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How to Understand and Calculate Minute of Angle (MOA)

Most shooters have at least heard of MOAs (minutes of angle, also sometimes called minutes of arc), a concept which is essential for hunters and precision rifle shooters to understand. On the most basic level, it's fairly simple, but it can quickly get complicated, especially when trying to hit moving targets at long range.

In this guide, we'll do a deep dive into minutes of angle and review everything you need to know to clarify your understanding of the fundamentals. We'll cover definitions, terminology, MOA reticles and tips for doing math quickly in the field.

Note that an article covering everything you might conceivably see on a rifle scope would be many thousands of words, so we won't cover advanced skills or highly specialized equipment here (though our beginner's guide to long-range shooting has more introductory information).

What Is a Minute of Angle?

Many people think that an MOA is a measure of distance. It's not, but this confusion is understandable because it is related to distance. It's actually a measure of angles. Bullets are, of course, affected by gravity — they're pulled toward the ground at a constant rate while in flight. Bullet drop is, in part, why you can shoot at a target 300 yards away with seemingly perfect aim and miss if your rifle isn't zeroed for that distance (be sure to read up on how to zero a rifle).

MOA calculations help you adjust your aim to compensate for bullet drop, as well as other factors like wind and elevation (but these last two are different topics for another article). At ranges shorter than 50 meters or so, bullet drop and wind are generally so minor that they're irrelevant, so you can shoot pistols and shotguns without ever worrying about MOAs. You will, however, have to become thoroughly familiar with them if you're serious about mastering long-range rifle shooting.

MOA vs. SMOA

Shooters use the term "MOA" more often than the related term "SMOA" (shooter's minute of angle), and some people use the former when they really mean the latter. But they are different things, and although the difference is negligible at short or medium range, it becomes more important the farther away your target is.

An MOA is an angular measurement equal to 1/60th of 1 degree. In shooting, this translates to a circle 1.047 inches in diameter at 100 yards (not centimeters or meters — you can use the metric system to make shooting calculations, but we'll get to that a bit later). MOA is always measured in these terms, so 1 MOA is 2.094 inches at 200 yards, 3.141 inches at 300 yards, and so on. If you hear a shooter refer to their rifle as a "one-MOA gun," that means that it shoots (roughly) 1-inch groups at 100 yards.

Distance to Target MOA Size (Rounded) MOA Size (Precise)
100 yards 1 inch 1.047 inch
200 yards 2 inches 2.049 inches
300 yards 3 inches 3.141 inches
400 yards 4 inches 4.188 inches
500 yards 5 inches 5.235 inches
600 yards 6 inches 6.282 inches
700 yards 7 inches 7.329 inches
800 yards 8 inches 8.376 inches
900 yards 9 inches 9.423 inches
1000 yards 10 inches 10.470 inches

An SMOA is simply an MOA rounded down to 1 inch for easier math. At ranges shorter than about 1,000 yards, the difference between an MOA and an SMOA is so small that it's irrelevant in nearly all cases. At 1,000 yards, the difference between 1 MOA and 1 SMOA is 0.47 inches — still not a big difference, but depending on how precise your shot needs to be, it could matter. The difference continues to grow linearly as the target gets farther away.

For most shooters in most situations, it's fine to use SMOA and to refer to it as "MOA" for convenience. Just keep the difference in mind should it ever become important.

Radians and Mils

Should you prefer to use the mil/radian system (more common in European countries), you can, but the units and calculations are different. This system is often referred to as the "metric" system of shooting for convenience, but it actually uses a combination of metric and SI (International System of Units) measurements. The most important thing to remember is that you need to choose either MOAs or mils/radians and stick with it — you can combine them, but there's no reason to do so because it just makes the math more complicated for no benefit.

In trigonometry, a radian is a unit of measurement used to describe a "slice" of a circle wherein the length of the curved portion is equal to the circle's radius. The easiest way to think of it is that it's an equilateral triangle — one in which all three sides are the same length — but one of the sides is curved. There are always 2π (~6.28) radians in a circle regardless of its size, but you don't need to remember that number for shooting purposes.

