MRAD vs MOA: Mil-dots and Minutes-of-angle -From a Technical Perspective

If you’ve always wondered what those little dots are for on a military rifle scope’s reticle (cross-hairs), then look no further. I hope to explain, in a clear and concise fashion, how the mil-dot reticle works and also what “minute-of-angle” means.

The term “minute-of-angle” (MOA) is used regularly by target shooters at the range, but is probably understood, thoroughly, by few (the same goes for mil-dots). Defined loosely, one MOA = 1″ @ 100 yards; so, if you shot your rifle 5 times into a 100-yard target and every shot went into a one-inch circle you had drawn on the paper, then your rifle could be said to shoot 1 MOA. Likewise, if every shot goes into a two-inch circle at 200 yards, then you’re shooting 1 MOA. A 10-inch group at 500 yards would be 2 MOA.

Now for the fun part. There are 360 degrees in a circle. Each degree can be broken down further into minutes. There are 60 minutes in a degree. Likewise, there are 60 seconds in a minute. Now, to figure out the distance subtended by 1 minute at any particular distance, we need merely to plug those two values into a simple trigonometric equation. The tangent function fits the bill nicely. Here’s the equation:
tan(angle) = distance subtended/distance to the target (units must be consistent–e.g., 1/36 of a yard [1″] divided by 100 yards)

Now, we know the angle (1 minute or 1/60 of a degree) and we know the distance to the target (100 yards), but we need to figure out the actual distance subtended at the target (i.e., is 1 MOA actually 1″ @ 100 yards?). What we need to do is solve for “distance subtended.” Here’s our final equation:
tan(angle)*distance to the target = distance subtended

Make sure your calculator is in “degree” mode (as opposed to “radian” or “gradian”) and type in 1/60 (for degrees) and hit the “tangent” button. Then multiply that by 100 yards. This should give you the distance (in yards) subtended at 100 yards. Multiply this by 36 to get inches. The answer should be:

This is just a hair over the commonly quoted “one inch.” At 1000 yards, this would be almost 10 1/2 inches. Apparently, it is just a coincidence that 1 MOA happens to be REALLY close to 1″ @ 100 yards. It is, however, quite convenient.
The Mil-Dot

The “Mil” in “Mil-Dot” does not stand for “Military”; it stands for “milliradian” or MRAD. The radian is a unitless measure which is equivalent, in use, to degrees. It tells you how far around a circle you have gone. 2 PI radians = 360 degrees. Using 3.14 as the value of PI, 6.28 radians take you all the way around a circle. Using a cartesian coordinate system, you can use “x”- and “y”-values to define any point on the plane. Radians are used in a coordinate system called “polar coordinates.” A point on the plane is defined, in the polar coordinate system, using the radian and the radius. The radian defines the amount of rotation and the radius gives the distance from the origin (in a negative or positive direction).

ANYWAY, the radian is another measurement of rotation (the degree/minute/second-system being the first). This is the system used in the mil-dot reticle. We use the same equation that we used before, but, instead of your calculator being in “degree” mode, switch it to “radian” mode. One milliradian = 1/1000 (.001) radians. So, type .001 into your calculator and hit the “tangent” button. Then multiply this by “distance to the target.” Finally, multiply this by 36 to get inches subtended at the given distance. With the calculator in “radian” mode, type:
tangent(.001)*100*36 = 3.6000012″

So, one milliradian is just over 3.6 inches at 100 yards. If we extrapolate, two milliradians equal about 6 feet at one-thousand yards. You’ll see the importance of this, shortly.
The Mil-Dot Reticle

The mil-dot reticle was designed around the measurement unit of the milliradian. The dots, themselves, were designed with this in mind and the spacing of the dots was also based upon the milliradian. This allows the shooter to calculate the distance to an object of known height or width. Height of the target in yards divided by the height of the target in milliradians multiplied by 1000 equals the distance to the target in yards. For example, take a 6-foot-tall man (2 yards). Let’s say that the top of his head lines up with one dot and his feet line up four dots down. So: (2/4)*1000 = 500 yards away. This same tecnique can be used to estimate lead on a moving target or to compensate for deflection on a windy day.

The distance from the center of one dot to the center of the next dot is 1 milliradian. We are told (by the folks at Leupold) that the length of a dot is 1/4 MRAD or 3/4 MOA (Given this much information, one can determine that the distance between dots is 3/4 milliradian.).* I use the term “length” because the mil-dot is not round. It is oblong. The “dots” on the verticle crosshair run oblong in the vertical direction. The dots on the horizontal crosshair run oblong in the horizontal direction (i.e., they are lying on their sides). The width of each dot is an arbitrary distance and is not used for any practical purpose. Like a duplex reticle, the mil-dot reticle is thicker towards the edges and uses thin lines in the middle where the dots are located and the crosshairs cross. The distance between the opposite thick portions is 10 milliradians.

