Part II MOA Scopes:

First let’s be sure we know what ‘minute’ means in reference to scope specs. The MOA (Minute Of Angle) spec is an angular specification that is essentially independent of range. You might imagine a gun barrel perfectly horizontal and we fire a bullet at a target 100 yards away. Well, the bullet would hit really low. So to raise the POI, we would want to angle the muzzle of the barrel upward. We would use an angular measurement to describe how much we ‘tilted’ or angled the barrel. E.g. we could tilt the barrel upward by 1 degree and shoot again and see how that affects the POI. The problem is one degree is far too coarse of an adjustment to set the POI precisely. So we could change the tilt by tenths of a degree. But we would find that’s still too coarse to set the POI precisely. We need an even smaller change in angle to get the precision we need – enter the minute. A minute is one sixtieth of a degree and even that’s too coarse, but it is the basis of the MOA specification. So if we say a gun will shoot 1 MOA, it means that the gun can place hits within a cone that’s one-sixtieth of one degree. If a gun could shoot 1/2 MOA, it would be twice as accurate as the 1 MOA gun. Notice in none of this is anything mentioned about range. The spec is complete without a range dimension. Notice also how this contrasts with the 1/4” per click at 100 yards spec, where the 100 yards is an integral part of the spec.

You may have heard that one MOA is 1” at 100 yards. Well, that’s close, but not quite. Changing the angle by one minute, would change the POI at 100 yards by 1.047”, not the 1” we hear so often, it’s really closer to 1-1/16” than 1”. But 1” may be close enough and if it is we can treat the sighting in of an MOA scope as if it was 1/4” at 100 yards and use the very same method to zero the scope that we did for a true 1/4” per click at 100 yards scope IF the clicks on the turret were 1/4 MOAs. That would still introduce a 4.7% error however.

So, if we change the turret by one click on a MOA scope, how much does that change the POI? That depends on how the particular scope is set up and the range. For example, a Vortex Viper HS scope is a MOA type scope with 1/4 MOA per click. A Vortex Razor scope is also a MOA scope, but it has a 1/2 MOA per click. But the question stands, how much does one click change the POI? Let’s use the Razor in an example.

We know one click equals 1/2 MOA. But how much that changes the POI, depends on how far away the target is. Let’s say the target is 100 yards away. At 100 yards one click will change the POI by 1.047”. How do we know that? Well, trigonometry is one way: POI = Range (inches) X Tan(1°/120). Or, we simply know, or accept that 1 MOA at 100 yards yields a value of 1.047”. So one-half MOA would change the POI by 0.523”. As you can see that’s a pretty coarse adjustment. A scope with 1/4 MOA per click would be close to the same as a 1/4” per click at 100 yards scope. In fact 1/4 MOA at 100 yards would give a change in POI of 0.262”

Using the 1.047” at 100 yards we can calculate the clicks required to move the POI by the necessary amount to zero the scope.

Other than treating a MOA scope like a 1/4” at 100 yards scope, there are two ways to determine the number of clicks required, one is to use a table – if you have one, the other way is to calculate the change per click. Here’s a formula to use for any range and any MOA.

POI change per click = MOA change per click x 1.047 inches * range (yards) / 100 yards

Where MOA change is the change per click, e.g. 1/4 MOA, 1/2 MOA and range is the distance to the target in yards.

The 1.047 inches is the change in POI for 1 MOA change at 100 yards.

So let’s plug in some numbers. Let’s use a range of 175 yards and a 1/2 MOA per click:

POI change per click = 0.5 MOA x 1.047 * 175 yards /100

POI change per click = 0.916”

I actually used a completely different method - .5 MOA x 175yds * 3 ft/yd *12 in/ft * tan(1/2 MOA) and got exactly the same answer - just a corroborative calculation.

Well that doesn’t sound very easy, especially in the field. But that’s what it takes – I know of no shortcuts other than calculating or table lookup. Bear in mind, a rangefinder won’t help at this stage; remember we already know the range - 175 yards.

Ok, but let’s do a click calculation. Let’s use the very same measurements I used for the 50 yard bolt rifle in the 1/4” at 100 yards example:

The range is 50 yards and the group was low by 2-1/2” and wide by 2”. So now, at 50 yards, with a 1/4 MOA scope, I have to calculate clicks required to bring the scope to zero. So first, as before, I have to calculate how much 1 click (1/4 MOA) moves the POI at 50 yards, so we use the handy formula from above.

POI change per click = MOA change per click x 1.047 * range (yards) / 100 (yards)

POI change per click = 1/4 * 1.047 * 50 yards / 100 yards

POI change per click = 0.131”

Notice the answer, 0.131”, is very close to the 1/8” (0.125”) per click we got with the previous bolt rifle example using the 1/4” per click at 100 yards type scope.

So now, knowing the change in POI per click - at 50 yards, we can calculate the number of clicks needed to zero the scope by dividing the inches we need to move by the amount per click. Here's the calculation for the vertical:

Number of clicks = 2-1/2” / 0.131” = 19.1 clicks.

Again, notice how close 19.1 clicks is to 20 clicks we got in the previous bolt rifle example using the 1/4” per click at 100 yards type scope. The difference is that the click in the 1/4” (0.25”) per click is slightly smaller than 1/4 MOA (0.262”) for the same range.

Next, we’ll look at the MIL system.