Ryan Cleckner [above] was a special operations sniper team leader in the US Army’s 1st Ranger Bn (75th) and a sniper instructor with multiple combat deployments. Click here to order his book Long Range Shooting Handbook- A Beginner’s Guide to Precision Rifle Shooting from Amazon. Here’s chapter 18 on estimating and adjusting for target distance . . .

I strongly believe in learning how to shoot a rifle with iron sights before putting glass on your gun. It should come as no surprise that I also encourage learning and practicing to estimate a target’s distance with angular measurements — using the Mil or MOA marks in a scope — before buying or using a laser range finder. So let’s get to it!

18.1  Angular Measurements (“Milling”)

There’s an inverse relationship between how big an object appears and how far away it is. As the distance to an object increases, the size of the object appears to decrease. Imagine a target at 100 yds as a starting point. See Figure 18.1-1.

If you moved that target to half the distance (50 yds) from your vantage point, it would appear twice as large. Likewise, if you moved the 100 yd target twice as far away (200 yds) it would appear to be half the original size. And if you moved it four times as far away, (400 yds) the target would appear to be one quarter the size.

This predictable relationship allows us to estimate a target’s distance based on how big or small the target appears.

You can measure a target’s size in a scope using the marks in your reticle, which are either MOA (Minute of Angle, explained here) or Mil (Milliradians, explained here). Using the apparent measurement of the target, you can determine the distance to the target.. In order for this to work, you have to know the size of the target.

18.1.1  Calculating Distance with Mils

To calculate a target’s distance with
Mils, multiply the known size of the target by 1000 and the divide that number by the size of the target measured in Mils through your scope (See Figure 18.1-2).  Note that the distance to the target will be in whatever unit of measurement was used for the size of the target. If you measure the target’s size in yards the distance determined from the formula will be in yards. The same is true if you use meters or any other linear measurement. Remember: a Milliradian is 1/1000th of any distance (See Chapter 9).

18.1.2  Calculating Distance with MOA

To calculate a target’s distance with MOA, multiply the known size of the target in inches by 95.5 and then divide that number by the size of the target measured in MOA through your scope (See Figure 18.1-3). Unlike the Mil formula, this formula should only be used when working with target sizes in inches and distances in yards. If needed, however, there are alternate numbers that can be used in the  formula (See Figure 18.1-5).

18.1.3  Alternate Units with Mil and  MOA Calculations

Sometimes you might need to use one unit of measurement for the size of the target and another, non-standard unit of measurement for the distance to the target. For example, you may have a rifle scope which measures in Mils and a target size in yards and you need your distance in meters (instead of yards). Or you may have a scope which measures in MOA and a target size in inches but you need your distance in meters (instead of yards).

If you’re trying to determine the distance of a target in a non-standard size and distance unit combination, you have a few options. 1) Convert the actual size of the target into a different unit, 2) alter the formula, or 3) convert the calculated final distance into the desired unit. To try out each of these options, let’s use the following hypothetical:

Let’s say you have a target that is 12 inches tall which measures 1 Mil tall in your scope and you need your distance in yards.

Option 1: Convert the size of the target into a different unit.  In our hypothetical above, we can convert the target size from inches to yards to get a distance calculation in yards.  The linear unit conversion chart in Section 9.2 of this book (Figure 9.1-3) shows that to convert from inches to yards, you divide the size in inches by 36 (the number of inches in a yard).  (12/36=0.333).  After converting to yards, we can use the standard Mil formula:

Option 2: Alter the formula. In our hypothetical above, we need to alter the Mil formula to allow us to start with a target size in inches and end up with a distance in yards. The chart in Figure 18.1-4 below shows that in order to input inches into the Mil formula and end up with yards, you replace the “1000” in the Mil formula with “27.77”. Now we can use the altered formula:

Option 3: Convert the distance into the needed unit. If we used a target size in inches from our hypothetical and we used the standard Mil formula, our target distance would be in inches and need to be converted to yards. The linear unit conversion chart in Section 9.2 of this book (Figure 9.1-3) shows that to convert from inches to yards, you divide the size in inches by 36:

