Minute of Angle (MOA)
Minute of Angle (MOA) or Minute of Arc is a unit of angle measurement and is used extensively with shooters that are used to an imperial measurement system.
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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.
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 millimetres. 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.
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
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 Calculators
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.
Minute of Angle explained - How MOA is used in practice
This is an example of how MOA is used on the range.
Target range is 200 yards
Scope is zeroed at 100 yards
5 shot group is 2 inches low
Scope elevation is calibrated at 1/4 MOA per click
We need to adjust the scope “up” 2 inches
MOA calculation
Target Range MOA = 200 yards
MOA inches at 200 yards = 2.094 inches
Formula - Inches per Minute of Angle (MOA)
Range to the target in yards ÷ 100 = Inches per MOA
200 yards ÷ 100 = 2 inches per MOA at 200 yards
Formula - Minute of Angle (MOA)
Inches per MOA ÷ Range to the target in yards x 100 = MOA
2 ÷ 200 x 100 = 1 MOA
Zero Range MOA = 100 yards
MOA at 100 yards = 1.047 inches
MOA to adjust = Target Range MOA – Zero Range MOA
= 2.094 inches – 1.047 inches
= 1.047 inches
Clicks required for adjustment = MOA for adjustment ÷ MOA per click
= 1 MOA / 1/4 (0.25)
= 4 clicks “up”
A video on understanding Minute of Angle
FAQ (Frequently Asked Questions)
What is a Minute of Angle?
A Minute of Angle (MOA) is a unit of angle measurement and is equal to 1/60th of one degree. There are 360 degrees in a full circle, therefore, the MOAs in a circle is equal to 360 x 60 = 21,600.
What does MOA mean?
MOA means Minute of Angle which is a unit of angle measurement. This assists telescopic sight adjustment for a variety reasons including elevation and windage.
What is Minute of Angle (MOA) used for?
MOA is a measured way of using a firearm’s sights to:
- Allow for bullet drop over distance due to gravity.
- Compensate for windage.
- Determine range to a target.
- Use effective holdovers and holdunders.
- Lead moving targets.
How many inches is a Minute of Angle (MOA)?
As Minute of Angle is in degrees, the number of inches, therefore, is dependent on the range.
At a 100 yards 1 Minute of Angle (MOA) equals 1.047 inches.
This is often rounded to 1 inch and referred to as Shooters Minute of Angle (SMOA) or Inch per Hundred Yards (IPHY).
1 Minute of Angle (MOA) at 100 yards equals 1.047 inches or 1 inch Shooters Minute of Angle (SMOA).
1 Minute of Angle (MOA) at 200 yards equals 2.094 inches or 2 inches Shooters Minute of Angle (SMOA).
1 Minute of Angle (MOA) at 300 yards equals 3.141 inches or 3 inches Shooters Minute of Angle (SMOA).
Refer to the tables or calculators on this page for more.
What does MOA stand for?
MOA stands for Minute of Angle, which is an angle of measurement. One (1) MOA is 1/60th of a degree. MOA is used to adjust telescopic sights for elevation and windage amongst other things.
What is MOA?
MOA means Minute of Angle which is a unit of angle measurement.
- 1 MOA = 1/60th of a degree.
- 1 MOA = 1/21600th of a full circle.
- 1 MOA = 1.047″ at 100 yards.
- 1 MOA = 10.47″ 1000 yards.
A Milliradian or (MRAD) is a unit of angle measurement. Milliradians, like Minutes of Angle (MOA), are a way of adjusting a firearms sights for elevation and windage.