## Minute of Angle: Explained for Shooting Applications

“What the heck is a Minute of Angle (MOA)?” I can’t recount how many times my friends have asked me to explain the concept of MOA during a range session or prior to sighting in a new rifle. “Doesn’t a minute of angle equal 1-inch?” No, not exactly. Below, in a series of simple steps, I answer the question, “What is a minute of angle?” and illustrate how we employ the concept to make minute of angle scope adjustments for shooting applications.

## The Basics of Angles and Circles

First, we must understand that a minute of angle is an angular measurement. Most people quickly recognize the box symbol at the vertex of an angle as the symbol of a right angle, which measures exactly 90 degrees. Much like the 90-degree angle, a minute of angle is a unit of angular measurement, but it measures 1/60^{th} of one degree.

The symbol for a minute of angle is the apostrophe. An angle measuring one minute of angle would be written as follows: 0°1’

Second, we need to understand that all circles contain 360 degrees.

Third, like an hour of time, which can be divided into 60 equal minutes, each degree in a circle can be further subdivided into 60 equal parts. Each 1/60^{th} of a degree is called a minute of angle. As stated above, one MOA = 1/60^{th} of a degree.

To summarize:

- 1/360 of a circle = 1 degree, or; 360 degrees = 1 circle
- 1/60 of a degree = 1 minute of angle, or; 60 minutes of angle = 1 degree.
- Every circle contains 21,600 minutes of angle, because 360 degrees * 60 minutes = 21,600 minutes of angle.

A minute of angle is a very small angular measure, which lends itself well to making fine adjustments in rifle optics at typical rifle ranges (100 yards to 2,000 yards). Most scope manufacturers produce optics with controls (turrets) that allow adjustment in 1/4 MOA increments, further enhancing the level of precision adjustment possible from the optic.

## Vertex, Rays, and Angles

__Rays__ – The sides of an angle.

__Vertex __– The common endpoint of two rays.

__Angle__ – The measurement (about the vertex) of two rays that share a common endpoint.

When applying the MOA concept to shooting, we must understand, that the vertex of an angle measuring 1 MOA __does not change__ regardless of the shot distance. Let me repeat that, **the vertex of an angle measuring 1 MOA does not change, regardless of the shot distance. **The vertex of a 1 MOA angle **ALWAYS** measures 1 MOA. However, the distance __between the rays__ of an angle measuring 1 MOA will change, depending on the distance from the vertex. See the image below, which illustrates this point.

**A minute of angle is an angular measurement of the vertex, not a measurement of the distance between the rays!** This is the __critical concept__ to understand when learning about MOA as it relates to shooting.

**“Doesn’t 1 MOA Equal 1-inch?”**

One MOA equals 1-inch is an old rule of thumb that doesn’t quite tell the whole story. Let’s look at the geometry behind the actual calculation of the measurement between the rays of a 1 MOA angle at 100 yards.

From the discussion above, we know every circle contains exactly 21,600 MOA. In this example (100-yard shot), we know the radius (the distance from the shooter to the target) is exactly 100 yards. To find the circumference—the distance around the perimeter of the circle—we use the formula for the circumference (C) of a circle, which is 2 multiplied by Pi (π) multiplied by the radius (r) of the circle, which can also be written as C=2πr.

Therefore, C=2πr or C = 2 * 3.14 * 100yds, which equals C = 628 yards.

This solves for the circumference in yards, but we want to look at the result of the calculation in inches, a more typical unit of measurement for shooting sports. To convert to inches, we apply the following conversion rates:

- 1 yard = 3 feet, and;
- 1 foot = 12 inches.

Therefore, the circumference of our circle with a 100 yard radius, in inches, is:

C = 628 * 3 * 12 = 22,608 inches.

