Buckle up, I’m about to talk nerdy to you. Once you spend enough time learning about optics and setting up a rifle for long range precision, you will inevitably come across the MRAD vs MOA debate. These represent the two most common marksmanship measurement systems with modern optics: the milliradian (MRAD) and the minute of angle (MOA). In this article, I want to define them, explain how to use them, and help you determine which one you should use.
Fair warning, there’s a fair bit of math involved. I think it’s important to understand the why behind the systems as we go.
Talking in Angular Measurement
Let go of is thinking in terms of linear measurement for the moment. By that, I mean you need to stop thinking in terms of inches, yards, centimeters, or meters.
Milliradians and minutes of angle are geometric concepts for measuring angle. For marksmanship, we are specifically measuring the angles from the sighting device to a target. We then convert those measurements into linear values as needed.
What kind of things do we use these angles for?
- Estimating the distance to target of known size
- Determining the size of a target at a known distance
- Applying the correct amount of compensation for bullet drop at distance
- Adjusting the impact of a bullet due to wind
Those last two points aren’t actually measuring anything. You could turn those angular adjustments into a linear value, like saying the bullet will drop 14 inches at 400 yards, but it’s ultimately not all that useful.
I mentioned that both MRAD and MOA are geometric tools for measuring angles. Let’s take a closer look at how they do that.
It All Comes Back to the Circle
The easiest way to imagine this is with a land navigation compass. Recall your geometry class from back in the day. There are 360 degrees in a circle, and our land navigation compass also has 360 degrees, represented as tic marks. Keep this visualization in mind for amoment.
You probably also remember using protractors in school. These devices helped you measure the angle produced by two adjoining lines.
In this animation, the angle is 115 degrees. We can use all manner of calculations to figure out the distance between the ends of each green line. The useful trick is knowing what happens to that distance as the length of the green lines, the distances, changes.
Here’s another graphic to illustrate what I’m talking about. The red line in this diagram is the important part. The distance represented by the red line is an example of measuring the size of a target, drop due to gravity, or the push of wind. We can calculate that regardless of the length of the green lines, or the distance between the center of the circle and the target, represented by the dotted orange line.
Everything relies on the geometry of arcs, which is a key element of shooting. Now, let’s take a deeper look at the math involved.
MOA: Minutes of Angle
Go back to our land navigation compass. The distance between two adjacent degree markers appears very small when the compass in our hands. Now imagine two lines extending out from those two tick marks a single degree apart, things diverge slowly.
Using the circle image, imagine the dotted orange line was 10 feet long. This represents our distance from the target. If the angle between green lines was a single degree, the red line would only be two inches long at 10 feet. If we extend the dotted orange line out to 100 yards, the red line grows to about five feet. At 1000 yards, it’s over 50 feet long.
Now you see the conundrum. For marksmanship, a full degree of divergence is too large to be useful. We need to further divide that degree. Like a clock, we divide that degree into 60 evenly distributed minutes of angle.
Doing the Math
Let’s assume our target is 100 yards away. Set a scientific calculator to degree mode and press “tangent.” Input 1/60 and multiply it by 100. That gives you the size of 1 minute of angle in yards at a distance of 100 yards. Then multiply that result by 36 to convert from yards to inches.
Tangent(1/60) * 100 * 36 = 1.047
From this, we see that 1 MOA equates to 1.047″ at 100 yards, or 10.47″ at 1000 yards.
This is a more useful measurement for precision, and it’s easy to convert in your head. A lot of shooters just round it off to 1 inch.
In the past, you might have seen optics marked with IPHY, which means “Inches Per Hundred Yards.” This is a bit more old-school but represented a rounding of 1.047″ to just 1″ in the optic. I don’t see optics that still use IPHY, but we often still talk like it. The Army even still teaches it in publications like TC 3-22.9
Applying MOA to Rifles
1 MOA adjustment increments are common for rifle sights. Both the M1 Garand and the M14 followed that pattern for their elevation and windage increments. The M16A2 rear sight was the same, at least for elevation.
To get even more precise, we further subdivide those minutes of angle into 60 seconds of angle. Whereas a minute of angle is 1/60th of a degree, a second of angle is a mere 1/3600th of a degree.
