The Mil-Dot system is exceptionally versatile – if you know how to use it. If you drive a submarine, you can use them to figure out how far away you are from a ship that needs torpedoing. If you shoot a rifle, you can use mil-dot to hold the correct amount over a distant target. Or, if you have the system on an optic like a spotting scope, rifle scope or binoculars, you can use it to accurately figure out how far away something (or someone) is.

There’s a lot of fancy math behind the whole mil-dot thing, but we’re going to ignore most of that here and explain the concept, and more importantly, how you can use it, in plain English. There won’t even be a quiz at the end, I promise.

## The Math

The biggest problem with mil-dots is that most people try to explain them using big words like tangent, subtension, and fractions. We’ll try to avoid that here. I’m going to break my promise about not talking about math, but only for a second, so hold your nose and read on. I’ll make it painless, really.

Mil-dot is an abbreviation for “milliradian” and “dot”, which is from the English word meaning, dot. A milliradian is 1/1000th of a radian. What’s a radian? It’s a measure of distance traveled around a circle. So if you start eating the crust of a whole double-cheese and sausage pizza and work your way exactly half way around, you’ll have eaten 3.14159 radians of pizza crust. That’s half a circle, or three slices, as I like mine cut. It doesn’t matter how big the pizza is because radians measure the amount of travel around a circle of any size. Radians basically measure an angle. If you think of the same amount of munched pizza crust in terms of degrees, those 3.14159 radians are the same as 180 degrees.

Recognize that 3.14159 number? Yep, that’s Pi. Amazing coincidence that I used both Pi and pizza in this example, isn’t it? If you remember junior high math, Pi helps measure circles. Half the diameter of a circle, times two, times Pi, equals the distance all the way around. So, there are 6.28 radians in any circle. Since there are 1000 milliradians in a radian, a circle is comprised of 6,280 milliradians.

## Just because!

Here’s where people who really hate math make things a bit confusing. The U.S. Army says that there are 6,400 milliradians in a circle, not 6,280. Just because. It’s like arguing with your little brother. You can end debate by saying “Because!” with lots of conviction and volume. You know the Army has lot’s of conviction and even more volume. The Russians certainly aren’t going to agree with the U.S. Army, so they say there are 6,000 mils in a circle. Again, just because. We won’t get into a debate here of whether “because” from the Americans wins over “because” from the Russians. So, for this reason of “just because” from here on out we’re going to go with the theory that there are 6,400 mils (milliradians) in a circle. Just because.

## What exactly is a milliradian?

So what’s a milliradian? It’s a pretty small angle in practical terms. If you stand at the shooting bench and hold your arms out in a really, really small angle of exactly one milliradian and looked between your outstretched hands, you would only be able to see 3.6 inches of your target if it was 100 yards away. Since angles work proportionally, if you looked at something 200 yards away, you would see 7.2 inches. If you looked at an object 1,000 yards away, you would see 36 inches of your target. See how that works? The angle of a milliradian translates to 1 yard at 1,000 yards range or just 3.6 inches at 100 yards range.

## Mils and rifles

When you shoot a rifle exactly parallel to the ground, the bullet starts to fall immediately. Because gravity. This applies to both the U.S. Army, the Russians, and all the rest of us. When people talk about a bullet “rising” at first, that’s only because the barrel is pointed slightly upward from exact parallel due to the arrangement of the scope to the rifle barrel.

So, if you’re trying to hit a target 100 yards away, you have to aim a little “up” and if you’re trying to hit a target 1,000 yards away, you have to aim a lot “up.” You could work all this out in inches, meaning you would figure out you need to aim maybe 1.5 inches high for the 100-yard target and something like 400 inches high for a target 1,000 yards downrange.

The problem with using inches is that you can’t create scope adjustment dials with all those numbers marked in inches. If each click of your scope corresponded to an inch, what distance would that work for? Maybe 100 yards? What if you’re shooting at a target 367 yards away? Then how many inch-clicks do you turn? Imagine your spotter has figured out you need to aim 13.7 inches high to hit a target 441 yards away. When he says “adjust up 13.7 inches!” you’re like… what? How many clicks is that?