Next, to calculate distance between the rays at 100 yards of an angle measuring 1 MOA, we simply divide the total circumference of our circle, 22,608 inches, by the total number of MOA in a circle (21,600) to solve for a 1 MOA section of the circumference with a radius of 100 yards. Therefore, 1 MOA @ 100 yards = 22,608/21,600 = 1.047 inches.

Does 1 MOA equal 1 inch at 100 yards? Not quite, it equals 1.047 inches, which is close, but only at 100 yards.

As a result, most hunters and casual shooters round 1.047” to 1”, with many people incorrectly believing that 1 MOA and 1 inch are synonymous. They are not, and it becomes apparent at any distance other than 100 yards. Next, we will take a look at how this assumption becomes problematic.

For a lot of shooters, the assumption that 1 MOA equals 1 inch at 100 yards represents the depth of their knowledge on the topic of MOA, and the beginning of __where the real problems arise__. Next, we will perform the same calculation for a shot distance of 500 yards. First, the circumference.

Again, C=2πr. In this case, C = 2 * 3.14 * 500. The circumference of the circle with a 500-yard radius is 3,140 yards. Now, we convert yards to inches by multiplying yards by 3 (number of feet in a yard) and by 12 (number of inches in a foot). Therefore, 3,140 yards * 3 * 12= 113,040 inches.

Next, to calculate distance between the rays of an angle measuring 1 MOA at 500 yards, we simply divide the total circumference of 113,040 inches by the total number of MOA in a circle (21,600). Therefore, 1 MOA @ 500 yards = 113,040/21,600 = 5.23 inches. So, does 1 MOA equal 1 inch at 500 yards? No, it’s not even close! At 500 yards, 1 MOA equals 5.23 inches. Let me reiterate the key principle; 1 MOA is the angular measurement of an angle’s **vertex** __NOT__ the distance between the rays! The greater the distance from the vertex, the larger the distance __between the rays__ will measure for the same 1 MOA.

## Practical Applications

Once we understand the MOA concept mathematically, we can look at some practical applications.

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__Zeroing Your Rifle Scope at Any Distance__

**Step #1 Identify the Distance**– Laser rangefinders are the most common and practical method of measuring distance accurately. Another viable alternative is to attend a known distance shooting range, where the distance from the shooting station to the target is a known distance.

**Step #2 Determine the value of a MOA at the specified distance**– Divide the shot distance (in yards) from step #1 by 100, and then multiply the result by 1.047”. For example, at 500 yards, perform the following steps: 500/100=5. Then, 5*1.047=5.235”. Therefore, at 500 yards, 1 MOA = 5.235”.

**Step #3****Determine (in inches) the adjustment necessary**– I like to use a sight-in target with a 1” grid pattern.**Tip**: use a bubble level to ensure the target is level when secured to the backstop. For long range shooting, a properly leveled scope is also critical.

Next, fire a round.

Finally, determine the distance (in inches) the bullet impacted from the bullseye by using the 1” grid on the target or by measuring with a tape measure.

**Step #4 Make the appropriate scope adjustments**– Divide the number in step #3, by the number in step #2. For example, if the fired shot is 10” low (step #3) at 500 yards and 1 MOA at 500 yards equals 5.235”, then 10”/5.235”= 1.91 MOA adjustment required to impact the bullseye.

**Step #5 Round the solution in Step #4 to the nearest 1/4 MOA**– Most riflescopes adjust in 1/4 MOA increments, therefore, we would round 1.91 MOA to 2 MOA and adjust the scope 2 MOA in the up direction. Adjustment shown below on a Vortex Viper PST Gen II

**Step #6**Fire at least three additional rounds to confirm a proper zero**Step #7**Repeat step #3 through step #7 as necessary

## Example #1 - Correcting a Bullet Impact @ 100 Yards

In this example, we assume a shot distance of exactly 100 yards and a bullet that impacted 4 inches to the right of the bullseye and 2 inches low of the bullseye. We now know that 1 MOA = 1.047” at 100 yards. To correct our miss, we would adjust left 4 MOA, and up 2 MOA. Please note, __most__ riflescopes adjust in 1/4 (or .25) MOA increments. Therefore, a 4 MOA adjust left would require 16 (4/.25=16) clicks on the scope’s windage turret, and a 2 MOA vertical adjustment would require 8 (2/.25=8) clicks on the scope’s elevation turret.

