Hunting rifle accuracy is pretty much defined by the size of a group of shots fired at a target 100 yards distant. Minute of Angle (MOA) is the most convenient unit measure for such accuracy. A minute of angle is one 60^{th} of one degree. Most folks would know that a full circle takes in 360 degrees. Therefore, 1.000 MOA is simply one sixtieth of one degree, which is invariant at any distance. At 100 yards one MOA corresponds to 1.05 inches, or 26.6 millimetres.

**MOA – Minute of Angle size at varying distances**

The group size is the smallest circle that can be drawn through the centre points of the holes left by the bullets in the target. Shooters just measure the two furthest apart holes and count that as the group size. Most times that is good enough but, when the group is essentially triangular in shape, that approach can be a bit out. Mathematically determining the exact smallest circle through the holes is actually a challenging exercise that requires a computer.

I got a maths whiz to build me a program to do that. The other advantage of that calculator, apart from determining exactly the correct group size, is that it also gives me the true group centre point. That information can be useful for correctly setting your scope sighting, but more when looking for optimal loads.

Ideally, hunting rifles are sighted to give a point of impact (POI) about 1.5 inches high at 100 yards, which generally (depending on the calibre) gives a dead-flat range out to about 200 yards. However, I only fully sight a particular load once I am happy with it. Until then, it is group size that matters, not the actual POI.

In the target shown I have measured the centre point distance of each bullet hole relative to the vertical and horizontal axis. Applying my calculator to a typical triangular shaped group it returns a true group size of 23mm (rounded to nearest mm). Measurements are relative to the point of aim (POA) which is always the target centre. Entering that data in the calculator then allows the exact diameter of the smallest circle, and its centre location, to be generated.

**Actual Target showing group of bullet holes**

**The Minimum Circle Calculator for ammunition accuracy**

Don,

using the “computer” which figure is the true group size? Xo, Yo, r ? I would assume its Xo at 22.369 mm ? What role does the r value give ?? ( maths and calculus – yuk!!)

Its a great tool indeed.

Con

Hi Con

The calculator returns Xo and Yo which is the centre of the smallest circle that fits the group. That centre point is the average point of impact for the group of holes.

“r” (11.7755) is the radius of that circle. You have to multiply that by 2 to get the diameter, which is the group size, 23mm close enough.

cheers

Don

Don – “r” is for radius of course

rx2 = diameter!!

Viola

Cheers

Con