This is one of the reasons why we use milliradians to standardize the amount of adjustment we’re going to make. If we need to aim 3.6 inches high for a 100-yard target, we make a one milliradian adjustment. If we need to aim 7.2 inches high to hit a target 200 yards away, we make a one milliradian adjustment. See how that works? Now, your spotter can just tell you something like “add one mil of elevation.”

Just so you know I didn’t forget, all this applies to windage (sideways) measurement too, it’s just easier to use elevation, or bullet drop, examples. An angle is an angle, regardless of whether it measures something up and down or sideways.

## How to figure it out

Next, we need a way to calculate inches at a certain distance to the standardized mil measurement. If you range a target and figure out that it’s 428 yards downrange, you can use a ballistic program or chart to determine how far your particular bullet will drop at that range. That will depend on your caliber, cartridge, and gun combination. For example’s sake, let’s assume we’re shooting a .308, and we figure the bullet will hit 36 inches low at that distance. How many mils do you adjust your scope elevation to get an accurate hit?

Fortunately, there’s a really easy way to calculate this without using complex math stuff like tangents and cotangents. The number of mils equals the amount of bullet drop (measured in yards) times 1000, divided by the distance to target in yards. In our example, we have 36 inches, or one yard of bullet drop and a range of 428 yards.

Mils = (1 yard * 1,000) / 428 yards = 2.3 mils.

If your scope is measured in 1/10th mil clicks, that’s 23 clicks in upward elevation adjustment. Make sense?

## Mil-dot reticles

Mil-dot scope reticles look really cool. They will have normal crosshairs with a series of dots, evenly spaced horizontally and vertically along the crosshairs. The distance from the center of one dot to the center of the next is exactly 1 milliradian, or mil. Most traditional mil-dot scopes have graduations that show 10 mils vertical and 10 horizontal. There is no dot in the exact intersection of the crosshairs as that would be annoying and block your view of the target. Consider the intersection of the crosshairs as the center of a dot, so the distance from that intersection to the center of a dot in any direction is exactly one mil.

In our example, we talked about using turret click adjustments to move the crosshairs to exactly the right place to account for elevation changes, but you can also just use the dots on the reticle. If you have to aim exactly 3 mils high to hit a distant target, you can place the ~~second dot~~ (*Correction: “Second dot” was a typo, it’s the third dot!*) below the crosshairs on your target to achieve exactly the same thing. It’s a quick and easy way to adjust, although not as precise as making fine click adjustments.

You can use the horizontal mil-dot markings to lead moving targets by the right amount also. I you have to lead a target by 36 inches and it’s 1,000 yards away, then place the first horizontal crosshair dot over the target.

## Then what the heck is Minute of Angle?

Some scopes have turrets that make adjustments measured in mils, with .1 mil per click being common. However, many optics use a similar, but different, way to measure angular adjustments called minute of angle, or MOA for short. Your optic might have turrets that move one, ½ or even ¼ minutes of angle for each click.

A minute of angle also represents a slice of a circle, just measured differently. If we sliced our pizza into 360 pieces of equal size, each piece would be a degree as a circle contains 360 degrees total. If you divide each degree, or single slice, into 60 equal parts, those would be called minutes. Since each degree is divided into 60 minutes, a complete circle has 21,600 minutes of angular measurement. With me so far?

Using the same concepts that we used to translate an angle to a number of inches at a certain distance, we can do the same with minutes of angle. Instead of one minute of angle translating to 3.6 inches at 100 yards, it works out to 1.04 inches at 100 yards. A minute of angle is an even narrower measurement than a milliradian.

The basic math process to figure out how many minutes of angle correspond to inches of bullet drop (or windage adjustment) at a given range works like this.

Minutes of Angle = Correction in inches / Hundreds of yards.

So, using our earlier example, if we have to aim 36 inches high to hit a target at 428 yards downrange, then the equation works like this:

MOA = 36 / 4.28 hundreds of yards = 8.41 MOA.

Since MOA’s are “smaller” you need more of them than mils to make the same amount of adjustment. If your scope adjusts in ¼ MOA clicks, then you will raise your desired point of impact 8.41 MOA / .25 MOA per click, or 34 clicks. It’s actually 33.6 clicks, but you can’t do .6 of a click!