In each of the three options, we can  calculate that a 12 inch target measuring 1 Mil tall in a scope is 333 yards away. It’s up to you to determine which method is easiest or best for your needs. Generally, I prefer the first option; you won’t always be converting target sizes in inches to distances in yards. In fact, you may want a distance in meters or you may have target size in centimeters, feet, or some other unit of linear measurement. Although it’s easy to convert feet to inches, you’re still converting units prior to using the formula. If you’re already converting from one unit to another, then why not just convert to yards, so that you can use the standard formula with “1000”? If I’m in a situation where all of my target sizes are known in inches and I want all of my results in yards, I will make an exception and alter the formula to use “27.77” instead of 1000.

To help you with entering one target size unit into the Mil formula in Figure 18.1-2 or the MOA formula in Figure 18.1-3, and calculating a target distance in another unit, see Figures 18.1-4 and 18.1-5.

18.1.4  Measuring Target Size with Mils and MOA

As targets get further away, it’s harder to calculate range using Mils or MOA. For one thing, smaller appearing targets are harder to measure For another, a small percentage error can magnify the  result.

For example, when a 1 meter tall target measures 10 Mils tall in your scope, it is 100 meters away. At this distance, it’s difficult to make a 10 percent error. Even if you make a 10 percent error, and mistakenly measured the target to be 11 Mils tall, you’d conclude that the target is 91 meters away. Even so, your mistake would have a negligible effect on your ability to hit the target.

On the other hand, if the 1 meter target was 1000 meters away, it would measure 1 Mil tall in your scope. At this distance, when the target appears so small in your scope, it’s easy to make a 10 percent error. The mistake has a much larger effect on accuracy.

For example, if you mistakenly measured the target as 1.1 Mils tall, you’d think the target is 910 meters away. If you tried to shoot a 1 meter tall target at 1000 yards with the elevation adjustment on your scope set for 910 yards, you’ll miss the target. Completely.

To get the most accurate measurement possible from your scope, your rifle must have a stable platform. The most difficult part of measuring a target with your reticle: holding the rifle steady enough to line up one part of the reticle with one edge of the target, and then shifting your focus to the other edge of the target to see where it measures on the reticle. It’s difficult to ensure that one edge is lined up properly while looking at the other.

Here’s a trick that helps: use the edge of a mil-dot — instead of the middle of the dot — as a starting point. By doing this, you can better keep track of its alignment while I’m looking at the other edge of the target. It’s easier to ensure a specific edge is aligned, as opposed to trying to make sure the edge of the target is still exactly in the middle of the dot. See Figure 18.1-6.

Some targets are narrower than the mil-dot. By using the edge of the mil-dot, you won’t have to keep moving the mil-dot to confirm where the location of the target’s edge.

For example, it might be easier to measure a certain target’s width rather than its height. In the military, we often used “E-type” targets which measured 1 meter tall and 1/2 meter wide. It was sometime difficult to determine whether one of these targets measured 1.6 or 1.7 Mils tall in a mil-dot scope. So we used the target’s width oand the dimensions of the mil-dots in our scope to our advantage.

Our rifle scope’s mil-dot had dots that measured 0.2 Mils in diameter spaced 1 Mil apart. From a particular spot on one dot (e.g. bottom, middle, or top) to the same spot on an adjacent dot was 1 Mil. (See Figure 18.1-7.) By using the width of the dots to our advantage, we could precisely measure 0.8, 0.9, 1.1, and 1.2 Mils.

From the outside edge of one dot (e.g. the bottom) to the outside edge (e.g. the top) of an adjacent dot was 1.2 Mils; the bottom of one dot to the bottom of the next dot is 1 Mil plus the width of the top dot is 1.2 Mils. Using the same math, we knew that the inside edges of two dots were 0.8 Mils apart.  (See Figure 18.1-8.) By combining the edge of one dot with the center of another, we could measure 0.9 and 1.1 Mils. (See Figure 18.1-9.)

Back to the example above of not knowing whether an “E-type” target was 1.6 or 1.7 Mils tall . . .

