Many times, at the range I hear people burbling away about MOA, minutes of angle or more rarely minutes of arc (which is correct).  Eves dropping on the conversations it is obvious that a lot of people only approximating MOA as 1inch group at 100yards.


During a rare idle moment, I paused to think about our great MOA and why rifles are sold ‘sub MOA’ and what it actually means.


To calculate MOA

From school days and trigonometry, some of us may remember the acronym SOHCAHTOA, this is a little ‘ditty’ to help you remember how to calculate angles in right angled triangles.  It breaks down to:

Soh…Sine = Opposite / Hypotenuse

cah…Cosine = Adjacent / Hypotenuse

toa…Tangent = Opposite / Adjacent

Normally the angle Ѳ is measured in degrees,

now more school stuff, there are 360 degrees in a circle and 60 minutes in a degree and 60 seconds in a minute.


So, what the heck has this got to do with shooting you say?


Well if we say the Adjacent side is 100m in length, and the opposite length being you group size you have just shot say a 20mm group

We would now get a very long skinny triangle.


So now we get in to the maths bit

Tan Ѳ = 0.02/100 (i.e. 20mm /100m)

Tan Ѳ = 0.0002


But we need the angle not the tangent of the angle, so out comes the smart phone and scientific calculator.  Most will show the opposite to tangent as tan-1       


So, tan-1 0.0002 = 0.0115 degrees

But we need the measurement in minutes of arc.

So: our group size is actually 60 x 0.0115 = 0.6875 MOA


So: there you have it a 20mm group at 100m is actually 0.6875MOA


Ref: Wikipedia

MOA=minutes of arc or arcminutes

The arcminute is commonly found in the firearms industry and literature, particularly concerning the accuracy of rifles, though the industry refers to it as minute of angle (MOA). It is especially popular with shooters familiar with the imperial measurement system because 1 MOA subtends 1.047 inches at 100 yards (approximately 3 cm at 100 m), a traditional distance on U.S. target ranges. The subtension is linear with the distance, for example, 500 yards = 5.235 inches, and 1000 yards = 10.47 inches. Since many modern telescopic sights are adjustable in half (1/2), quarter (1/4), or eighth (1/8) MOA increments, also known as clicks, zeroing and adjustments are made by counting 2, 4 and 8 clicks per MOA respectively.

Mike Simms