*NOTE: 1/4 MRAD = .9″ and 3/4 MOA = .785″, so, obviously, a mil-dot cannot be both 1/4 milliradian and 3/4 MOA. I called Premier Reticles (they make Leupold’s mil-dot reticles) and got an explanation: the dots on their mil-dot reticles are 1/4 mil. They are not 3/4 MOA. Apparently, they (Leupold?) just figured that more shooters understand MOA than milliradians, so they just gave a figure (in MOA) that was close, but not super precise. You can contact Premier Reticles via e-mail and request literature or ask questions.

To use a mil-dot reticle effectively, all one need remember is that the distance between dot centers is 36″ at 1000 yards. This lets you determine the range of a target of known size. At that point, you can dial the scope in for proper elevation OR use the dots to hold over the proper amount. The dots on the horizontal crosshair can be used to lead a target (if you know the range to the target, then you’ll know the distance between dots, and thus the distance to lead) or to compensate for deflection.

All you ever wanted to know about mil-dots and minutes-of-angle, and then some!

The Real Truth About Mil Dots

I have now read three separate articles on the Mil Dot, minute of angle, and the non-existent difference between Army and Marine Mils.

First what is a mil? It is a shorten name for a milradian. That is it is 1/1000th of a radian. So, what is a radian? “A radian is an angular measurement that is equal to the angle formed at the center of a circle by two radii cutting off an arc whose length is equal to the radius.” That is a direct quote from the Webster’s New World Edition Dictionary. Look at it as a slice of pie in which the “outer rounded side” is equal to the two straight sides. The angle at the pointy end is one radian. How do you find this great angle? OK, radian = 2 pi r/r is the standard formula. So a circle with a five inch radius becomes (2 * 3.1416 * 5)/5 = 6.2832 radians to a circle of 360 degrees. By dividing 360 degrees by 6.2832, you find that there are 57.2956 degrees in a radian. You also know that there are 6283.2 MRAD in a circle. Either of these can give you the number of minutes of angle in a milradian or mil. That magic number is 3.438, which is commonly rounded to 3.44. This is a mil is a mil is a mil. There is no difference in Marine or Army mils. The problem is the military compass.

The military compass is marked to show 6400 mils in a circle. The reason behind this I do not know for sure but have been told by numerous sources that is was easier to mark off compasses in 6400 than in 6283. This is also the source of the myth that the Russians use different mils then the US. Their compasses are marked with a different number of mils in a circle. However, again a mil is a mil. It is based on a set mathematical formula that was used by the scope manufacturers in their marking of the reticles. Leupold marked their mils as mils. There are 3.44 moa in a mil. There are no Army and Marine mils. There are only mils.

There are differences in the mil dots however. The Marine mil dot is stamped on wire and the dot is 1/4 mil length or longwise. The Army dot is etched on glass and is 3/4 of a minute of angle or .22 mil. While the Marine dot can be easily broken down into 1/8th increments the Army dot can be easily broken down into 1/10 increments. This is very accurate and breaking the mils smaller then 1/8 or 1/10, when ranging with mils, is asking for a disaster and a miss at longer ranges. The mils are easily broken down to 1/4 mil increments for leads, wind calls, and holds for elevation or missed shot correction. None of our students have had any real problems with misidentification of 1/4 and 3/4 mil increments. It is called training.

While I do not know how all of the scope manufacturers make their mil dots, I do know that all of the scope manufacturers do know what a mil equals. I would be very cautious with the table shown on one of the articles purporting that some are “Army” dots and others are “Marine” dots. The biggest problem in the Mil Dot arena is the introduction of myth verses reality. Such as the great 3/4 mil, mil dot of John Plaster.

Using mils to judge distance is very easy and mils are very flexible for this purpose. Now the mil formula works by dividing the size of the target in millimeters by the apparent size of the target in mils. This is why the 1000 formula works so well. Size of the target in meters times 1000 divided by the apparent size in mils. 1000 is the number of millimeters in a meter. Thus if you have a one meter target and multiply it by 1000 you have converted the 1 meter into 1000 millimeters. Now the neat thing about the mil formula is that it assumes that everything is meters and dutifully gives answers in all manner of sizes. Thus if you were to say the size in yards then the answer would be in yards, if in feet the answer in feet, inches answer inches. Thus a 2 yard tall target milled at 4 mils would become 2 times 1000 divided by 4 which equals 500 yards distance. A 6 foot target milled at 4 mils becomes 6 times 1000 divided by 4 equals 1500 feet which also seems to be 500 yards. I could continue in inches but my head is already hurting. This is great for those easy to do times 1000 deals but car tires, tank fenders and a few others may be a bit more problematic. 45 inches does not do well times 1000 converted into meters or yards. You can convert 45 inches into meters but why not simply multiply 45 times 25.4 (number of millimeters in an inch) and divide that by the apparent size of the target in mils. So now 45 times 25.4 divided by 4 mils equals 285.75 meters. For those of you that wish to work in inches you can use 27.7 instead of 25.4. This tricks the formula into converting the range into yards for you. While this is not perfect, it works. Example is the two yard tall target, 72 inches times 27.7 divided by 4 equals 498.6 meters versus 500 yards using the 1000 formula. I can live with the error. When using the mils you must be able to break the mils into 10ths. This can be done based on the dots themselves. The dots are .22 mil but half is .11 mil. Using this information you then rest the target on the top or bottom of a mil and then measure up. Say, top of one mil to bottom of second mil and the reading is 1.8 mils. Another example would be bottom of one mil and top of second mil and you have 2.2 mils. Combinations of the above will give you anywhere in the tenth scale.