We knew the width of these targets was half their height. Therefore, if we used the edges of the dots to our advantage and measured the width, we could see whether the target was exactly 0.8 Mils wide. Which meant it must be 1.6 Mils tall. (See Figure 18.1-10.)

Angled Target Measurements

Often, targets are not perpendicular to your line of sight. In other words, targets don’t always appear perfectly flat towards you. Sometimes you are at an elevated vantage point looking down at a target Other times you may be looking at a target from the side. (See Figure 18.1-11 for examples.)

An angled view of a target makes at least one dimension appear smaller than it really is.

For example, assume that the targets “A” and “B” in Figure 18.1-10 are both 25 inches tall and they’re both the same distance from your position. Target “A” is directly in front of you while target “B” is below you (you’re looking down at it). You measure target “A” to be 1.1 Mils tall and you measure target “B” to be 0.9 Mils tall.

If we don’t compensate for the angled view our Mil calculation based on the height of the target may lead us to think that target “B” is further away than target “A”.  (Remember: targets appear smaller as they are farther away.) For example, a 25 inch target measured at 1.1 Mils tall would be 631 yards away and the same target  measured at 0.9 Mils tall would be 730 yards away.

There are two methods of compensating for angled targets: mathematically compensating for the smaller-appearing dimension and using a non-skewed dimension for measurement.

To mathematically compensate for an angled view, multiply the angle’s cosine by the distance calculated by the Mil or MOA formula. (See Figure 18.1-12 for a table of angles and their corresponding cosines.)

In our example, target “B” is 30 degrees below us. The cosine for 30 degrees is 0.866. The 730 yards calculated from the angled view of target “B” multiplied by the cosine for the 30 degree angle of target “B” equals 632 yards. Although the corrected distance for target “B” of 632 yards is not exactly the 631 yard target distance of target “A”, it’s nothing more than a rounding error. It won’t have an effect on hitting the target.

It is important to note that this will only work if the target is straight up and down from the ground.  If a target is 30 degrees below you and angled back 30 degrees, then you would see the full size of the target and an angled-view compensation is not required.

The other method for compensating for an angled view of a target: use a non-skewed dimension.

For example, although the height of a target “B” and the width of target “C” appear smaller, the width of target “B” and the height of target “C” are unaffected by their angles. If the target is angled forward or back — because it’s not level with the ground or it’s above or below you — use the target’s width for your Mil or MOA calculation. No adjustment to the formula or result is required. Likewise, if a target is twisted to one side or it is angled away left or right, then use its height. This method  only works if you know both the target’s height and width dimensions.

I know this seems like a lot of math, because it is. But once mastered, the mathematical formulas are easy to use, accurate and extremely rewarding. Especially when you hear the word “hit.”

1. Anyone seriously interested in long range shooting should check out tiborasaurusrex’s Sniper 101 series on youtube. It is far and away the best, easiest to understand, and most thorough work on distance shooting.

I love to shoot close up, but it gets expensive quick. I can shoot long distance with just a handful of rounds and have just as much, if not more fun than putting 300 rounds of .40 S&W down range.

• Thx. I’m a subscriber, but I must have missed those videos. I’m a complete novice with scopes. I’ve had my semi 308 for four years now and still haven’t put any glass on it. I spent many hours researching this topic and still haven’t pulled the trigger.

2. This is why I use the fixed 4x POSP scopes on my long range rifles….. Has a neat little graph BUILT into the scope on the lower left (unused area) to figure the range without a calculator. As long as you are looking at “zombies” that are 1.7 meters tall,walking around you can range them. I have no idea why more scope builders don’t use this????

• There are many other scopes with rangefinding reticles like that. Most of Primary Arms scopes have a variation, for example.

The nice thing about mils, though, is that they let you range against any object, so long as you can estimate the size, and not just humans.

