I was reading a post and the point of MOA kept coming up and I thought to myself, do I really understand what MOA means, so I did a search. I have read the following info, and believe I understand it, but want to sleep on it and check back. If you have comments on the borrowed info, please do so. Info source is:
http://riflestocks.tripod.com/


Minute of Angle


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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.
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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
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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. Below is a procedure learned from Varmint Al's Shooting Page for better determining the value of each click of the scope turret.

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.

Calculating Rifle Precision

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First, precision and accuracy are not the same. A rifle grouping 1/4 MOA is very precise for a firearm. If that 1/4 MOA rifle puts groups off the aiming point it is not accurate. Rifle precision is a measure of how close it will hit to the same point it had before. Rifle accuracy is hitting the aiming point. Equally though, it is true that if you are shooting for groups and do not wish to destroy the aiming point but rather have the shots hit somewhere else on the target the rifle is accurate if it does what you wish. All of the above assumes, of course, that no blame can be proven on the operator of said rifle.

For the purpose of determining rifle precision I will discuss only two methods. The 'extreme' or 'maximum spread' method is the usual and quickest method used by most of us while in the field. It is not accurate in fairly determining the performance of a rifle but becomes a less inaccurate method as group size decreases. For very tight groups it is a good method of measure because the distinction between it and the 'average group radius' diminishes. The 'average group radius' method is the best and most difficult I know of in determining rifle precision. Determining average group radius involves time consuming measurements and calculations in order to determine center of group and then average shot placement relative to that center. It is a highly accurate means of calculating rifle precision.

77 Yard Target calculations are compliments of RSI Shooting Lab Software http://www.shootingsoftware.com/ Using the Maximum Spread Method the above 3 shot grouping measures 0.70 MOA; the Average Group Radius is 0.33 MOA.
Average Group Radius tells us how far from center of group we can expect the shot to be. Maximum Spread emphasizes the worse shot.

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Maximum Spread

Sometimes referred to as 'extreme spread' maximum spread is a measure of the distance between the centers of the two furthest shots within a group. It is often thought to be a measure of the smallest circle the group will fit into. This is misleading because the method does not distinguish between a tight group that has a dissimilar shot and a not so tight group that is evenly dispersed. The maximum spread method is acceptable for measuring tight groups that do not have so called flyers and a reasonable measure for groups with all its shots evenly dispersed. While in the field, I will usually rely on this method for a quick idea of what the group is. If the group is interesting enough or important enough I will later take the time to calculate the average group radius.

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Average Group Radius

First find the group center. Measure distance from center of group to center of each shot. Average the distances. The result is the average group radius. Double that would be the average diameter of the group but this figure is not normally expressed. The average group radius is the average distance of the center of shot to center of group.

To manually find the center of group draw a horizontal line through the center of the lowest shot. Draw a vertical line through the center of the leftmost shot. Measure and add the distances from the center of each shot to the horizontal line. Average the sum of these distances by dividing it by the number of shots. This gives the distance from the horizontal line to the vertical center. Measure this distance from the horizontal line and mark that location on the target. Measure and add the distances from the center of each shot to the vertical line. Average the sum of these distances by dividing it by the number of shots. This gives the distance from the vertical line to the horizontal center. Place rule across vertical line and mark made at vertical center. Measure the distance of the horizontal center from the vertical line and mark it on the target. This last mark is the statistical center of the group.

There is a ballistics program available that includes the unique feature of entering a target grouping into the program. It will analyse the group and give statistical data on it. Included in the analysis is the average group radius. It is easy to enter. You press the target to the video screen and click on each bullet hole with the mouse. You can also scan the target in. There is a feature the software includes to calibrate the aspect ratio of the video input so that the distances in both horizontal and vertical directions are correct. The software can be found at Recreational Software Inc. http://www.shootingsoftware.com/ and is the software used to analyse the above target.

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A further discussion on measuring rifle precision is provided by selecting 'Measuring Targets Tech. Article' at Tech. Articles http://www.shootingsoftware.com/tech.htm.

Hey Joe,

Thanks for the detailed explanation of MOA. The difficulty does (IMO) not concern your clear view on this subject, but the intelligence of the avarage hunter.
I always consider the MOA phenomenon as a means to calculate the distance at which you can reliably shoot at animals of known sizes of the heart-lung diameter.
And I 'translated' the MOA to metrics, thus:

1 MOA = 1,047 inch at 100 yards (91,44 meters). As we relate our accuracy in Europe always to 100 meters, 1 MOA means 26,6 mm at 100 yards and 29,1 mm at 100 meters, this is the factor (for simplicity) 0.29.
It is important than, to know your shooting capabilities in your favourite shooting position. Say you like to shoot sitting, elbows beside your knees and with the hasty sling method. I instruct to fire at least 16 rounds, preferably on several days, not changing your scope and exactly in the same position and distance. You can shoot these 16 rounds at every distance you want, it does not matter for your MOA.
If you shoot these 16 rounds at 125 meters in a circle of 132 mm, your MOA will be 132 : .29 (correction factor) : 125 (meters) = 3,6 MOA.
This knowing, you could shoot a target of about 250 x 250 mm (deer) at
250 : .29 : 3,6 MOA = 239 meters. You could use other shooting positions, they will give another avarage MOA.
Of course you should know your bullet path and corrections for wind and slope.

Nice day,
Jan.

As you point out, a minute of angle = 1.047" at 100 yards 2 X 1.047" @ 200, etc.

But where many hunters go wrong is making the assumption that a rifle that will shoot 1" groups at 100 yards will keep its' bullets in 2" at 200, 3" at 300, etc., etc. This is usually not the case for a number of reasons, and the only way to know what yours will actually do at extended ranges is to shoot groups at those ranges.

whew!! thats a lot "only in terms of correctness."
moa to means 1" at 100 yards.
and 10" at a 1000 yards.
you need a ballistics chart and an accurate velocity to get on targer, oh and a resonable range estimate.
I like to try and keep it as simple as i can.
Dave

Does this mean that I now have to carry a computer to the range to shoot accuratly?