The standard for milling the human body is the crotch to top of head in conjunction with the shoulder to shoulder measurement. Using smaller than this and be accurate, and you will be in the 6 inch point blank zero range anyway.

Mils can also be used to hold for winds and it is taught that way in SOTIC. Dialing on winds can be a disaster when you have only seconds to engage in changing wind situations. The mils will hold at 1/4 mil increments easily which is just smaller then 1 moa or .86 moa. This will get you a hit and if you were real anal, then a light 1/2 mil would be 3/8th of a mil or .43 moa. To me this is just too anal. Wind calls are taken from the center of the target as a standard reference point.

The Mil can be used very successfully in holds for elevation. With the criteria of bullet path based on a 500 meter (or yard) zero, the sniper can place 500 on his scope and hold for any target from push the barrel through his guts to 700 meters. We use this info for our students and give them a standard chart that contains that info. That info is only good for the M118 SB and the M118LR. However, anyone can reconstruct one for his or her particular bullet. You are merely compensating for bullet path within the scope. As an example the shooter would hold 5 mils low for a 100-meter shot with 500 meters on his weapon. He would also hold 1 mil high for a 600-meter shot with 500 on the weapon. The usual problem is that the shooter must hang the target in space for long shots while holding for elevation AND wind.

The mil can also be used for engaging moving targets and here the best practice is to use the leading edge for a trigger point. This is due to the problem of shooters looking at the target to find the center of the target. We have our students use the leading edge to stop this problem. There are three general methods of target engagement with moving target. One is ambushing or trapping. We use this method to teach new students moving targets. Another is tracking and is similar to the quarterback pass. And the third is a combination method. In any of these methods the leads are called in mils based on the leading edge of the target. Engaging movers past 400 meters becomes a pain due to wind considerations. Again mil dots will help. As an example, say the lead for the moving target is 2 mils and there is a 3/4 mil wind. Now if the target is moving into the wind then the lead would be two mils PLUS the wind of 3/4 mils so the observer would give a lead of 2 and 3/4 mils. However if the mover is moving with the wind then the wind is subtracted and the lead becomes 1 and 1/4 mils. Fun huh!

Well this is a quick down and dirty and hope that it clarifies some of the info put out in some of the other articles floating around.

Scott – On the wind formula, they can’t all be correct. The problem comes about due to using different drag co-efficents in the orignal model. Since the Marine answer is 10 moa, I must assume that you are talking 168 gr. At SOTIC use a constant of 10 for the formula and while not dead on it is within .5 moa at that range. If the G1 model is used you will get one answer and if you use the correct boat tail co-efficent you will get another. The rossettes were modeled on a multiple constant that had a basic flaw and gave way toa low of a moa adjustment. The Sierra program uses the G1 drag and comes up about 1.5 moa short. The army figures compute, by error, to be .5 increments instead of 1 moa increments. So double the army answer and you are close. I know, I really didn’t answer your question, but that’s as close as I can come. I do know that if you use wind speed in knots, times range in hundreds, divided by the constant of ten, you will have a moa adjustment that will hit a mansized target at 1000 yards. Use the same formula from 100 to 1000 and you will start out being .5 moa too strong and end being .5 moa too weak. But, hey what’s .5 inches to 5 inches among friends? By the way, don’t forget spin drift.

Rick, thanks for the reply. The thing that makes the windage issue so “interesting” is that at times I have used several of these formulas and had center mass hits with them all, both in competition and on the UKD range. What this tells me is that my wind estimation was OFF and I was essentially just getting lucky. Example: The Army chart gives 4.5 minutes for a full value 10 mph wind at 800 Meters. I have used that figure repeatedly to ding the target. Yet when compared to the balistic program for the same round, that call is off. So my assumption is that my wind call was actually off. This is kind of like voodoo! Why is this bugging me right now? I am trying to develop an accurate wind chart for my 26″ PSS. Gathering all the various data has brought to light (at least for me) all the varying data out there. Guess I’ll just have to stick with the Sierra program as verifying the windage for every 100 yards and every 3 mph all the way to 1000 would take a life time in waiting for each condition.

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