A single second of a degree is a too fine for practical use, so most optical sights adjust several seconds at a time. The most common are 30 seconds and 15 seconds per click, otherwise known as 1/2 MOA and 1/4 MOA.
Before we dive down the rabbit hole of comparing MOA to MRAD optics, we also have to define the MRAD.
MRAD: The Milliradian
While degrees are easy to visualize, which makes them more common for learning circle geometry, there is another way to do a similar task.
A radian is another way to measure the arc of a circle. A single radian (denoted as rad) is a segment of the circumference of a circle equivalent to the radius (denoted as r) of the circle. Half of the circle is π*rad, and the whole circle is 2π*rad.
This graphic shows it better than I explain it:
When we talk about milliradians, we are taking 1/1000th of a single radian. We often abbreviate milliradian as MRAD or mil
Doing the Math
Let’s do some back-of-the-napkin math to figure out some distance equivalents.
Once again, let’s assume our target is 100 yards away.
Set your scientific calculator to radian mode and press “tangent.” Then multiply .001, for 1/1000th, by 100, the distance to the target. Now you have the size of one mrad in yards at a distance of 100 yards.
Next, multiply that result by 36, which converts the result from yards to inches.
Tangent(.001)*100*36 = 3.6000012″
That’s the dirty way of saying that one MRAD is about 3.6 inches at 100 yards. It’s not exact, just like one minute of angle isn’t a perfect 1″, but it’s close enough to work with.
In fact, it makes things a little easier. If we multiply the distance by 10, the result is 36 inches at 1000 yards. So one milliradian equals one yard at 1000 yards. Coincidentally, a six-foot object at 1000 yards measures two mils tall.
That’s pretty easy.
The system doesn’t care what linear measurement you use, either. Let’s use 100 meters instead, and multiply by 100 to get centimeters.
Tangent(.001)*100*100 = 10.00335 cm
With this, you see that one mrad equals about 10 centimeters at 100 meters away. Or, alternatively, 1 meter at a distance of 1000 meters.
Tangent(.001)*1000 = 1 m
Like using a full degree, a full milliradian is too coarse for good precision out of a rifle. Luckily, we also subdivide MRAD to make adjustments in 1/10th of an MRAD per click. This works out to .36″ per click at 100 yards, or 1 CM per click at 100 meters. Notice the distinction I did there, I didn’t say CM per 100 yards or inches per 100 meters. I suggest picking imperial and metric measurements and sticking to it. You’ll see why in a minute when I get to the formulas.
You’ll find that the Army also teaches this in their marksmanship manual. It’s notable that they don’t really have to round off the MRAD/CM numbers like they do with inches.
MRAD vs MOA for Rifle Marksmanship
Remember, that the same math worked to show that one mil equals one yard at 1000 yards. The complicating factor is that one yard contains 36 inches, which isn’t as easily divisible.
Another way to look at this is ratios. A milliradian work on a 1:1000 ratio. To visualize it, a 1 inch tall object measures 1 MRAD in your optic when it is 1000 inches away. If it’s 1 yard tall, it will measure one MRAD when it it’s 1000 yards away.
MRAD is always 1:1000.
MOA, on the other hand, works on a ratio of 1:3438
So which is better between MRAD and MOA? Well, that depends on your point of view and the task at hand.
MRAD vs MOA Adjustment Increments
The most common adjustment interval for an MRAD-based sighting system is 1/10th of a mil per click. At 100 yards, that’s .36″ or just under 1 centimeter.
The most common adjustment for MOA-based sighting systems is 1/4 MOA per click. At 100 yards, that’s .25″ per click of adjustment. I’ve seen some optics that go even finer than that, offering 1/8 MOA per click.
If you’re looking purely from a precision perspective, then MOA wins here because of a finer adjustment method. This is why you’ll typically see MOA scopes with 1/8 MOA adjustments in extreme precision sports like F-Class.
Let’s illustrate this a bit more. At 1000 yards, a common distance in F-Class, that 1/8 MOA click moves the impact by 1.3″. A 1/10 mil adjustment at 1000 yards equates to 3.6″. Even the more common 1/4 MOA adjustment is still finer, moving the impact 2.6″ at 1000 yards.