## Practical application

So all this abstract stuff is great, but what do you do with it?

For starters, use these concepts to zero your rifle at the range. Plenty of folks zero their rifle for 100 yards. Without fail, I see folks with their new rifle at the range firing a shot, spinning the dials randomly, then repeating the process. They’ll spend lots of time and ammo hoping to get on target by trial and error. Here’s how easy it is to use some basic math to get on target quickly.

- Fire a shot or small group at your target, 100 yards down range.
- Measure how many inches you need to move the hits to be exactly where you want them. Suppose your bullets are hitting 3 inches above the bullseye.
- Since you are shooting at 100 yards, you need to move your scope adjustment down 3 inches, which conveniently works out to 3 MOA.
- If your scope has ¼ MOA click adjustments, then turn your dial 12 clicks (¼ per click times 3 MOA) to get on target.

Piece of cake, right?

## What’s next?

This article is a basic introduction to the concept of mils and how to convert bullet drop measurements into milliradian adjustments. But mils are much more powerful than that. You can also use mils for range estimation, just by looking at objects of known size through your binoculars, spotting scope, or rifle scope. Next time, we’ll cover that topic.

Did I miss where you said that these calculations only work at one magnification? Not an issue in a fixed 10x scope but on a 4-16x or other variable power scope with a second focal plane reticle the dots are only accurate at one magnification. I put a 10 cm ruler at 10m then adjust magnification until the mil sub tends the ruler then use a paint marker to identify that power setting.

Thank you for this clear, logical and succinct explanation of some complex math principles. If my high school math teacher had been so gifted, I just might have stayed in trigonometry! So many would rather prove they are smarter than you instead of helping you understand.

LOL. I really enjoyed this story; it highlights two things about Math and the Internet. One, you first have to understand something to explain it and two, it never goes away.

Good article and explanations. But I need more help.

I’m trying to explain a quote in a letter from my late father (1920-2013) talking about artillery training at Fort Sill in 1943. He wrote: “. . . but A and C fluffed their first shoots badly and spread 100 mil errors all over the range. Errors are one thing the school cannot abide, and I cannot say I blame them.”

What is the significance of 100 mil? Does this mean they *really* made a hash of things? Thanks for any help.

S

A click = 1 cm at 100 meters …. 1 mil = 10 cm at 100 meters … no MOA, no YARD Sorry, it’s metric system the mil-dot is the same, why merge with inches and yards??????

why is it that when people talk about MOA and practical application it is shoot at 100 yrds then see how many inches it is off from center, 3 inches them click 3 MOA what about MRAD which is what the article was about?

Guess I’m a bit late to the party. I have to say, my understanding of mils and moa is no better now than before I read the article. On a positive note, my head hurts worse. Not once have I actually had time to whip out pencil and paper or a calculator while in a tree stand or blind. Kentucky windage has always worked well for me. I don’t miss often.

Great article about : “MILDOT Made Easy”. Very well written and straight to the point. However I do have a question others have asked me but I didn’t know how to respond. Maybe you could shead light on the subject. If I’m ranging a target say a white tail deer (30″ chest to back) but I want to increase the chances of hitting within a six inch vital zone, would using 6″ to calculate range and calculate come ups cause a miss? I use 30″ then come up and hold dead one knowing my bullet may strike anywhere in that 30″ tall area. What do you say?

I might be misunderstanding the question, but when I hear “ranging” that means determining the exact distance to target by looking at how big an object of known size is compared to the scope reticle markings. For example, if that 30″ chest to back covers 9 minutes of angle hashmarks in your scope view, then it must be 318 yards away (30 inches / 9 MOA) * 95.5. Knowing the exact distance allows you to aim exactly where you want if you know your bullet type and its velocity. Tons of smartphone apps, cards, etc can tell you the exact holdover or scope turret adjustments if you know the exact range to target. See https://www.gunsamerica.com/blog/optics-buying-guide-finding-range-scope/ for more info on the whole ranging thing.

this is the worse explanation ever, as the author made it harder to understand the concept by using the Inch instead of centimeter… the MRAD is better (higher granularity) and easier (no fraction) when compared to MOA.