## Example #2 - Correcting a Bullet Impact @ 300 Yards

In this example, we are shooting 300 yards and we have a bullet that impacted 4 inches to the right of the bullseye and 2 inches low of the bullseye. We now know that 1 MOA = 3.14” at 300 yards (Remember 300yds/100 = 3 -> 3 * 1.047 = 3.14″). To correct our miss, we would adjust 1.27 MOA left.

Here is a look at the math for the windage (left/right) correction:

- 4” miss to the right
- 1 MOA at 300 yards = 3.14”
- How many times does 3.14” go into 4”?
- 4”/3.14”=1.27 MOA

However, most scopes adjust in 1/4 MOA increments and we adjust to the nearest quarter, or 1.25 MOA left in this case.

Here is a look at the math for the elevation (up/down) correction:

- 2” miss low
- 1 MOA at 300 yards = 3.14”
- How many times does 3.14” go into 2”?
- 2”/3.14”=.64 MOA.

However, most scopes adjust in 1/4 MOA increments and we adjust to the nearest quarter, or .75 MOA up in this case.

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Hopefully, this article cleared up the confusion surrounding the concept of minute of angle (MOA). If you have any other helpful tips or tricks for using MOA calculations, leave a comment below!

My scope reads 0.2 moa as the smallest measurement. Can you brake down 1 moa to 0.?. Does it brake down into 10th, 20th ect

Thanks

Hi Heart, first, double check that your scope is a MOA model and not a MIL model. If it is indeed MOA, then 1 MOA @ 100 yards = 1.047″, therefore 0.2 MOA = .2094″ @ 100 yards (because 1.047/0.2=.2094). So, every click of your scope (0.2 MOA) will move the bullet impact .2094″ @ 100yds. If you move out to 200 yards, every click of your scope (0.2 MOA) will move the bullet impact by .2094″ * 2 = .4188″. At 300 yards, every click of your scope (0.2 MOA) will move the bullet impact .2094 * 3 = .6282″ and so on. Hope that helps!

Since December 2020 I began researching scopes and the process is fascinating! This article I reference all the time! In your examples showing impact point and WITHOUT reading the answer I’d think it through. Due to prices Of ammo and life in general I don’t shoot consistently. Therefore I have to reference this article to stay sharp. THANK YOU👍

Hi Rich, thanks for the comment, and I’m happy you’ve found it to be helpful!

One thing that should be understood is that it is extremely rare for a scope to adjust according to the manufacturers advertised MOA adjustments. I have zeroed many dozens of premium and budget scopes and red dots by a variety of manufacturers and I have NEVER encountered a single scope that was true to its advertised click value. I can zero just about any scope in less than 10 rounds by accepting that the advertised MOA click value is complete fraudulent BS and assuming that each click is actually closer to 1 MOA. Almost always, that turns out to be pretty close to what it actually is. If I believed the manufacturer and corrected my reticle according to math I would be way off.

Hi Justin,

Great point. I have seen this as well, although not nearly as often with modern premium level optics. As with most things, it’s best to collect in the field data. Thanks for reading, and happy shooting!

Very helpful. Made it easy to understand.

Well done, but still have to adjust in field, scopes are different easy to do math and then realize scope is in eighths. Lol…

Many thanks to Mr. Weiler -.what a relief to realize my scope’s MOA adjustment is NOT ¼” but “errors” out to ½” – actually doubles the distance of adjustment! (cheap scope). I’ve been going bat-shit crazy doubting my math, when the culprit was the manufacturer’s (suggested) stated MOA adjustment. Just another case of “buyer beware!”. Always confirm claims yourself!