But that doesn’t tell the whole story, there’s more to this math than adjusting your scope. These numbers are interesting, but you have to remember that this is just the raw calculations and the actual margin of error caused by the rifle itself, ammunition, and environmental effects are often quite a bit larger than the difference between 1.3″ and 3.6″ at 1000 yards.
MRAD vs MOA for Ranging
One of the classic “killer features” for both milliradians and minutes of angle is the ability to use them for determining range and holdover. Using your reticle to determine range is a bit of an old-school skill, especially in an era of affordable laser rangefinders. But I find the math interesting, so let’s go there.
By reversing the tangent formulas I presented earlier, you can use the known size of a target and what it measures within your scope to find the range to the target.
MOA Ranging Formulas
Use these formulas for determining the range to the target using MOA reticles. You shift the numbers around using algebra to determine other figures as needed.
Something important to note for each of these. The multiplier number is often rounded. The first one, for finding yards given inches, says to multiply by 100. A lot of people use 95.5 as the multiplier number instead, which is closer to the actual value of 95.28.
Here’s the thing, though: yes, precision in the math is important. Rounding errors are still errors that compound over distance. These deviations become very significant at very long range. But at practical distances most people tend to shoot, it’s within the natural deviation of the rifle, ammunition, and weather conditions anyway.
You’ll notice the 3438 and 34.38 on the last two. Recall that that’s the ratio I mentioned earlier with minutes of angle 1:3438. You’re seeing it come up because those last two use the metric system , and the ratio comes in to convert between the systems.
The random 87.3 you see on the second formula also comes from converting inches to meters. It’s the result of dividing 3438 by 39.37, the number of inches in a meter. This is why I mentioned earlier that it’s best not to mix imperial and metric.
These formulas do the same thing but utilize an MRAD reticle for the measurement. Again, a lot of these multiplier numbers are rounded and you see some oddball numbers coming from the imperial system. The 27.8 in the first one, for example, comes from dividing 1000 by 36 (36 inches per yard). The 25.4 comes from dividing 1000 by 39.37, the number of inches per meter.
MRAD vs MOA Takeaways
That’s the last of the math for today. There’s only one takeaway I want you to have from this. The first, and probably most obvious, is that working in multiples of 10 is simply easier. MRAD dovetails nicely with that, and so I think it gets the nod for ease of use when it comes to estimation.
That said, I highly doubt any serious shooter would ever be whipping out a calculator in the field to run these formulas. If they didn’t have a laser rangefinder, then a tool like the Mildot Master makes short work of it.
The ability to correctly range a target is vital to actually hitting the target. The Precision Rifle Blog did a study where they gauged the importance of correct ranging on distant targets and the results are clear. Even a little ranging error will cause a miss, and using your reticle to range a target introduces far more margin of error.
So, in short, the ranging argument. is interesting but not necessarily satisfying.
This is where the distinction between linear measurement and angular measurement gets important.
Let’s say you take three shots at a target placed 650 yards away. You hit the paper, but miss the x ring a little high and right. Your shooting buddy is looking through a spotting scope to give you a correction. There are three ways they could communicate this:
- “You need to come down a little lower and to the left.”
- “I think you should come down twelve inches and adjust ten inches to the left .”
- “Adjust down .5 mil and left .4 mil”
When it comes to precision shooting, the first method is useless. So let’s ignore that one.
The second method at least has numbers in it. How the spotter would actually know to come down twelve inches a to the left ten inches is another story. But assuming he’s right, we could figure it out in our head using some rounding. At 650 yards, 1 MOA is roughly 6 inches. So you figure that you need to come down 2 MOA and left 1.75.
With that method, you’d be closer. But the rounding errors are starting to add up. That rough 6 inches is actually 6.8 inches, so your actual adjustment is less than you thought. What happens if you don’t actually know the distance to the target? Well, then you’re back to option number one.
The third method is ideal. Your spotter looks at the target with his reticle and measures the offset of the shots as he sees it. The linear measurement doesn’t matter, because you already have the angle. If the spotter says to move .5 mil, then you simply dial .5 mil of adjustment on your optic.
So Which is Easier?