1 MRAD corresponds to 10 cm exactly (centimeter) at 100 meter … exactly with no fraction

vs

1 MOA corresponds to 1.047 inch at 100 yard

that’s all !!!

Base MRAD, US MRAD or Russian MRAD? They are all different…only one of them is accurate to your description.

Thanks, this was a great article.

Must be an American who writes a whole article about MILs without using the meter … the point is, that 1 mil is 1 cm in 100 m or 2 cm in 200 m. 2 mils is 2 cm in 100 m. And that you can calculate. So, please folks behind the pool, forget about your ridcolous inches and furlongs and yards and lines and chains and pegs and poles and miles and all of that medevial fairytale crap.

100% agree. Although it’s basically taboo to say that here… The American system makes zero sense, but who am I to talk?

Here, in Americia, it makes perfect sense. Sorry it hurt your Metric heads 😉

No it’s not. It is 10 cm at 100 m or 1m at 1000. Think twice Mr. Metric.

Another way to look at it (since the mil is SI equivalent to “millimeter per meter”), is that 1 mil equals:

1 mm at 1 m, or

10 mm at 10 m, or

100 mm at 100 m,

1000 mm at 1000 m, etc.

For instance

50 mm at 500 m would be: 50/500 = 0.1 mil.

3 mm at 100 m would be: 3/100 = 0.03 mil

The “What’s next example” would have been better, had you given the example of being at the range sighting-in your rifle using milliradians. Especially for those of us who are using a scopes with turrets in milliradians. Your explanation of milliradians was great and easy to understand however I was thrown for a loop when you gave the example of being at the range and using MOA. I thought we were talking milliradians. So to come up 0.9 mils for a 3.24 inch elevation at 100 yrds. I guess?

I only used the MOA example because the majority of affordable scopes out there with mil-dot reticles still use 1/4 MOA click adjustments on the dials. Why? Got me… Like you I think, if my reticle is in milliradians, I want the dials set that way too 🙂

A click = 1 cm in 100 meters …. 1 mil = 10 cm in 100 meters … no MOA, no YARD Sorry,

1/2 the diameter x 2 x Pi = perineter ( asshat that =D divided by 2 x 2 x Pi = perimeter or briefly Pi x D = perimeter

The article stated :

“Half the diameter of a circle, times two, times Pi, equals the distance all the way around”.

But in actuality; Half the diameter of a circle, (squared), times Pi, equals the distance all the way around.

Pi times radius squared is the area of that circle. Two Pi times the diameter is the circumference.

Almost. The product of Pi and the diameter is the circumference (or 2πr).

The army uses 6400 mils to the circle because for artillery and mortars because it is divisible evenly into 4 1600 mil quadrants. Using 6280 mils would introduce too many opportunities for error in computation of firing data. The difference between 6400 and 6280 mils for quadrant (range) and deflection (direction), 120 mils, would introduce a constant error of 10 feet per thousand yards or 3 meters per kilometer which is programmed into the manual firing tables or fire control computers. When you have a casualty producing radius of 50 meters with the 105mm High Explosive round and 100 meters with the 155mm High explosive round this error is negligible. I was an artilleryman in the Army so I can’t give an informed estimate for the 60 and 81mm mortars of the infantry.

Thank you for sharing the details on the Army numbers! Interesting stuff and that makes a lot of sense. Now if we could only figure out the Russians’ logic…

Excuse the math error that should read 100 feet at 1000 yards or 30 meters per kilometer. That’s why there’s tabular/graphic firing tables and fire control computers. Sunday PM brain fart.

If I remember correctly, the killing radius of an 81mm mortar was 20 meters; and, the killing radius of a 4.2in mortar was 35 meters. With VT (variable time) fuses, you get a nice air burst, about 20 feet over the target, that increases the effectiveness. I’m a former Army infantry forward observer. We used the “WORM” formula (Width of adjustment in meters equals Range in meters, divided by 1000, times mils to the target) to compute lateral corrections to bring a burst onto the target. It’s a lot easier to work out in your head using 6400 mils than it would be using 6280!

