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Advanced Marksmanship Somebody Please Explain Math on 3.5 mils = 1 moa

C

CPEC0402

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Minuteman
Jun 3, 2009
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Indiana
Greetings everyone, new member here. I'm not very internet savy, however I came across this website and see a wealth of knowledge exists here. I have a simple question: how is it determined that 3.5 moa exist between every mil in an M3A Leupold Scope? Every training environment and FM I have read always refers to 3.5 moa = 1 mil in regard to holdovers. However, i cannot seem to find this number in my own calculations. Please read my reasoning, and correct me where I may be wrong.

1 inch = 2.54 cm
100cm/2.54 = 39.3 inches
Therefore 1 meter is approx 39 inches.

Now that it has been determined that 1 M = approx 39 inches, the mil value for that range is determined by the following utilizing range estimation:

size target (inches) x 25.4/mils = range target Meters

(X inches)(25.4)/1 mils = 1000M;

24.5X inches = 1000M;

X inches = 1000M/25.4;

X = 39.3 inches

THIS HOLDS that 1 mil = 39.3 inches @ 1000M, and 3.9 inches at 100M

I know that 1 moa is 3 cm @ 100M, and 1.18 inches at 100M. However, i cannot visualize cm like I can inches so I still assume 1 moa = 1 inch at 100 M because it helps me visualize proper corrections quicker. The error in utilizing 1 inch instead of 1.18 inches only results in an error of less than 12 inches at 1000 meters, which will still hit the enemy that distance(and gets you much closer than using 3.5moa=1mil). I will give another mathematical example to illustrate why I use 3.9 moa=1mil:

(X inches)(25.4)/1 mil = 254M
X inches = 254/25.4
X = 10 inches

So at 254M, one mil covers 10 inches.

1 moa @ 254M = approx 2.54 inches

10 inches/2.54 inches = X moa for 1 mil

10/2.54 = 3.93 moa for 1 mil

Hopefully the math illustrates my reasoning. And yes, I have tried this formula for holdoffs on the range for both myself and others and it works much more accurately than 3.5 (for us, at least!). One reason I like 3.9 is because I can calculate holdoffs for wind and elevation quickly in my head without using a calculator by rounding 3.9 to 4. Keep in mind, rounding to 4 is for QUICK mental calculations, and has worked very well for me. When rounding, 1 mil = 4 moa, and 1/2 mil = 2 moa. I know this isn't for punching paper in a competition, but in that arena I don't think holdoffs would be used anyways. But it is certainly accurate within a moa.

Could someone please explain to me...how is 3.5moa=mil is derived for an M3A scope? Thank you for your time, I know it's a long read...Keep your powder dry.
 
Re: Somebody Please Explain Math on 3.5 mils = 1 moa

The post that Niles points you to gives you all the specifics, so I'd suggest you read them. The short answer, however is your rounding errors are compounding as you go.

1 MOA = 1.047" @ 100 yards
1 Mil = 3.6" @ 100 yards, .1 mil = approx 1/3 of a MOA
1 Mil = 3.438 MOA
1 Mil = 1 yard @ 1000 yards or 1 meter at 1000 meters

At 254 meters, 1 MOA = 2.898", not 2.54".
254M * 1.09 = 276.8 yards
1.047 * 2.768 = 2.898" = inches in 1 MOA at 254m

1 Mil = 3.438MOA * 2.898 = 9.96" at 254M
if you try 3.9 * 2.898 you'd have 11.3", that is incorrect.

If you use 4 MOA to a mil, and try to hold over 8 MOA by holding 2 mils, you'll be .32 Mil off, or more than 1 MOA of error, and it gets worse as the holdover amount increases.

if 600 on the gun is 15 MOA up, and 900 needs 30, that's a 15 MOA holdover

15 / 4 = 3.75, in reality is only 12.9 moa of actual holdover, more than 2 moa of error, over 18"

15 / 3.438 = 4.36 call it a 4.4 hold, .04 mil error, less than 1/6 moa of error

15 / 3.5 = 4.28 call it a 4.3 hold, .06 mil error, less than 1/4 MOA of error
 
Re: Somebody Please Explain Math on 3.5 mils = 1 moa

Cory gave you the numbers. Here's what it's based on.

Both a milliradian and an MOA are measurements of angle.

One milliradian is an angle which subtends an arc whose length is 3.6 inches at a distance of 100 yards. That's not an approximation - it's an exact figure.

One MOA is an angle which subtends an arc whose length is 1.047 inches at a distance of 100 yards.

3.6 / 1.047 = 3.438

So, one milliradian equals 3.438 MOA.

And if you want to start rounding things off, start doing some calculations to see how much error you're introducting into your calculations, as Cory did.
 