• Yes, the ACSS reticles available in some of the Primary Arms scopes (and coming to other things, like the Trijicon ACOG) are freaking amazing and SO easy to use. I’ve had a 1-6x ACSS scope on my AR since early summer and have yet to review it, but I’ll get to that very soon. There’s no math and it’s both accurate and instant. The first chart in this article (18.1-1) sums up how it works, in that the change in target size is known as the distance changes. So instead of measuring and then doing math, how about just building it into the reticle? The width of the elevation lines correspond to an 18″ wide (person’s torso or the vital zone of a lot of game animals… or any object if you can estimate 18″ worth of size on it) target at each range down the elevation tape. Match the target’s width with the width of one of those lines and pull the trigger, because you’re already holding correctly for that distance. If you can’t accurately measure torso width (e.g. person is standing sideways) then there’s a tape on the right side of the reticle for measuring based on 5′ 10″ height. If the person is behind cover and you can only see from the waist up to the top of the head then that’s half their height. The reticle also has leads for shooting at a running target and range-appropriate hold dots for windage. Anyway, it’s easy, it works with a high degree of accuracy, and it’s instant because there’s no math and there’s no dialing in the settings. Just match the width of the target to the width of one of the lines on the reticle and pull the trigger.

Here’s a review on the .22 LR one: http://www.thetruthaboutguns.com/2015/08/jeremy-s/gear-review-primary-arms-6x-acss-22-lr-scope/ …the .223/.308 one works the same way as far as ranging and holdovers and such, but it’s designed to range people whereas the .22 one ranges bottles, cans, and clay pigeons 🙂

3. I think often times people do not realize that under real life hunting conditions there is no time to do mathematic calculations coupled with the fact that animals do not come in uniform sizes even those of the same age. When you couple this with shooting uphill or downhill and add in the wind factor as well you can begin to see how complicated this becomes and you may only have a couple of seconds to shoot or let go a trophy of a life time.

Jack O’Connor many years ago before the advent of laser rangefinders or the use of mil dots in common hunting scopes simply bought a rifle (270 Winchester) that had an average velocity of 3,000 or more fps. This was a fairly flat shooting rifle for that time period that had lower recoil than the shoulder bruising and ear splitting magnums but was still not that far behind the magnums velocity considering the fact that most magnums back then often came with 24 inch barrels which caused them to lose a lot of their published velocity.

Jack simply sighted in 3 inches high at 100 yards and a dead on hold out to 300 would be more than sufficient to hit a big game animal in the kill zone. At 300 yards you would be a little low but not enough for a miss. Assuming of course you were firing on flat land not hilly land.

What you did need was simple experience to estimate hold under for up-hill and down-hill shots and of course some experience to know when you were shooting beyond 300 yards. But lets face facts. The average hunter is in no way practiced enough under field conditions to shoot more than 300 yards and the truth is many cannot even make hits at 100 yards under field conditions. It takes a tremendous amount of practice shooting in the prone, sitting and standing positions to learn muscle and eye and breathing and concentration control which is so necessary in developing rifle marksmanship. The average hunter does not have the time or money to spend on ammo to accomplish this. Using a .22 rim-fire or even low priced home made cast bullet loads is a way to get a lot of practice at lower cost when developing shooting in field positions irrespective of range. In other words practicing these field positions at even ranges as close as 50 yards will help develop your field shooting skills.

Practice on paper targets at know ranges and set also at ranges up-hill and down-hill will give you the skill to know about how low to aim when switching from shooting at an animal on a relatively flat surface as opposed to one on a hill side. Again all this is practice that takes time and todays stressed out short of time hunter has little time to accomplish this.

Let us not loose sight of the fact that “a really skilled hunter” studies the habits of wild game and the territory they live in. Jack often got above wild sheep and goats and was able to stalk as close as 25 yards making for an easy shot even with a bow (which he did not use). Blasting away at long range and hoping for a hit is the behavior of the “slob hunter” which is a category which way to many hunters these days fall into. Saying if I wound one horribly, who cares, there will be another shot on another day so screw it. Not the type of people who give hunting a good name.

Another factor is your physical condition. Even a mild jaunt in the woods if you have not been building up your strength and stamina walking and climbing in hilly country is the best way I know of on how to commit suicide. A hunter in good physical condition knows his limits and can hunt longer and not get winded to the point that he can no longer even shoot off of a bi-pod or set of cross sticks standing.