The SI equivalent of 1 MOA is 1 mil (milliradian), 1/1,000th of a radian. This is equal to a circle 10 centimeters in diameter at a distance of 100 meters. You may have noticed that 10cm is about 4 times bigger than 1 inch, so 1 mil is still too big a unit of measurement to be useful for precision shooting. This is why most scopes that use mils adjust in increments of either 1/10th mil or 1/20th mil.

Most American shooters use MOAs, so the rest of this guide will assume you've made that choice. Should you prefer to use mils, the numbers change, but the basic concept is exactly the same.

Understanding and Using MOA Reticles and Scopes

If you've ever looked through a rifle scope that has MOA markings, you may have been thoroughly confused. Some such scopes have so much information on the reticle that it can look like alien gibberish. Fear not: once you understand the basic language of MOA adjustments, the reticles quickly start to make more sense.

Types of Scopes and Reticles

The first thing to know about choosing an MOA scope is that some are generic whereas others are designed for specific rifles or types of ammunition. Unless your goal is to shoot with extreme precision at ranges beyond 1,000 yards, a generic one will probably be fine.

When it comes to the markings you might see on a scope or reticle, the possibilities number in the dozens. Because this is an introductory guide, we'll stick to basic crosshairs and MOA markings for now.

Reticle and Crosshair Size

When looking through a rifle scope with MOA markings, the size of the dot or thickness of the crosshair is important. If it's a 1-MOA reticle, that means that the dot (or the thickness of the crosshair lines) covers a 1-inch area at 100 yards. In other words, assuming the shooting conditions and the rifle's zero are perfect, every shot at 100 yards will land within the area visibly covered by the dot or crosshair line. Some scopes have concentric circles or multiple crosshairs for different MOA values.

Subtension Values

Subtension markings on a reticle are used to quickly estimate MOA values at a given distance. If you've ever looked through a scope and noticed that the crosshair or reticle lines were thinner or thicker in different places, those were subtension markings. Each section of the line may have numbers next to it. If there are no numbers there, they'll be in the scope's manual and you'll have to memorize them.

Let's say that the crosshair lines are divided into two sections. The thinner section is marked 0.2 and the thicker part is marked 0.5. This means that, at a given level of magnification, the thinner part of the line covers 0.2 MOA and the thicker part covers 0.5 MOA. Typically, the subtension markings are accurate only at the scope's maximum level of magnification; refer to the manual to be sure.

Subtension markings are still useful even when not at maximum magnification. Whenever you adjust the magnification, just mentally do the opposite to the subtension values — if the scope is zoomed in halfway, double the subtension numbers. Using the example numbers above, the subtension values at half power would be 0.4 and 1.0. So, if you need your next shot to be higher by 2 MOA but don't want to adjust the scope, move your point of aim upward a distance equal to twice the thickness of the thicker line.

How to Make MOA Adjustments

Many shooters understand MOA adjustments on paper but get confused when it comes to actually doing them. The best tip we can offer is to get in the habit of thinking in MOA "chunks" — not in terms of distance or number of clicks on the turrets. Remember that MOA is a measurement of angles, nothing more. It helps you calculate distance, but you can't substitute distance for MOA when making adjustments, which is what many new shooters try to do.

Suppose you're shooting at a target 500 yards away and your shots are hitting 5 inches too low. Recall that 1 MOA is 1 inch at 100 yards — and therefore 1 MOA is 1 inch per 100 yards — so 1 MOA is 5 inches at 500 yards (the common mistake here is to think "500 yards, 5 inches, therefore 5 MOA"). To change your point of impact by 5 inches, you need to adjust your scope by 1 MOA.

The majority of scopes adjust in increments of either 1/4; or 1/8; MOA, but other variations exist. If yours is 1/4 MOA per click, then you need to move 4 clicks to equal 1 MOA. This will change your point of impact by 5 inches at 500 yards. Only at this stage in the process should you start converting MOA into scope clicks — bringing clicks into the equation before now will be confusing.

