly at 20MOA it would line up just shy of 21" (20.94") at 100 yards, and 30MOA would measure 31.41". Much easier to see than .047".

Additionaly you can test the accuracy of your scope clicks in a similar fashion. Dial on 10 MOA and the bullet should hit about 10.5" from the point of aim +/- the accuracy of the rifle/ammo/shooter combo.

If you do have an MOA reticle you would need the formula

<div class="ubbcode-block"><div class="ubbcode-header">Code:</div><div class="ubbcode-body ubbcode-pre" ><pre>

Target size (in) * 95.5
range (yds) = ----------------------------
Image size in MOA

</pre></div></div>
Cheers, Doc
 
Re: MIL and MOA Range Equations Explained & Derived

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: Lindy</div><div class="ubbcode-body">The formula for that is:

<div class="ubbcode-block"><div class="ubbcode-header">Code:</div><div class="ubbcode-body ubbcode-pre" ><pre>
target size(in) * 100
range(yds) = --------------------------
image size

</pre></div></div>
</div></div>

The moa formula is very easy to work with (although the mil formula isn't hard). It took me a while to grasp that the Horus reticle I spec'd in my USO ranges with an moa graduated scale (Horus calls it inch of angle but it is the moa formula) while the main reticle is mil based for quick holdovers. The math for moa ranging that Lindy posted is fast and easy; size of target in inches divided by the image size in moa, then add two zeroes. If needed I can range with the main reticle using the mil formula also. I used both methods in a class and it helped me commit both to memory.

Since Horus' formula uses 100 rather than 95.5, I guess the ranging scale is shooter's moa rather than true moa. I will check using doc's info the next time I am out at the range. It makes quite a difference; on an 18" target that reads 2 moa the difference would be 900 yards (shooter's) -VS- 859 yards (true).

What is the standard in moa scopes; shooter's or true moa?

H25reticle.gif
 
Re: MIL and MOA Range Equations Explained & Derived

Inches are Inches
MOA is MOA

Don't get them confused, they are NOT interchangeable. This becomes increasingly more critical the farther out you go.

Example:

21" target * 100 / 2.5MOA = 840yards
21" target * 95.5 / 2.5MOA = 802.2 yards
The MD Master says 800 yards
wink.gif


This gives you an error of ~40 yards or the difference between your 800 yard dope and your 850 dope, in my rifle that's 3 MOA or about 25".

If your retical subtends minutes, use the MOA formula, if it subtends inches use the inches formula.

Cheers, Doc
 
Re: MIL and MOA Range Equations Explained & Derived

Ronald,

Good question. DWood, doc76251 and Lindy above did a great job explaining an answer to your question. I suspect it is actually a MOA reticle(1.047 inch at 100yds) and not an actual "1 inch" reticle (at 100yds). Try doc76251's method:

"Instead of measuring each line at 100yds, measure 10MOA at 100yds. That will give you a measurement if it's in MOA of 10.47". It the reticle lines up on the 10" mark it would be 1" graduations but if it lines up on the 10.5" mark you DO have an MOA reticle. Similarly at 20MOA it would line up just shy of 21" (20.94") at 100 yards, and 30MOA would measure 31.41."

...and tell me what you get, I'm curious. Thanks,runner.
 
Re: MIL and MOA Range Equations Explained & Derived

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: doc76251</div><div class="ubbcode-body">
If your retical subtends minutes, use the MOA formula, if it subtends inches use the inches formula.

Cheers, Doc </div></div>

That is my question Doc. I want to confirm that my Horus is actually graduated in shooter's moa; I assume it is since they call it inches of angle and use 100 rather than 95.5. I haven't seen other manufacturers use the term "inches of angle", so my question is how is the moa reticle typically graduated? The method you posted is a fast method to test that I will try next time out.

As you pointed out it makes quite a difference and using the correct formula for the reticle is important. I hope mine is shooter's moa because it makes the math used in ranging faster, unless I use my new Swaro rangefider. Thanks.
 
Re: MIL and MOA Range Equations Explained & Derived

DWood,

Looks like you were editing whilst I was typing based on your original post
blush.gif
You can check the reticle without firing a shot (yard stick) and you can check the "clicks" in the same manner but need to put rounds on target. The hardest part is getting the range to be EXACTLY 100 yards. I'd like to know what you find with your Horus.

