Most firearm sighting scopes incorporate windage and elevation adjustments
referenced to MOA (minute of angle). Each click of the scope turret is usually
1/4 MOA change and on some scopes 1/8 MOA. Normally, shooters refer to these
adjustments as a change of a fraction of an inch at 100 yards rather than the
true value of MOA for which they are supposedly calibrated to. The value of inch
is a nice easy number to work with and most of us can easily visualize its
length and its multiples without the aid of a calculator. Actually the
comparison is close enough to not be of practical concern, especially at
distances up to a few hundred yards, and the real difference is a mere 0.47 inch
at 1000 yards. For serious target shooting and as shooting distances increase
the attention to MOA value relative to sight adjustment becomes more essential.

Calculating Minute of Angle

The angle of an arc is expressed in number of degrees. There are 360 degrees
of arc to a full circle. Each degree consists of 60 minutes of arc. The distance
covered by the measure of arc is relative to the circumference (total distance
around the circle) it is contained within. Knowing the radius (distance to
center of circle) circumference is easily calculated by using the constant *pi
*. The ratio (represented by *pi *) of circumference is constant to
diameter (radius x 2) regardless of circle size. The precise value of *pi *
is so far unknown to man but is normally resolved to 3.1416 or 3.141 for our
purposes.

Suppose a circle with a 6 inch radius. Circumference can be calculated as:

circumference = (radius x 2) x *pi *

circumference = (6 x 2) x 3.1416

circumference = 12 x 3.1416

circumference = 37.6992 inches

The distance covered by 1 degree of angle (37.6992 / 360 or, circumference
divided by 360 degrees) is 0.1047 inch at 6 inches from center of circle.

And, 1 minute of angle represents (0.1047 / 60 or, 1 degree divided by 60
minutes) 0.001745 inch at 6 inches from center of circle.

Knowing what MOA represents allows us to calculate its value to any distance.

Six inches (the radius of the above example) is 1/600th of 100 yards: (100
yards x 36 inches) / 6 inches = 600

Therefore, the value of MOA at 100 yards is 1.047 inches (0.001745 x 600 =
1.047)

At 50 yards 1/2 the 100 yard value; 70% @ 70 yards; twice @ 200 yards; 6 times
@ 600 yards; and so on.

So, the difference between thinking in inches as opposed to MOA is 0.47 inch @
1000 yards

Four (4) clicks of the scope adjustment equals 1.047 inch change @ 100 yards for scopes of 1/4MOA per click.

Where group size is expressed in inches the word 'inch' should be spelled.
Writing the symbol commonly used to represent the measure of inch (") is not
accurate here, and in fact misleading since that symbol also represents 'second
of angle' (1/60 of a minute of angle). Therefore, a group of 1 inch would
properly be written as '1 inch' not 1". It could also be written as 1' since
that symbol (') is used to represent minute of angle but that might be
misleading to those thinking in feet.

Why Use MOA

As shown above, the value of a measure of angle can easily be calculated to
any distance from its source of origin - center of circle or muzzle of barrel.
Such measures as MOA (minute of angle) are also part of our only universal
language - mathematics. While knowing a rifle has a
precision of a certain value of the inch at a
particular distance also makes it simple to calculate its precision at other
distances, one would have to know both the distance and the measure in inch
(example: 1 inch @ 100 yards) before calculating it to other distances. In
contrast, knowing only the measure of angle is needed to do the same. An example
of the contrast is expressing 0.73 inch @ 100 yards *verses *0.7 MOA (0.73
/ 1.0472 = 0.697). The two equate practically the same (1 MOA = 1.047 inch @ 100
yards) but the expression using MOA is more concise since no distances are
included in the expression.

Two informative sites for further discussion of MOA relative to firearm use:
What Is MOA and Is It Really an Inch
At 100 Yards? and
Mil-dots
and Minutes-of-angle, From a Technical Perspective

**In metric measuring system countries it is used 27.77 mm @ 100 meter to
be in the same proportion of the 1 MOA = 1.000 inch @ 100 yard**

Calculating Scope Click

For long ranges where shooting distances may vary considerably it is wise to
know the actual value of each scope adjustment. This is especially true if scope
settings are changed in the field as shooting distances change. Not all scopes
are precisely calibrated to MOA (minute of angle) or to the inch.

Shooting from a solid bench rest, determine the center of group using the
Average Group Radius method. Without reaching
the adjustment limit of the scope, make and record as many scope elevation
clicks as will still keep the group on the target while shooting at the same
aiming point as before. Again determine center of group using the Average Group
Radius method. Return the scope elevation to its previous setting. Determine the
distance between the center of the two groups. Divide that distance by the
number of elevation clicks used to achieve group two. That is the calculated
value of change for that distance for each click.

For high power rifles it is recommended the target be no less than 100 yards
distance as some projectiles may not completely stabilize at shorter distances,
thereby giving a false indication of true performance.