Minute of Angle (MOA)

MOA Explained

Scopes

Minute of Angle

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Minute of Angle

Minute of Angle (MOA)

A Minute of Angle (MOA) is a unit of angle measurement and frequently appears in discussions about rifle accuracy.

MOA is a measured way of adjusting a firearm’s sights elevation to compensate for bullet drop over distance due to gravity. It can also do the same laterally to compensate for windage.’

In mathematics the term is referred to as Minute of Arc or Arc Minute (arcmin) and is equal to 1/60th of a degree.

  • A full circle is 360 degrees, so, one degree is 1/360 of a circle.
  • A degree is 60 minutes, so, one minute is 1/60 of a degree.
  • A minute is 60 seconds, so, one second is 1/60 of a minute.
360 degrees
MOA 1 degree
1 minute
MOA

MOA is used extensively with shooters used to an imperial measurement system and manufacturers based in countries still using that system (USA). Where rifle ranges are measured in yards rather than meters and in inches rather than millimeters. Americans for example and many of our ranges in Australia still have 100 yard mounds. A leftover from our use of imperial units.

Calculating MOA

Calculating the MOA at a given range requires some trigonometry.

Consider a target at 100 yards.

  • Range = 100 yards = the circle radius (R)
  • MOA is in inches so convert 100 yards to inches (1 yard = 36 inches)
  • R = 100 x 36 = 3600 inches
  • From trigonometry we get the circumference(C) of the circle from
  • C = 2 x π(Pi) x R
  • C = 2 x 3.141592654 x 3600 = 22610.46711 inches
  • The minutes in a full circle = 360 x 60 = 21600
  • We divide the Circumference by the minutes to obtain the MOA
  • MOA = 22610.46711 / 21600 = 1.047197551 inches

While I am sure we all love the math. Unfortunately, the target died of old age while we were working it out.

So 1.047 inches at 100 yards is quite reasonably accepted as 1.

The MOA is deemed useful because the ratio of inches to yards applies in a linear manner over distance. 1 inch at 100 yards, 2 inches at 200 yards, 3 inches at 300 yards etc.

Scope turret with quarter MOA adjustment

Since most modern scopes using MOA are calibrated with adjustments of ⅛ eighth MOA, ¼ quarter MOA and ½ half MOA clicks (one increment of a turret adjustment). This can be easy for a shooter to calculate on the fly without referring to a range card.

For example a scope with:

Elevation adjustments (clicks) ½ MOA
Range 200 yards
Adjustment required 2 inches up

Required clicks = 2 inches divided by ½ an MOA per click multiplied MOA at 200 yards
= 2/0.5 * 2
= 2 clicks up

minute of angle

It is common in Australia to have a scope that is calibrated in MOA using yards as its base calculation being used on a range that is measured in meters. 

The tables below illustrate the difference.

Table MOA (Yards)
MOA (inches) Rounded to (inches) Range (yards) Range (meters)
1.047 1 100 91
2.094 2 200 183
3.141 3 300 274
4.188 4 400 366
5.235 5 500 457
6.283 6 600 549
7.33 7 700 640
8.377 8 800 732
9.424 9 900 823
10.471 10 1000 914
Table MOA (Metres)
MOA (inches) Rounded to (inches) Range (yards) Range (meters)
1.145 1 109 100
2.290 2 219 200
3.435 3 328 300
4.580 5 437 400
5.726 6 547 500
6.871 7 656 600
8.016 8 766 700
9.161 9 875 800
10.307 10 984 900
11.452 11 1094 1000

If you want to calculate other ranges use the calculator below.

Minute of Angle Calculator

Simple MOA Calculator

MOA

Shooters Minute of Angle (MOA)

Instead of the mathematically correct 1.047 inches, certain high-end scopes are calibrated so that a one MOA change on the scope corresponds to exactly one inch of adjustment on a target at 100 yards.

This is called the Shooters Minute of Angle (SMOA) and it can, in some circles, be called Inch Per Hundred Yards (IPHY).

Whilst even at 1000 yards the difference between MOA and SMOA is only 0.47 of an inch. The problem is that it compounds. So an adjustment of two MOA = 2 x 0.47 = 0.94 inches.

If you have to make an adjustment of 20 MOA, that adds up to 9.4 inches. A hell of a lot if you are into competitive target shooting.

A video on understanding Minute of Angle

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