Surprised the 4.2 didn’t have a larger killing radius. Interesting ’cause 4.2 is nominally equivalent to the 105mm. Different projectile weights? The 105 HE projectile weighed apprx. 35 pounds.

I know that I’m very late with this reply; but, the 4.2″ mortar round also weighed 35 pounds.

Yup its the exact same for 60’s and 81’s

Sunday PM brain fart: the comment should read 100 feet per thousand yards–a 10 percent error or 33 meters per kilometer.

6400 is great to work with math-wise. 45 degrees = 800mils in the US system whereas it’s 750 in the Russian system. Every octant around the circle is 800 mils. Subcardinal directions (NW, SE) always resolve to an easy number.

US wins on this one.

A click = 1 cm in 100 meters …. 1 mil = 10 cm in 100 meters … no MOA, no YARD Sorry,

Trying to discuss mils and using the Imperial system as your reference is just wrong. Mils were designed to be used with the metric system. 1 mil of angular deviation is roughly 1 meter on the ground at a distance on the ground. I say roughly because it’s actually not, due to the error of saying there are 6400 mils in a circle when there really are 6280, and we introduce a constant error, that we in the artillery community call the “smart guy factor” of 1.0186 (6400/6280 =~1.0186). This factor works when you’re converting meters into mils, but not in reverse. To convert mils to meters you need to use 0.98125 (6280/6400). Using inches and mils together causes computational errors and will not give you an accurate ballistic solution without needless additional math steps.

-Captain Paul Willard, USMC, Gunnery Instructor, US Field Artillery School

1 mil of angular deviation is roughly 1 meter on the ground at a distance of 1000 meters away from you.

Heres a question: you have a scope that measures in m.o.a. & it has a ballistic reticle in the second focal plane calibrated for 8x. If you turn the power up to double, or 16x (to see the target better), does it effectively half the measured distances of the ballistic reticle subtensions?

an easy way to sight in is to get a large target backer place a mark or a bull’s eye on the target aim at said bullseye fire a shot notice the point of impact. place your crosshairs back onto the bullseye make adjustments with your scope to bring the crosshairs into or on your point of impact from previos shot this allows you to adjust the scope without having to measure anything fire another shot at the bullseye and repeat the process until you’re dialed in properly I can dial in a scope within 3 to 5 shots very easily using this method

Thanks for the information on Russian mils. Now I know why a PRC made knock off of a GI compass was marked 6,000 mils to a circle.

The U S Arm (and NATO standard) uses two miles: The Artillery mil is 6,400 to a complete circle, çlose enough for government work’.’ The Engineer mil comes 6,280 to a ccomplere circle which is closer to the actual vale of 2 pi times 1,000, or 6,283.

Minutes of angle at 100 yards is pi/3 inches, o about 1.047 inches, better round to 1.05 inches in lieu of 1.04 inches. And a 1/4 m.o.a. click at 100 yards is about 0.26+ inches.

A 1/10 (0 0.10) mil click is 0.36 inches (exactly) at 100 yards.

Most ‘scopes these days have the reticule in the second focal plane. For these second plane ‘scopes, the difference between mil-dots varies with the magnification. Typically, on such ‘scopes, the reticule is set up so that at one specified magnification, the distance between dots is correct…typically about 10 X.

To have a mil-dot ‘scope with clicks in some fraction of m.o.a. or in fractions of an inch is absurd and makes things much more complicated than necessary.

I’ll never willingly go back to a second focal plane reticule or to either fractional m.o.a. or in c.o.a. makes no sense; the math to convert the one to the other is cumbersome. I have used a relatively inexpensive first focal plane (reticule) scope with mil-dot reticule and clicks in 1/10 mil. and I’ll never want any other arrangement than first focal plane mil-dot reticule with adjustments in clicks of 1/10 mil(or 0.10 mil.) That ‘scope is the BSA scope made for MidwayUSA. I keep plaguing both Larry Potterfield at MidwayUSA as well as B S A to get a similar ‘scope with higher magnification–the preesnt one is about 4 to 14 X and one in 6 to 20X or even better, 6 to 24X would be really great.