In practice, either an MRAD-based scope or MOA-based scope works the same way. Both the spotter and the shooter measure the required adjustment and communicate. As long as their both using the same system, it’s pretty easy. So, for me, it comes down to the numbers involved.
Look at this ballistic chart I compiled for a Berger 175gr .308 projectile firing at 2650 FPS.
Compare the mil numbers and MOA numbers for both drop and windage. Both represent the same amount of linear drop at each distance. When you consider that MRAD-based scopes adjust in .1 increments, it’s very easy to identify how many clicks of adjustment you need for each of those distances.
For MOA, you’re dealing with larger numbers as well as rounding errors. Most MOA scopes adjust in .25 MOA increment. If I said you need to come down 17.9 MOA, is that closer to 17.75 or 18 MOA?
You also have to do more math in your head. For example, imagine you’re in the field right now and your spotter says to adjust 32.7 MOA. How many clicks is that with a 1/4 adjustment?
Now try MRAD with 1/10 adjustment. How many clicks is 13 mils?
Both of these scenarios are the same amount of clicks: 130. How much longer did it take you to figure that out with MOA?
MRAD takes it here for ease of use.
MOA vs MRAD Optics
I’m not going to spend a lot of time here. The truth is that both systems work well for optics. Look at these reticles designated EBR-2C by Vortex Optics.
Both of these are perfectly usable as long as the turrets of the optic work in the same system as the reticle.
Up until fairly recently, a lot of American rifle scopes had mil-dot reticles but MOA turret adjustment. We call that mil/MOA. There is no good reason to do that to yourself.
To work with this, it requires more math. You need a conversion factor of 3.43, which is the rounded version of 3438 divided by 1000 (the two ratios representative of each system).
Put it this way:
Scenario #1: You take a shot and watch the impact in the reticle, measuring it as 1.8 mils high. To convert that into minutes of angle, you multiply 1.8 x 3.43 and get 6.174 MOA. Divide 6.174 by .25 (MOA per click), and get 24.696. Now you adjust the elevation turret by either 24 or 25 clicks to get “close enough.”
Scenario #2: You’re now using a mil/mil scope and take another shot. You measure the impact as 2.3 mils low. In your head, move the decimal one place to the right (the result of multiplying by 10) and you get 23. Adjust the elevation turret 23 clicks.
Scenario #3: Someone handed you a MOA/MOA optic. You fire and measure the impact as 17.9 MOA low. Divide 17.9 by .25 and you get 71.6. Adjust the elevation turret 71 or 72 clicks.
Which of those is the most convenient? For me, it’s the Mil/Mil option, as the numbers tend to be lower and easier to work with.
Whichever system you choose, buy a scope with matching reticle and turret sub-tensions.
Hopefully you now have a good understanding of these two angular measurement systems. This was a lot of fairly technical information, with plenty of math.
The takeaway is that when it comes to MRAD vs MOA, neither system is absolutely superior to the other. They both have their perks depending on what you need to do with it.
Minutes of Angle are an easy way to teach someone if you’re sticking to the imperial system, but it does end up being more difficult to work with later on. A minute of angle is a more precise unit of measurement when you’re trying to squeeze maximum accuracy.
Milliradians are convenient to use with the 10-based metric system. It also works with inches and yards with a little bit of math. The real benefit to MRAD is that it’s faster to communicate and make adjustments. The 10-based math makes calculations significantly quicker.
The final thing to keep in mind is that it’s not all about you. Consider what those around you are also using. If you are shooting PRS matches and get teamed with a bunch of guys using mil-based optics, it’s going to be much easier to communicate if you’re using the same. Otherwise, you’ll be doing lots of math to translate between the two systems.
Ow, my head hurts. I hate math. Especially having to do it in my head, on the fly, under time pressure.
I’ve been using MOA for so long that I “see” in minutes, and holdover/holdoff or adjustments are almost automatic.
On the other hand, I just dug out an AR scope I bought years ago and finally mounted it on my AR. Guess what, it’s in mils. Going to have to learn something new I guess.
Not gonna lie, doing the math quickly is hard. Most precision rifle courses I’ve seen say to bring along a calculator for that very reason. It’s also the reason I advocate for tools like the Mildot Master, which take the math out of it.
Excellent article. Going to print this out, laminate it, and it’s going in the range bag.
