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 1/60th 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 1/60th of a degree is called a minute of angle. As stated above, one MOA = 1/60th of a degree.
- 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.
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!