Let's work through a slightly more complicated example. The distance to your target is 750 yards and your shots are off by 18 inches. The math doesn't change, even if the numbers aren't quite as clean and easy to work with.

This is where it's most helpful to start your calculations by thinking in MOA chunks. At 750 yards, 1 MOA is 7.5 inches. How many 7.5-inch chunks fit into 18 inches? 18 divided by 7.5 equals 2.4 MOA, so adjust your scope that much. If you're working with mils, just substitute meters for yards and centimeters for inches. See? Easy.

Alternatively, if your scope has subtension markings, you don't need to adjust it at all. In this case, don't even worry about the distance in terms of inches or yards; just use the subtension markings to eyeball the new point of aim. If your previous shot was off by a distance equal to twice the thickness of the crosshair, just move your point of aim two crosshair-widths in the opposite direction. This method is slightly less accurate than adjusting the scope, but it's a lot faster.

How to Choose the Right Scope

The question of what features to look for in a scope or red dot sight depends primarily on what you intend to use it for. Most people say either home defense, long-range precision shooting or hunting.

Home Defense

For home defense needs, simpler scopes/sights with larger MOA dots are generally best unless you live on a large plot of land. In that case, you may want to choose something closer to a hunting scope, which we'll get to in a minute.

If you're shopping for reflex or holographic sights (both are types of red dot sights), look for simple designs that have minimalist reticles and large MOA dots. These are best for short and medium-range engagements because they prioritize speed over pinpoint accuracy. The larger the MOA dot, the easier it is to see, which means you can acquire your target more quickly. Your shot might be off by a few inches at ranges of 25 to 50 yards, but that's usually not a critical miss. Read our guide to find out whether a reflex or holographic sight would be a better choice for you.

The same basic considerations apply if you prefer a traditional scope with an etched crosshair and reticle. The hallway in your house (probably) isn't 50+ yards long, so you don't need multiple crosshairs or subtension marks. Opt for simplicity and speed.

Long-Range Precision Shooting

When it comes to scopes, the sniper's needs are largely opposite those of the suburbanite who just needs a home-defense gun. For long-range shooters, accuracy and precision usually trump speed, so it makes sense to choose a scope or sight that gives you more information. Smaller MOA dots are harder to see but much more accurate at long range. Similarly, multiple crosshairs, concentric reticles and/or subtension marks allow you to make tiny adjustments on the fly without needing to adjust the scope itself.

Hunting (or Long-Range Home Defense)

If you're shooting at moving targets between 100 and 1,000 yards, choose a scope that falls somewhere between the two kinds described above. When you're hunting or defending a home on a large plot of land, you need versatility: a good balance of speed, accuracy and precision.

Should you choose a red dot sight, a 2 MOA or 4 MOA model with an etched reticle may be ideal (read our guide on how to choose a red dot sight for more information). If you opt for a traditional scope, consider something in the range of 2x to 8x magnification with subtension markings. When speed matters, you won't have time to adjust your scope, so you'll need to be well-practiced at using the crosshair and subtension markings to quickly estimate different points of aim at a variety of distances.

Other Considerations

There are a few other things to think about when you're shopping for a scope or practicing your long-range marksmanship.

Scope Quality

Because long-range shooting demands extreme precision at extreme distances, scopes must be manufactured at a very high level of quality in order to consistently produce the desired results. Simply put, some less expensive scopes may not be up to the task. If you need the smallest possible margin of error, you'll have to invest in a high-quality, more expensive scope.

Making a Dope Card

A "dope card" (Data Observed from Previous Engagements) is basically a cheat sheet with a table of MOA adjustments for common distances and magnification levels. Some websites and stores sell pre-made dope cards, and although these will generally get you in the ballpark, you'll probably want to make your own at some point because different rifles, scopes and ammunition loads will produce slightly different results. Many shooters tape dope cards to the stocks of their rifles for quick and easy reference.

Now that you know the basics of MOA calculations and adjustments, the best way to take your knowledge to the next level is to hit the range and start practicing; take a look at some shooting drills to help get yourself started. Once the fundamentals become second nature, it will be much easier to learn more advanced aspects of long-range shooting.

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