Re: Somebody Please Explain Math on 3.5 mils = 1 moa

The problem is that you are trying to relate linear measurments to an angular system.

They are both systems that measure angles. You do not need to know what the linear distance is for either system.

The only time that a linear measurement is equated with mils or MOA is when you are estimating range to a know size target.

After that, forget about how many inches or centimeters such and such equals, it does not matter.
 
Re: Somebody Please Explain Math on 3.5 mils = 1 moa

what I was taught is this... the Mil we use is actually rounded, the Army uses one reticle, the Marines another, civilian scopes who knows sometimes.... anyway depending on country, reticle style, etc, etc a Mil can = 3.4XX MOA or 3.6ish MOA, use 3.5... UNLESS you KNOW what your reticle was designed with
 
Re: Somebody Please Explain Math on 3.5 mils = 1 moa

That formula you're using is wrong. It's not 25.4, it's 1000/36 (usually seen as 27.78).

All that number means is that you're dividing the inches by 36 to get yards in decimal, and from there the formula is identical to the one used for ranging in meters, except the output is now in yards (inches/36*1000/mils=target range in yards). As is the case with the mil formula, the units you put into it equal the output units. This is the reason for converting inches to yards prior to doing the calculation.

If you work the math through with 1000/36 in place of 25.4, you come up with 3.6" per mil at 100 yards, which is the correct value.
 
Re: Somebody Please Explain Math on 3.5 mils = 1 moa

<div class="ubbcode-block"><div class="ubbcode-header">Quote:</div><div class="ubbcode-body">what I was taught is this... the Mil we use is actually rounded, the Army uses one reticle, the Marines another, civilian scopes who knows sometimes.... anyway depending on country, reticle style, etc, etc a Mil can = 3.4XX MOA or 3.6ish MOA, use 3.5... UNLESS you KNOW what your reticle was designed with.</div></div>

You were taught incorrectly.

All U.S. and Europeans mil scopes use the correct definition for the milliradian in the reticles - except for the Leupold M3A, which had a reticle based on 6400 graduations in 360 degrees. And it adjusted in MOA.

 
Re: Somebody Please Explain Math on 3.5 mils = 1 moa

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: Lindy</div><div class="ubbcode-body"><div class="ubbcode-block"><div class="ubbcode-header">Quote:</div><div class="ubbcode-body">what I was taught is this... the Mil we use is actually rounded, the Army uses one reticle, the Marines another, civilian scopes who knows sometimes.... anyway depending on country, reticle style, etc, etc a Mil can = 3.4XX MOA or 3.6ish MOA, use 3.5... UNLESS you KNOW what your reticle was designed with.</div></div>

You were taught incorrectly.

All U.S. and Europeans mil scopes use the correct definition for the milliradian in the reticles - except for the Leupold M3A, which had a reticle based on 6400 graduations in 360 degrees. And it adjusted in MOA.

</div></div>

+1. There is no approximates. 1 mil=3.6 inches@ 100 yards
1 MOA is 1.047 inches @ 100 yards
1 mil=3.438 MOA @ 100 yards
 
Re: Somebody Please Explain Math on 3.5 mils = 1 moa

Thank you everybody for your responses, again the level of knowledge on this site is amazing. CoryT I've read some of your previous posts and know that you know your shit, Lindy the same for you as well. I was hoping you both would respond to my question. I see now how rounding a moa to 1 inch can compound the error at a distance, and how 3.5 moa = 1 mil. I think I was getting wrapped around the linear distance 1 mil creates at 100 M, without regard for a moa being an angular measurement. Thank you very much for your help, because when I am proven wrong I learn.

Don't you hate how the military is all jacked up in measurements? Air Force distance is in yards, Army is in Meters, Air force is nautical miles, Army Aviation is Kilometers...then we get into precision shooting, which combines both mils, moa, yards and meters. I'm not even going to touch on the Marine Corps mils scale; I know nothing about it. Granted, I know what a data book is for, but I try to keep everything consistant in Meters. I even shoot my bow in meters; just a habit.

So to check myself and see if I fully understand this concept now, can you guys check my math just for shits and grins? My objective for this excercise is to determine how many linear inches a mil covers at 100 Meters:

1 MOA = 1.047" @ 100 yards
1 Mil = 3.438 MOA
1.1 Meters = 1 Yard

100M*1.1 = 110 Yards

(1.1)(1.047) = 1.1517 inches
1.1517*3.438moa = 3.9595 inches

So 1 mil would encompass a target that measured 3.9595 inches at 100 M, right? Or am I still jacked up?

Checking myself with range e...