I conclusion every wannabe Daniel Boone thinks all I have to do is buy a super duper accurate rifle and the latest and greatest gizmo wiz bang range finder, do 10 hours of mathematical mill dot calculations while the wild animal who is of a standard size and also stands there in a picture like pose will assure my being able to make a successful long range shot. Sorry Jethro real life is not like that. Its practice developing the shooting skills, being in good physical condition and knowing the real life habits of wild game and knowing where they will be at certain times of the day is what assures success. Otherwise you may be better off taking up watching the ball game while guzzling a six pack of beer, you will be happier and richer to boot.

• Or you spend 30 seconds ranging a target with a laser and plugging the range into your ballistic solver that’s trued to your gun and ammo. Congratulations, you now have your hold. Technology. It’s great.

• The problems is that you may not often have 30 seconds (and usually it takes you longer than this anyway) and the info you get is not written in stone either. In other words it is not foolproof.

• The information it spits out may not be perfect but it’s closer than anything else. A lrf is definitely more precise than your eye, for instance.

• Agreed. I use my phone’s GPS, and not a map and compass, to get around town. I spend good chunks of my book explaining how much of what people do at the range is unnecessary and has little application in the real world. In fact, I bet many of you will disagree with some of my “screw it, let’s shoot” approach. For example, I explain how I don’t even use a wind meter (gasp) because there’s a time for doing math and there’s a time for shooting. 🙂

• jlp, we might shoot for more than just hunting. I regularly shoot out to 800 yards (max length of my range.) Mostly because I enjoy it. The math part, and then testing my estimates (DAMN YOU WIND!), and my shooting, is a rewarding experience.
And also, sometimes people hunt far away. In some west Texas ram hunts I’ve been on, a lot of the shots were at 500 yards or more. Last year I shot two does back to back, one at 600 and the other at 640 yards. But I didn’t do a lot of math for them when I saw those deer show up. Because I had done it beforehand.
I made a range card. It’s just habit, and a good one that has many benefits beyond making the shot.
I used to shoot the flattest shooting round for the caliber I could get, so I wouldn’t have to worry as much about the range. Now I shoot a heavy for caliber round whenever I can, so I don’t have to worry as much about the wind.

• Testify. When I hunt, typically there’s not enough time to work math or calculators while I still have a clear shot, maybe I’m all amped up on buck fever, maybe I’m tired/cold/wet, etc. Experience has taught me not to trust BDC reticles, too. That’s why I practice KISS when hunting and use the relatively simple MPBR approach and know and accept my limitations. For my purposese, being “accurate enough” to get the job done is fine. Given the limited resources I have for practicing, I’ve got no business shooting at critters past ~300 yards. Doesn’t really matter, as the vast majority of decent shooting opportunities I get in SE PA are at 100 yards or (often) less, anyway.

• I totally agree, in my experience and with any rifle I’d actually take big game hunting (.270, .300 win mag, .300 RUM, .338-378) I don’t need any drastic ballistic compensation to shoot out to 300 yards. If the shot is any farther than that I just range it and dial in the range to my surprisingly affordable Leupold CDS, aim, and squeeze. obviously its hard to range a game animal at 350+ yards if its not standing still, but I would offer that if you can’t range it because its moving you probably ought not to shoot at it either.

• Remember too Jack used a 4x scope on that 270 Winchester. An 8x scope was common on a varmint rifle. Back then 1x per hundred yards of distance was the common formula. 4x was considered plenty of power for a big game hunting rifle. 300 yards was considered a long distance for a hunting shot at unwounded game.
How times have changed.

• That is rather true for that era. Off season target shooting was called varmint hunting. The main event of shooing inanimate targets was trap shooting.

• The same rules apply for warfare. Of course I will admit that you would sometimes have the time to do mental calculations if you were killing unsuspecting human beings that were eating their lunch, going to the bathroom or writing letters home to their parents as in a situation when a Sniper performs the most dastardly and disgusting form of warfare.

• Ditto.
Any time someone has a different way of explaining something that makes it easier to understand, it’s great.
Sign me,

• it is so cool to think that one can deliver a tiny piece of lead accurately from 1/2 a mile, and then repeat. so many variables too make it so interesting.

• For me, half a mile is solidly in the long range category. For someone with Mr. Cleckner’s resume, it’s likely twice that, or more.

