What is one MOA and why do we use it to measure a group?

A Minute of Angle.......What does that mean and why do we use it as a unit of measure?

What is a MilDot? Is that a unit of measure?

The MOA, minute of angle is often used to describe the accuracy potential of certain rifles. Some makers even offer guarantees their rifle will shoot to one MOA or even 1/2 MOA. One might ask; How good is that?

Lets look at a rifle shooter taking aim with his new rifle. He places a target up at 100 yards distant and seats himself at the bench, sand bags his rifle and prepares to make the shot. Lets move above the shooter in a low hover. Looking down upon the shooter, we draw a line from the muzzle of his rifle to the 100 yard distant target. This line is 100 yards, 300 feet, 3600 inches in length. Now lets draw a circle around our shooter starting at the target and making a complete, perfect circle, around behind our shooter and back to the target. This circle will be 200 yards in diameter but how far around?

Now lets move on to some simple math:

The circle:

Always measures 360 degrees.

There are 60 Minutes of Angle in one degree.

There are 60 * 360 or 21,600 minutes of angle in one complete circle.

This is true regardless the size of the circle so we can call this number a constant.

The circle is further measured in diameter, linear measure expressed in inches, feet, centimeters or furlongs. One half its diameter is the Radius. Our shooters circle has a radius of 3600 inches.

The Radius can be expressed in linear measure or angular measure,

Angular measure is defining the radius of a circle in degrees.

The radius of any circle, though a straight line, will equal 57.296 degrees when wrapped around the circle.

It is from this relationship we derive the quantity of pi.

One pi radius, now called a radian when we wrap it around the circle, will equal 180 degrees.

pi = 3.14159 One radian = 57.296 degrees.

When we multiply these together we get a number pretty close to 180. This 180 degrees is half the circle.

We can further measure any circle or partial circle in radians, or more correctly pi radians. One complete circle is 2 pi radians or 360 degrees.

2* 3.14159 * 57.296 = 360

We are now almost ready to make the shot, or several shots actually and measure the spread of those shots in MOA.

Remember our circle always has 21,600 minutes of angle but this circle of 100 yards radius has a certain linear measure we have yet to calculate.

The radius of this circle must be known to calculate the linear length of the circle.

Our shooters circle has a radius of 100 yards or 3600 inches.

100 yards = 300' = 3600" (inches).

This 3600 " equals 57.296 degrees.

If we multiply 3600 times 2 pi, we get;

3600" * 6.28318 (2pi) = 22,619.448"

This is the distance around our shooters circle in inches.

Now that our shooter has had time to shoot several shots to test his new rifle, lets look at the group and determine the group size in MOA.

Two sets of numbers are needed for this;

The angular distance around the circle. 21,600 MOA

And the linear distance around the circle. 22,619.448"

We divide the distance by the constant (21,600) we get;

22,619.448"/21,600 = 1.047"

1.047" = one MOA.

So, a rifle guaranteed to shoot 1/2 MOA should group three or five shots within, plus or minus, .524". This means the rifle will keeps it's shots within .524" of the point of aim (POA).

They could be .524" left or .524" right, high or low of POA and still meet the accuracy guarantee.

We could also just measure a group fired from a known distance and convert that to MOA. Generally when measuring a group we measure from center to center of the widest shots, in inches or centimeters, and convert to MOA.

If I have a group fired at 200 yards which measures 1.750" we can calculate the MOA size of that group.

200 yards = 7200" (r)

7200" * 2 pi = 45,238.9"

45,238.9/21,600 = 2.094" = one MOA @ 200 yards.

1.75"/2.094" = .8357 MOA

A very good group. Less than one MOA accuracy at 200 yards.

That's MOA as used to describe shooting accuracy.

So where does Mil Dot come from? What does it mean?

Mil is an abbreviated way of saying Milli-Radian (mr).

Remember a radian is 57.296 degrees.

Milli is represents the quantity of 1 * 10 to the -3 (Ten to the third negative power).

Basically .001 or 1 one thousandth. Or a thousandth of a radian.

Or quite simply, 57.296/1000 = .0573 degrees.

To convert this to MOA we simply multiply by 60 (number of minutes in a degree.)

.057296 * 60 = 3.43776 MOA

Or

3.43776 (MOA in 1 mr) * 1.047" (inches in MOA at 100 yards) = 3.599" = 1 mr

Thus one milli radian is equal to approximately 3.6" at 100 yards or 36" at 1000 yards.

Two milliradians at one thousand yards is approximately the height of adult male human.

More on the Mil Dot system of range finding will be found in the Mil Dot section.

From the bookThe Science of Shooting

ByJim Clopton