Using and Understanding Minute of Angle (MOA)

Hatcher's Armory
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Had a chat with a friend last night about Sub MOA and Rifles and though he had heard of the term Minute of Angle, he didn’t really know what a Minute of Angle was. No judgement, we all have to learn this stuff somewhere. For those that want to learn, here is a write up from Western Shooter which has a nice quiz at the end.

If you are already a Minute of Angle Expert, take our Minute of Angle Quiz

You should understand that an English inch and a Minute of Angle (MOA) is not the same thing. They are units of measurement that happen to be extremely close in value. However, they are close enough together that for the rest of this explanation please simply round down to an inch.

Exact Minute of Angle (MOA):
1 MOA = 1.0471996 inches @ 100 yards.
1 MOA = 5.24 inches @ 500 yards.
1 MOA = 10.47 inches @ 1000 yards.

Rounding MOA
1 MOA @ 100 yards = 1 inch
1 MOA @ 200 Yards = 2 inch
1 MOA @ 300 yards = 3 inch
1 MOA @ 400 Yards = 4 inch
1 MOA @ 500 yards = 5 inch
1 MOA @ 600 Yards = 6 inch
1 MOA @ 700 yards = 7 inch
1 MOA @ 800 Yards = 8 inch
1 MOA @ 900 Yards = 9 inch
1 MOA @ 1000 Yards = 10 inch

Minute of Angle as it applies to group size and drop
MOA is used to measure group sizes. A 1 inch group @ 100 yards is referred to as a 1 MOA group. A 2 inch group @ 100 yards is a 2 MOA group.

At 100 yards it seems simple enough to understand. However, it can get confusing if you’re not used to the terminology when you move beyond 100 yards. For example: a 3 inch group shot at 300 yards is also a 1 MOA group. A 6 inch group shot at 300 yards is a 2 MOA group. A 1 ½ inch group shot at 300 yards is a .5 MOA group.

Another way to look at it is like this:
½ MOA @ 700 yards is 3.5 inches
1 MOA @ 700 yards is 7 inches
2 MOA @ 700 yards is 14 inches
3 MOA @ 700 yards is 21 inches

3.5 inches @ 700 yards is ½ MOA
7 inches @ 700 yards is 1 MOA
14 inches @ 700 yards is 2 MOA
21 inches @ 700 yards is 3 MOA

Calculations:
How many inches equal 4 MOA at 700 yards?

  • (MOA x yards) / 100 = inches
    (4 MOA x 700 yards) / 100 = 28 in

How many MOA equal 21 inches at 700 yards?
*(inches / yards)100 = MOA
(21 inches / 700 yards) 100 = 3 MOA

5 inches = 1 MOA how many yards away is the target?
(Inches x MOA)100 = Yards
(5 inches x 1 MOA) 100 = 500 yards

You can drop the last step and make the calculations easier by moving the decimal on the yards two places to the left.
How many inches equal 4 MOA at 700 yards?
(4 MOA x 7.00 yards) = 28 in

How many MOA equal 21 inches at 700 yards?
(21 inches / 7.00 yards) = 3 MOA

Minutes of Angle and Rifle Scopes
Most hunting and target scopes adjust in Minutes of Angle (MOA). The most common adjustment is ¼ or .25 MOA per click. Although not as common, there are scopes that adjust in 1/8, 1/6/, 1/5, 1/3, ½, and 1 MOA .
¼ MOA at 100 yards literally means that each time the scope turret is clicked the bullet impact will move ¼ or .25 inches.

To move the bullet impact 1 inch you would need 4 clicks (.25 x 4 = 1) Example: When sighting in a rifle the bullet needs to move up 5 inches to hit the center of target. 5 in / .25 in = 20 clicks or you could think of it like this: need to move 5 inches, 4 clicks per inch, 5in x 4 clicks per in = 20 clicks.

Another application for understanding MOA and scope or sight adjustment is when shooting longer distances. Rifle is sighted in at 100 yards. Your ballistic program tells you that you need to come up 20 MOA to shoot at 600 yards. 20 MOA / .25 = 80 clicks Or 20 MOA x 4 clicks per MOA = 80 Clicks

Take the Minute of Angle Quiz
Below are some quiz questions that will help you think and talk in Minutes of Angle. (Answers are at the bottom of the page.)

  1. If you’re sighting in your rifle at 200 yards and your groups hit the target 6 inches low. How many ¼ MOA clicks do you need to turn your scope turret to hit the center of the target?
    A. 24
    B. 12
    C. 18
    D. 48

  2. How many inches equal a minute of angle at 625 yards?
    A. 1
    B. 3.75
    C. 5.5
    D. 6.25

  3. If I brag about my shooting and tell you I shot a ½ MOA group at 300 yards, what size group did I shoot?
    A. ½ inch
    B. 1 ½ inch
    C. 3 inch
    D. 1 inch

  4. If I can consistently get my rifle to shoot under 2 MOA, in theory, what is the smallest size steel plate I should be able to always hit at 700 yards?
    A. 10 inches
    B. 15 inches
    C. 18 inches
    D. 24 inches

  5. My group size is 4 inches and my rifle shot 1 MOA. How far away is my target?
    A. 40 yards
    B. 400 yards
    C. 444 yards
    D. 800 yards

  6. Many gun writers maintain that a gun that will shoot 2 Minutes of angle is adequate to hunt with. What is the maximum distance such a gun will consistently shoot 10 inch groups?
    A. 250 yards
    B. 750 yards
    C. 500 yards
    D. 100 yards