(3.9595")(24.5)/1mil = 100.572 M

I'm assuming the .572 is from not using the exact conversion from meters to yards? I hope this is right, let me know if I'm still jacked up! Thanks again everybody for your help
 
Re: Somebody Please Explain Math on 3.5 mils = 1 moa

You seem to be all set, Yes, the .572 is still from rounding error of the Y-M conversion.
Frankly, I never really care what range measurement is used, as long as the spotter and shooter use the same one. The data card just has the setting for each range, so what does it matter?
 
Re: Somebody Please Explain Math on 3.5 mils = 1 moa

One meter = 1.0936 yards = 39.3701 inches.

Another way to look at how many inches one mil subtends at 100 meters is that we know that one mil subtends 0.1 meters at 100 meters, or 10 centimeters.

That comes from the fundamental definition of a milliradian, so that a milliradian subtends an arc whose length is always precisely 1/1000 of the distance from the vertex, no matter what unit that distance is measured in.

If we convert 10 centimeters to inches by multiplying 39.3701 by 0.1, we get 3.937 inches.

I agree with Cory that it's not useful to get too wrapped around the axle in units.

If you want to do range estimation using a reticle, the best and fastest way to do the math is to use a Mildot Master.

And the Marine Corps mil is exactly the same as the true milliradian.
 
Re: Somebody Please Explain Math on 3.5 mils = 1 moa

3.5Mils does not equal 1MOA.

3.5MOA (or just a smidge <span style="text-decoration: line-through">less</span>, sorry, I guess it's <span style="font-style: italic">more</span>...) equals 1Mil.
 
Re: Somebody Please Explain Math on 3.5 mils = 1 moa

<div class="ubbcode-block"><div class="ubbcode-header">Quote:</div><div class="ubbcode-body">
+1. There is no approximates. 1 mil=3.6 inches@ 100 yards
</div></div>

Well, mathematically speaking there is an approximation there -- the arc subtended by one mil at 100 yards is *exactly* 3.6". However, when you are shooting at a target, it is a flat surface, not an arc. Fortunately, that difference is so infinitesimally tiny that for our purposes we can and should pretend it is exact.
 
Re: Somebody Please Explain Math on 3.5 mils = 1 moa

Well, for the math finikins, at 100 yards, the length of the flat surface on the target covered by an angle of one milliradian is 3.599999850000002 inches.

If you want to calculate that for yourself, the formula is:

c = 2 * r * sin(theta/2)

where

c = chord length (that's the length of the angle projected onto the flat surface of the target)
r = distance
theta = angle in radians

Note, however, that most handheld calculators will not calculate sin(.0005 radians) to sufficient precision to give you an accurate answer. Neither will common P.C.-based programs like Excel. You will need to find an online high-precision calculator.

So, the error from using the arc length instead of the chord length is 0.000004166666616672248 percent.

Even though I am an Arcanamaven, that's an error I will ignore.

When shooting, if I can't hold it, I ignore it.
 
Re: Somebody Please Explain Math on 3.5 mils = 1 moa

The chord length isn't the flat surface he's talking about. All you have to do is take the tan of one milliradian, multiplied by the range to the target.

In this case it would be tan(.001)*3600 inches = 3.600001200000480000194... inches at one hundred yards.

It has to be a greater distance than the chord length, since it's being projected on the target.


Oh and to the OP, I didn't realize you were wanting to get a range in meters from inches. Now I see why you were using 25.4.
 
Re: Somebody Please Explain Math on 3.5 mils = 1 moa

That's incorrect. We're not talking about a triangle here - we're talking about a flat surface placed across the arc created by the one milliradian angle. The chord length is <span style="font-weight: bold">always</span> shorter than the arc length. Think about it - how could a line drawn across the inside of a curve be longer than the curve? Of course it cannot.
 
Re: Somebody Please Explain Math on 3.5 mils = 1 moa

Tell me this, what angle with the horizontal does the chord of an arc that subtends one milliradian make? If it isn't pi/2, then it's not the flat of the target that matt is talking about.

It's about projecting the angle onto to the target, which makes the solution a simple triangle.
 
Re: Somebody Please Explain Math on 3.5 mils = 1 moa

Guys; honestly, who gives a shit? If you can hold the difference between 3.5MOA and 1Mil, my hat's off to you.
 
Re: Somebody Please Explain Math on 3.5 mils = 1 moa

Kombar: Here's a picture. The angle, of course, is one milliradian. You can see the relationship of the target to the arc. So, the line at the target across the angle is smaller than the arc. The drawing is not to scale, of course.

angle2.jpg

 
Re: Somebody Please Explain Math on 3.5 mils = 1 moa

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: Lindy</div><div class="ubbcode-body"><div class="ubbcode-block"><div class="ubbcode-header">Quote:</div><div class="ubbcode-body">what I was taught is this... the Mil we use is actually rounded, the Army uses one reticle, the Marines another, civilian scopes who knows sometimes.... anyway depending on country, reticle style, etc, etc a Mil can = 3.4XX MOA or 3.6ish MOA, use 3.5... UNLESS you KNOW what your reticle was designed with.</div></div>

You were taught incorrectly.