I'm not sure if I would be happy about the inch thing as I have been known to do hold overs. If the reticle is in inches and your adjustments are in MOA then you have to do that whole convert to MOA thing to inches to get the right hold. If they are both in inches then you could set up your dope cards in inches and be golden
laugh.gif


Cheers, Doc
 
Re: MIL and MOA Range Equations Explained & Derived

DWood,

I called Nightforce and asked them about my reticle. They and their booklet said to use the "100" instead of "95.5" multiplier, which would mean an actual 1 inch reticle, not 1.047 inch (MOA) reticle. But their drawings for the reticle say "All Values in MOA" (http://www.riflebarrels.com/products/npr1.pdf). I'm still trying to figure out the reason for their contradiction. runner
 
Re: MIL and MOA Range Equations Explained & Derived

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: doc76251</div><div class="ubbcode-body"> If the reticle is in inches and your adjustments are in MOA then you have to do that whole convert to MOA thing to inches to get the right hold. If they are both in inches then you could set up your dope cards in inches and be golden
laugh.gif


Cheers, Doc </div></div>

Not being an moa guy, please help educate me. Once you have an accurate range, why would you have to convert inches to moa if the dope for your moa knobs or holds has been accurately worked up?

Both my reticle and knobs are in mils. Once I have a range, I can hold mils with the reticle or dial mils based on my dope. That's what took a little getting used to with the Horus; an moa ranging scale with a mil reticle. I like it but have only begun to learn how to use it. Too bad it adds $400 to the price of an SN-3.

runner, let us know what you find out about the Nightforce moa issue. 100 is easie to calculate but will not be accurate if the reticle is true moa.
 
Re: MIL and MOA Range Equations Explained & Derived

OK, I get your point. You have to verify that your reticle moa and knob moa increments are the same.
 
Re: MIL and MOA Range Equations Explained & Derived

Does anybody out there have an MOA reticle whose instruction booklet says to use the 95.5 multiplier in the formula instead of 100? I'd like to know.
runner.
 
Re: MIL and MOA Range Equations Explained & Derived

The value of the moa reticle (1" VS 1.047") at 100 yards makes a significant difference when using the reticle to range, especially as distance increases (established by several comments above). But, doesn't it matter less when actually dialing or holding?

If 1" is used at 1000 yards, 1 moa is 10" and if 1.047" is used, 1 moa is 10.47". Unless I'm not getting it, the critical part to understand is the value for 1 moa in inches at 100 yards for <span style="font-weight: bold">your scope </span>when using the reticle to range.
 
Re: MIL and MOA Range Equations Explained & Derived

Most people with MOA reticles aren't holding big elevations like, say, the people with Horus mil reticles, who hold everything, so the difference between 1.000 inches and 1.047 inches, which is a 5 percent difference, aren't likely to matter much.

However, some scopes, like Leupolds with M1 dials, are actually one inch per four clicks instead of 1.047 inches at 100 yards.

At 1000 yards, <span style="font-weight: bold">THAT</span> difference is significant - to the tune of 20 inches in point of impact.
 
Re: MIL and MOA Range Equations Explained & Derived

OK I get it. If it takes 40 moa to reach 1000 yards:

40 X 10.47" = 418.8

40 X 10" = 400, almost 19" difference. Thanks.
 
Re: MIL and MOA Range Equations Explained & Derived

To go along whith what Lindy said about the Loopy M1 knobs being 1" it is also wise to check any scope as dpending on the milling tolerances of the mfgr your adjustment value may be MORE or LESS.
Loopies are notorious for being .94 - .96 MOA

If it takes you 38 MOA to get to 1K via your ballistics card/program what ever it is that tells you to dail up....

MOA = 1.047" X 380 = 397.86"
SMOA = 1.0" X 380 = 380.00"
Loopy MOA = 0.95" X 380 = 361.00"

If the MOA were correct via the ballistics program and the bullet/shooter/rifle combo was perfect the SMOA would hit 17.86" low and the Loopy MOA would hit 36.86" low. I think this in a large part is where alot of people get fustrated at ballistics programs. They dial on what the comuper tells them to and then miss. They blame the computer instead of verifying what thier component parts are doing.