4. I normally zero my rifles at 200. So I know it’s 2 inches high or so at 100 and 1 inch at 50 or so. I think the most important thing is to shoot,shoot,shoot. Prone,standing,leaning support and seated in the most uncomfortable chair you can find (tree stand) I swear tree stands are built by sadists that secretly work for PETA. I prefer using a ground blind with a folding chair that dosen’t suck.

*** not really related but I’ll test drive a hunting chair by placing it in my “man cave” and using it to play PS4 or watch movies to get an idea how it will work in the field. I’ve got a – Hunt More – chair that I’m pretty pleased with, if it only weighed less! Most of the time I end up with the \$14 dollar bass pro triangle torture chair because it only weighs about 2 lbs. I normally hike in about 2-8 miles to get to the good game. Far,far away from bubba-joe sixpack.

• “…TTAG regulars have neither the IQ, nor the tenacity to put this info to use.”

My goodness!

You most certainly are a very special snowflake!…

• None of the calculations shown are very difficult. For most people the use of a long range shooting app is available. I use the Lapua Ballistics app for android. I have it on my phone and tablet.
Since I use a zero stop Nightforce scope I can zero dope the scope at 300 yards and dope as I drop back. Where the calculator comes in handy is when you find yourself at an odd yardage. I set my dope at 100 yard intervals. I reload all of my ammunition so I have a consistent drop rate since I keep my powder charge and bullets consistent. I took my wife and some of her friends out shooting and let them shoot at 500 yards. They were ecstatic when the pinged from that distance.

5. I have an EDM 98 Windrunner in 338 Lapua Magnum with a Nightforce NXS 8-32×56 ZeroStop.

Once the scope was doped out and zeroed all I need to do is click to dope and estimate windage. The biggest problem with long range shooting is finding locations to shoot at 1000 meters plus. Most ranges in my area are 300 meters. I occasionally go to a friends farm and shoot to 1000 yards but it is unavailable during planting and harvest time.

• The range I typically shoot at is at the edge of a spur, with two deep draws on each side that come from two higher spurs on each side of the one the shooting station is on. Kind of like shooting from the center tine of a 3 pronged fork. There is a big valley in front of it, and another ridge perpendicular to the spur 800 meters away, where the target sits. The sound is really strange there (as is the wind.) Sometimes I can hear the echo of my shot coming back at me from the ridges to my right and left before I can hear the ring of the steel from across the valley.
BOOM, boomboom, pingboom

• “BOOM, boomboom, pingboom”

You ought to record that.

It would make a cool telephone answering message…

🙂

• I took one of my friends out on a 500 yard shoot and he did just that. The owner of the farm came by and said he thought we were firing two weapons with the loud ping from the steel plate. I enjoy shooting the 338 which means I also reload. I reload with 300 grain Sierra Matchking BTHP. Those are great flying bullets.

6. >> I normally zero my rifles at 200. So I know it’s 2 inches high or so at 100 and 1 inch at 50 or so.

If it’s a typical 16″ 5.56 AR, then zeroing at 200 yards will actually give you another zero at ~50, and the peak of ~1.5 inches above will be at ~130 yards with M855.

7. Screw that \$hit. I got a headache half way through. I bought a Silencerco Radius I plan on testing out this weekend.

• I agree with you although in my case it was more hilarious laughter as often articles like this are more fantasy than practical reality.

• I was hoping the cheaper Kindle version inspires folks to eventually get the paperback and also to leave good feedback. 🙂 As an FYI, for anyone who purchases the paperback, the Kindle version comes free. Also, 25% of the book’s proceeds goes to military charities (Special Operations Warrior Foundation and the Sua Sponte Foundation).

8. Want say thank you to Ryan Cleckner you published an easy to understand book, no wonder you where an instructor!! I just recently began trying some long range shooting and I purchased your book just before I started practicing, I never would have achieved any success with out!!! I’ve watched all your videos and have been spot on, help me a lot and you back to basic training without technical Mombo gumbo, if you not going for fun of it why bother doing ( a phase from Ryan ) I total agree at Thanks Again Ryan!!!