Trying to convert Mils and MOA is like the frustration we all have with trying to convert from our system of measurements (inches, fett, yards, etc.) to metric. I had an old Canadian soldier that I was working with tell me to stop trying to convert and to just think in the system you want to use. For example think in Mils. Don’t think in (for example) duhhh, my Mils equal 36 in at 1000yds and my MOA is 10 inches so I need to figure correction in inches divided by hundreds of inches or whatever. Buy a scope in whichever system you like and stick with it. Think in that system, live in that system and shoot in that system. If for some reason you are forced to switch to the alternate system, do like Chris said above and write your benchmarks on a card and tape it to the side of your rifle.

Me, I just use the Horus reticle and live, sleep, breathe that system.

My god boys it’s not that dam difficult. I use MOA I sight my rifles at 200yd zero, then I write on the stock of said rifle 200yd =0. 300yd = 7.8 and so on out to 1000yd the 7.8. (Is an example ) relates to the numbers and lines on your turret. So I would turn the turret until the number 7 is in line with the mark or line on the scope that 0 was in line with. Keep in mind the adjustment is in MOA so 7 is 7 minutes of angle .8 is 8 more clicks that are 1/4 MOA at 100yds.

How do I come up with that amount of adjustment. .A range finder a target and ammo. No chart no BDC. And I’ve dropped elk at 500 bear at 450 deer at 650 all with a savage 110 300 win mag and a Mark 4 LR/T 3.5 10 M1 turrets in MOA don’t over think it. Range it dial your scope pull the trigger

It works!!!!

Zoned out right after the promise of “no math” and then….it’s, wait for it, all math. There is much better instruction on this. Sorry.

Well I hate math, so I never have wanted to be a long range shooter. It could be fun though without the math. After reading this article I have decided if I want to make a long range shot I will just eat a pizza instead. Just give me an AK-47, a Glock 34, plenty of ammo and stand aside. Relax and everything will be good!

I’M TOTALLY CONFUSED. THERE WAS ENOUGH MATH IN THIS EXPLANATION TO MAKE ME THROW UP MY HANDS IN DEFEAT. I GUESS I’LL NEVER GET THE HANG OF THIS TYPE OF SCOPE. STILL MAKES NO SENSE TO ME.

Could you explain why you would use the 2nd dot below the cross hairs for a 3 mil correction?

Thank you. cblaz

Sorry Chuck, that’s a total typo! You are exactly correct in spotting the anomaly here, it should be the center of the third dot below the reticle for a 3 mil correction. I will fix that now and thanks for the heads up!

Seemed like a bit of a jump at translating mil dot to MOA. Aside from very basic math, please assume no knowledge on the part of your reader. We need caring tutorials and not the chat between peers that one so often finds in writers. One needs to understand the problems of the student, and then address that. It’s an empathy thing. Those who don’t have it are the most frustrating of teachers. JWC

Great article. Clear and concise. You must have a sub MOA rifle, consistant ammo and marksman skill while using mil-dot scopes or you will be chasing your tail. As you add distance you must add a correct caliber for terminal effectiveness. Precision work requires you to eliminate or accurately compensate for the variables. In real world application, you must be able to accurately measure the size if the target or something in the very close proximity. Is it a big man far away or a small man close? Is it a 55 gal. drum or a 30? 14 Or 17 inch vehicle rim? What do you “range” on in the bush where there are no man made clues? If you are willing to put in the time, then you will get much more then tacti-cool from a mil-dot and not need batteries. If you just want to hit a 3 foot plate at 600 meters save your money and just buy a bit more ammo.

Same typo in this formula MOA = 36 / 4.38 hundreds of yards = 8.41 MOA. True answer 8.21MOA

In the example the yardage was 428. So the forumla would really be…

MOA = 36 / 4.28 hundreds of yards = 8.41 MOA

😉

Dang those 2 and 3 keys! They really shouldn’t be right next to each other 🙂 Will fix…

Excuse the math error that should read 100 feet at 1000 yards or 30 meters per kilometer. That’s why there’s tabular/graphic firing tables and fire control computers. Sunday PM brain fart.