It's the concept of errors multiplying themselves. .047" isn't worth talking about, untill you have 38 of them stacked up then it has already become too significant to ignore.

Cheers, Doc
 
Re: MIL and MOA Range Equations Explained & Derived

Lindy said:
Runner: that would be a true MOA reticle. They exist - I've measured them, using the techniques described in the web page linked below. I don't remember the scope brand, though.

Yes, that is what I have on my scope. It says .25 MOA on the knobs which means each click equals .262 inches, meaning 4 clicks equal 1.047 inches. But my instruction booklet, and my call to them, both say use the 100 multiplier instead of the 95.5 multiplier in the formula to get the distance. I think (know) that is wrong. I want to know if anybody has a MOA scope out there whose directions actually say to use: Height in inches/Moa x 95.5 = Distance.
(instead of saying Height in inches/moa x 100 = Distance).

runner
Click to expand...
 
Re: MIL and MOA Range Equations Explained & Derived

Runner, I've checked my USO with the PCMOA reticle. The reticle is in INCHES. The knobs are in MOAs. I've put a 40 inch long stick at 100yds with dots every 5 inches. My reticle matches up perfectly with the stick. But when I put a card borad and shoot one round at the target at the bottom of the card board, then adjust 20 moas on the elevation dial the second shot will be roughly 21 inches high.

So when I use my reticle to range targets I should use the formula (Target in inches X 100 divided by image size) to get distance in yards?

Thanks
Ron
 
Re: MIL and MOA Range Equations Explained & Derived

<div class="ubbcode-block"><div class="ubbcode-header">Quote:</div><div class="ubbcode-body">So when I use my reticle to range targets I should use the formula (Target in inches X 100 divided by image size) to get distance in yards?</div></div>

Yep.
 
Re: MIL and MOA Range Equations Explained & Derived

Ronald,

I checked the US Optics website and it shows the PCMOA reticle as "MOA":

http://www.usoptics.com/upgradesD.php?recordID=RET-051

Therefore, If this is in fact true, I think you need to use:

H x 95.5 / moa = Dist.

Who's right? I believe you and your test but it contradicts the company website:

Again, this is my grip. I think many Optics companies are telling people to use 100 instead of 95.5 for a true MOA reticle. I can't figure this out. That is why I'm wondering if anybody has a MOA scope with a user booklet that tells them to use 95.5 and not 100 as the multiplier.

runner
 
Re: MIL and MOA Range Equations Explained & Derived

Instruction manuals are often written by technical writers unfamiliar with details.

The ruler cannot be in error, assuming that the measurement was carefully made at an accurate distance.

When making such measurements, I don't assume that the 100 yard mark at a range is actually at 100 yards - I measure it with a tape. A laser can be off by a yard or more, but a tape will not be.

If 36 MOA on the reticle subtends a distance of 36 inches at 100 yards, then use 100 for the range calculation.

If 36 MOA on the reticle subtends a distance of 37.7 inches at 100 yards, then use 95.5 for the range calculation.

Period. End of story.

Now, that's assuming a first focal-plane reticle.

If I had a 2nd focal-plane reticle, I'd find the point on the power ring where 36 MOA on the reticle subtended a distance of 36 inches, and mark that spot on the ring to use for ranging, so that I could use 100 as the factor in the range calculation.

 
Re: MIL and MOA Range Equations Explained & Derived

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: Lindy</div><div class="ubbcode-body">Instruction manuals are often written by technical writers unfamiliar with details.

The ruler cannot be in error, assuming that the measurement was carefully made at an accurate distance.

When making such measurements, I don't assume that the 100 yard mark at a range is actually at 100 yards - I measure it with a tape. A laser can be off by a yard or more, but a tape will not be.

If 36 MOA on the reticle subtends a distance of 36 inches at 100 yards, then use 100 for the range calculation.

If 36 MOA on the reticle subtends a distance of 37.7 inches at 100 yards, then use 95.5 for the range calculation.

Period. End of story.

Now, that's assuming a first focal-plane reticle.

If I had a 2nd focal-plane reticle, I'd find the point on the power ring where 36 MOA on the reticle subtended a distance of 36 inches, and mark that spot on the ring to use for ranging, so that I could use 100 as the factor in the range calculation.