Thanks, I’m glad you liked it. What part do you want to put in the range bag? The formulas? Perhaps I could work up some kind of printable just for that purpose.
The formulas mostly. Typically when I need this stuff I put it on 3×5 notecards, laminate them them put them on a ring to flip through when I’m prone.
Hmmm, good to know. Let me see what I can work up for you
Thank you so much for detail in easy words We hope more good info in futher once again thank you
for us in Europe and metric system MRAD is first choice as intuitive.
Already being familiar with metric certainly does make it easier!
I like your article…
I like the easy math with the MILS, however my shooting partner uses a Mil Dot scope and I plan on shooting PRC matches…the BIG catch here is, I have not purchased my scope yet….hows that for a fix…no, I’m not going to but two scopes.
My first comment I meant to say MOA scope…that my shooting partner uses.
Hi Michael, thanks for asking! So if I’m reading this right (with the correction), your partner is using a MOA scope and you’re deciding what to do yourself? If you plan on always shooting with that person as a spotter, then it makes sense to do the same for yourself. The math I listed up in this article is all about ranging targets with the reticle and such, but you actually don’t do that with precision rifle matches. If you listen to my interview with Mike Keenan, he told me that match directors often provide the distance to targets for… Read more »
The group I have been shooting with, we have been shooting for over 20 years, and some of us wanted to improve our skill set. after calling some of them, I’ll go with the MOA…they seem to be in agreement. The good thing is that my close shooting partner and I both shoot 300 win mag, so at least that part will be easy as I will be hand loading the rounds.
thanks again Matt.
Nice Matt! Always good to keep touching on the basics. I understand both systems fairly well – at 100 yds. There’s the problem – you can memorize and easily adjust for known 100 yd/meter increments but when the target is ranged at say 679 yds. – math changes so one needs to know how to work the formulas. It’s not hard but it does take practice. I usually only shoot one caliber at long distance and know where my zero is set. I’ve set up ‘math drills’ for myself to become familiar with increment changes (mils for me) at varying… Read more »
Hey Paul! The BDC vs MRAD reticle question is an interesting one, and one I’m going to tackle with Ilya during an upcoming livestream. I’m looking forward to that talk.
I also agree that its better to not overcomplicate things. Most people doing casual shooting probably don’t need to worry about what’s in this post. Really, this is getting into some more advanced shooting for precision rifle matches and such.
Hey Matt! I limit my few attempts at serious long range shooting to my 30-06 bolt actions where I see the need and use a basic (Weaver – last Japanese made model) 3-15 FFP scope with a Mildot reticle. Honestly – I would like to upgrade to a MRAD hash mark style reticle and slightly more powerful scope. Love the FFP though! I agree completely but do have a question. I’ve done little truly ‘long range’ shooting (800+ yds.). In keeping with the topic of MRAD/MOA/BDC, how much wind, in mph, does it take to significantly move a bullet off… Read more »
Unless you’re really into this stuff, I don’t think it’s worth swapping out a perfectly serviceable mil dot reticle for a mil hash one. The most important thing, IMO is actually the turrets and how well they track. As for wind, most tables I’ve made account for a 10 mph wind coming 90 degrees perpendicular to the bullet’s path. Every ballistic calculator will spit out wind adjustments at the same time it spits out elevation. If I run it for something like a .308 168gr SMK, a full 10 mph wind like that pushes the bullet 2.5 mils at 800… Read more »
Thanks Matt! I had an idea but didn’t realize the wind had that much effect on a 30 cal. bullet. You’re also right about the mildot scope. Since the Marine Corps made the mildot reticle famous and it is sitting on top of a model 700 HB in 30-06 (classic?) I’ll just get better at using it! Semper Fi!
Great for those that prefer to understand the basis of their calculations. Aside from the mil-relation formulas, I believe it is necessary to know the size of your target to determine range when using mil dot. For now I’ll stick to the quick and dirty one inch at 100- I/O 1.047),two inches at 200(and so on) with my moa scope. Eventually I’ll likely get a milliradian scope and keep it simple by rounding down to three and a half inches for the quick and dirty. Hence, 3.5 at 100 yards, 7 inches at two hundred, 10.5” at three hundred(and so… Read more »