All U.S. and Europeans mil scopes use the correct definition for the milliradian in the reticles - except for the Leupold M3A, which had a reticle based on 6400 graduations in 360 degrees. And it adjusted in MOA.

</div></div>

I think his instructors were actually pointing out the difference between IPHY turrets marked as MOA and true MOA turrets when combined with a Mil based reticle.
 
Re: Somebody Please Explain Math on 3.5 mils = 1 moa

All depends on how you set up the problem:

subtension.jpg


I'm thinking that for your way to work, the target would need to be tangent to the arc...

something like this:

angle2new.jpg


Otherwise your distance would be wrong, since the radius of your arc needs to be the same as the target distance.
 
Re: Somebody Please Explain Math on 3.5 mils = 1 moa

Whichever way you think of it, the difference is a difference which makes no difference. Mattj was quite correct when he said,

<div class="ubbcode-block"><div class="ubbcode-header">Quote:</div><div class="ubbcode-body">Fortunately, that difference is so infinitesimally tiny that for our purposes we can and should pretend it is exact.</div></div>
 
Re: Somebody Please Explain Math on 3.5 mils = 1 moa

Thanks again everybody for your responses. I believe I have everything down pretty good now. I know on the range many of these tiny details don't matter, just look at your data book for the dope you need whether it be yards or meters. But I like to completely understand everything forewards and backwards, and I appreciate all of your help.
 
Re: Somebody Please Explain Math on 3.5 mils = 1 moa

Wow, that is the most detailed explanation of mil I have ever seen. I will now forget most of it
smile.gif


Thank you,
Lance
 
Re: Somebody Please Explain Math on 3.5 mils = 1 moa

Sounds like you got it bud, remeber

Meters to yards- Meters X 1.094 = yards
Yards to meters- Yards/1.094 = Meters

I always convert the meters to yards or vice versa right off the bat.
 
Re: Somebody Please Explain Math on 3.5 mils = 1 moa

Yet more reasons to use a reticle that matches your turrets.
 
Re: Somebody Please Explain Math on 3.5 mils = 1 moa

runner,

Thank you for those PDF files. They are very helpful.

Bob
 
Re: Somebody Please Explain Math on 3.5 mils = 1 moa

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: BobinNC</div><div class="ubbcode-body">runner,

Thank you for those PDF files. They are very helpful.

Bob </div></div>

Agreed, that was the most concise explanation I have yet read on the subject.
 
Re: Somebody Please Explain Math on 3.5 mils = 1 moa

360 degrees in a circle
60 MOA per Degree
60 Seconds in a MOA

Therefore 1 MOA = 1/60th of 1 Degree
360 Degrees in a circle x 60 MOA per Degree = 21,600 MOA in a circle so 1 MOA = 1/21,600 of a circle

1.047 Inches in 1 MOA @ 100 yards is derived from the following equation:

Divideing the # of inches in a circle with a radius of 100 yards by the # of MOA in a circle.

100 yds x 36" = 3600"(Radius) x 2 = 7200" Diameter x 3.14 =

22,608 MOA

22,608/21,600 = 1.047" per MOA @ 100 yards

or

3.14 / 3 = 1.047"

1 Mil is equal to 1/1000th of the range you happen to be located.

ie 700yds x 3 = 2100 feet x 12 = 25,200 " / 1000 = 25.2 inches(1 Mil @ 700 yards).
or 3.6" x 7 = 25.2" Per MIL @ 700 yards.

Keep mind that there it is said there are 6400 mils in a circle. That is incorect, it has been rounded up for conveinience sake. There ae actually 6283.18 mils in a circle. That being said:

21,600 MOA in a circle
6283.18 Mils in a circle

21,600/6283.18 = 3.438 +/- MOA per mil @ 100 yards.

3.6" / 1.047" = 3.438 MOA @ 100 yards
7.2"/ 1.047' = 6.876 MOA @ 200 yards etc.

To convert your bullet drop in inches to MOA:

Divide your drop in inches by your range in 100 of yards:

A drop of 8.2" @ 200 yards
8.2"/2 = 4.1 MOA

Dont know if that helps anymore, but I understood the MILS/MOA better when the equation for finding each and how the numbers relate to one another was explained.I dont know if this was explained in the PDF files Runner posted, I was unable to pull them up on my computer. I apologize for repeating it if so.
 
Re: Somebody Please Explain Math on 3.5 mils = 1 moa

HogsLife:

Yes, they are fully explained in these papers, probably too much. You did a great job in also explaining them. Try these links. Bob

link 1

link 2

link 3

link 4
 
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