</div></div>

Lindy, I agree. It's just that the companies are not being clear or accurate in their description of the reticles they are using. Something tells me they are confused abut this issue.

runner
 
Re: MIL and MOA Range Equations Explained & Derived

Runner: I agree. The solution is not to rely on what they tell you. Check it yourself. Trying to get other people to change their behaviour is often a fruitless task. I just check what I need to know for myself.
 
Re: MIL and MOA Range Equations Explained & Derived

Lindy I did my test on our local range where the 100 yd line is established already and I used my LRF also and it showed 100yds.

I shot a match today and I did another test. There were known size and known distance steel plates at various distances all the way out to 874yds. I measured several of them with my reticle and used the 100 for the formula and came out with the correct distances. When I used the 95.5 I was off quite a bit, enough to miss the target.

Thanks
Ron
 
Re: MIL and MOA Range Equations Explained & Derived

Ronald said:
Lindy I did my test on our local range where the 100 yd line is established already and I used my LRF also and it showed 100yds.

I shot a match today and I did another test. There were known size and known distance steel plates at various distances all the way out to 874yds. I measured several of them with my reticle and used the 100 for the formula and came out with the correct distances. When I used the 95.5 I was off quite a bit, enough to miss the target.


<span style="font-size: 11pt">Ronald,

Nice job. I'm still curious why USO calls it MOA (1.047 in at 100 yds) when in fact it looks like it's "shooters MOA" (1 inch at 100 yds). Do the instruction booklets that came with it shed any light on that question?

runner </span>
Click to expand...
 
Re: MIL and MOA Range Equations Explained & Derived

Runner the USO PCMOA reticle it is in inches, call them and they will tell you that. Their knobs are in MOA, so every click is .25moa (I've checked by shooting and it is right where it suppose to be). I did not get any instruction booklet with my scope.

You should do what Lindy said, Check your scope for yourself and don't take anybody's word for what it is or what it suppose to be. Get a ruler and mark every 10 inches with a black marker so you could see it easily and place it at 100 yds. Put your rifle on the bench with sand bags so it won't move and look at it, If your reticle matches up with the ruler, your reticle it is in INCHES like mine. Then grab a big cardboard box and draw a line from the top all the way to the bottom of the cardboard, the longer the better (I had mine out to 50 inches). Mark this line with a cross or bulseye every 10 inches ( Make sure you measure with a ruler) and shoot 3 shots on the botom mark, than dial 10MOAs on your scope and aim at the bottom mark again and shoot 3 more shots, then dial 20 MOAs and shoot 3 more shots aiming at the bottom mark again. Repeat this process untill you shoot at all the marks on your cardboard. Go and check your target with a tape measure and measure the distance from your 3 shot groups to the actual 10, 20, 30, 40, 50 inch mark. You will see that the shots are not on the mark, they will be slightly higher which means your knobs are in MOAs.

When I shoot I always dial the elevation and hold for windage. It works pretty good for me. Now I have to master the technique on reading the wind correctly. If I get that down I will be winning matches... HaHaHa.

Ron
 
Re: MIL and MOA Range Equations Explained & Derived

Ronald,

I will check my scope out like you said. Nice job explaining it.

I'm just pissed that a few high end companies either: 1)can't get their verbiage right 2)are mistaken and don't now it 3) don't know what they are talking about 4)are totally confused or 5)all of the above.

True MOA and Shooters MOA are different, (check out my paper)and they require different formulas, and it would be nice if they were 100% clear on this with the scopes that they make. I can't understand why we even have to test our scopes out to tell what kind we have. I would expect that from some old Eastern Block scopes, but not from modern U.S. ones.

runner
 
Re: MIL and MOA Range Equations Explained & Derived

I confirmed yesterday that the ranging scale in the Horus H-25 is graduated for 1" = 1 moa (Horus calls it "inch of angle").
 
Re: MIL and MOA Range Equations Explained & Derived

We checked a friend's USO Type 1 MOA reticle yesterday and found that it was scaled to "Shooter's MOA". With the importance of having knobs and reticle calibrated the same, I'm baffled as to why they do this.
 
Re: MIL and MOA Range Equations Explained & Derived

rmfield: Did you check to see what the knobs were calibrated to? They may <span style="font-weight: bold">be</span> scaled to the same value.
 
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