  7. In standard Mil-Dot Reticles, from the center of one mil-dot to the center of the next mil-dot is 3.6 MOA at 100 yards. If you are sighting in your rifle at 100 yards and your groups are approximately the space between two mil-dots above the center, how many ¼ MOA clicks do you need to turn your turret down to center your group?
    A. 14 clicks
    B. 3.6 clicks
    C. 10 clicks
    D. 24 clicks

  8. If you shoot a .25 inch group at 25 yards, what MOA did you shoot?
    A. .25 MOA
    B. .5 MOA
    C. .75 MOA
    D. 1 MOA

  9. If your buddy tells you he can shoot 1 MOA at 1760 yards or 1 mile, approximately how big is his group?
    A. 100 inches
    B. 17.6 inches
    C. 20 inches
    D. 176 inches

  10. In 1000 yard F Class matches the X ring is 5 inches. If you were to place all your shots in the X ring, what MOA would you have shot?
    A. 1 MOA
    B. 10 MOA
    C. .5 MOA
    D. 5 MOA

  11. You’re going to shoot your rifle at 1000 yards. Your rifle is sighted dead on at 100 yards. The ballistics program says you need to dial in 28 MOA to reach 1000 yards. How many ¼ MOA clicks do you need to turn your scope turret?
    A. 28 clicks
    B. 280 clicks
    C. 112 clicks
    D. 64 clicks

  12. You and a buddy are out shooting balloons in the desert at 600 yards. The wind is blowing and your buddy is spotting your shots. After your last shot he tells you that your elevation was dead on, but your wind was off 2 MOA to the left. How many inches off to the left was your shot and how many ¼ MOA clicks to the right will it take to correct?
    A. 6 inches, 8 clicks
    B. 12 inches, 8 clicks
    C. 12 inches, 16 clicks
    D. 24 inches, 24 clicks

  13. Assume a 100 yard zero. If you have to adjust your scope up 28 MOA to shoot 1000 yards, how many feet is your bullet dropping?
    A. 28
    B. 10
    C. 55.7
    D. 23.3

  14. In theory. If you can shoot a 1 inch group at 100 yards, what size group should you be able to shoot at 400 yards?
    A. 4
    B. 8
    C. 1
    D. 2

Answers
[spoiler]

  1. B *(6in / 2.00 yards) = 3 MOA , 3 MOA x 4 clicks per inch = 12 clicks
  2. D *(1 MOA x 6.25 yards )= 6.25
  3. B *(.5 MOA x 3.00 yards) = 1.5 inch group
  4. B 2 MOA = 14 inches @ 700 yards.
  5. B (4 inches x 1 MOA) 100 = 400 yards
  6. C
  7. A
  8. D
  9. B
  10. C
  11. C
  12. B
  13. D *(28 MOA x 10.00) = 280 inches 280in / 12in = 23.3 ft
  14. A
    [/spoiler]
3 Likes
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I think this picture helps a lot.

Read more at this site:
http://guntoters.com/blog/2016/07/21/minute-of-angle-and-point-blank-zero-what-the-heck-are-they/

4 Likes
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Cool data about MOA. MOA has been co-opted by long range shooters (and others), but is a basic principle in math. 1 minute of angle is simply one-sixtyth (1/60) of one degree. People commonly refer to angular measurements in degrees minutes seconds (DMS). 1 second of angle is 1/60 MOA. You’ll commonly see latitude/longitude coordinates reported in DMS.

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Seems like there should be some kind of marketing tie in there for DMS (us) and that concept…

3 Likes
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Good information for any scope user.

You can also use a scope to estimate range, if you know a target’s size. This is typically done using a scope with a reticle marked at certain angular intervals.
image image
Example, if a coyote normally standing about 20 inches tall, subtends 6 MOA in your scope, how far away is he?

Simple formula: SizeTarget (inches) ÷ Size (MOA) x 95.5 = Range (y)

Thus, the Coyote is 318yds away, and you can set your come-ups based on that.

Most long range shooters tape a table of come-ups at various ranges to their stock for easy reference.

Should also be noted, that a majority of long range shooters use Milradians to accomplish the same things. Mils are used similarly to MOA, with different formulas. It doesn’t matter which you use, just use whatever angular measurement that matches the adjustment value of your scope. Most mil/mil scopes use 1/10Mil per click.

SizeTarget (inches) ÷ Size (MILs) x 27.77 = Range (y)

2 Likes
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Don’t forget Milrad. Then there are conversion factors too to go from one to the other.

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Memory joggers/crutches are absolutely wonderful/necessary!:rofl:
Glad to see someone else learned something useful in the public schools.

1 Like
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This depends on if your scope reticle is first surface or second surface. If your reticle doesn’t change size when adjusting the magnification your example will only work at one magnification setting. If it does change it doesn’t matter what magnification setting is and this will work fine.

Russell

3 Likes
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Well, was really just adding a footnote to Nick’s post, which I enjoyed. Didn’t wnt to get into the specifics of scope operation. That being said, it isn’t the first or second surface, but rather the first and second focal plane you’re referring to. Its definitely true, that first focal plane scopes have fixed magnifications at which they measure 1:1 in MOA or Mils. Second focal plane scopes can be read directly at any magnification. First focal plane scopes require you to measure at about 10x magnification for ranging.

Most people want second focal plane scopes, but they sure can get expensive. Falcon makes a second focal for about $450 or so, and its pretty decent, but you can easily spend 3,000-4,000 on a high-end scope for long range shooting.

i don’t know if its because I learned how using first focal scopes, but at this point I still prefer the proportional reticle. I’m weird that way. But most will prefer the second plane scopes.