## Rifleman basics: sight width and battle sight zero

What is the width of your rifle’s front sight, in minutes of angle? How can you use this bit of information to find a target’s range?

First, a minute of angle (hereafter, MOA) is 1/60th of 1 degree of a circle, or 1/21600th of a circle. You can calculate your sight’s MOA width using this formula^{*}:

(21600 X W)/(2 X pi X R) = MOA

where W is the sight width and R is the sight radius, both in inches. To calculate range, use this formula:

(S X 100)/MOA = R

where S is the target size and MOA you calculated from above.

Why is this useful? Because in order to hit your target you need to know whether it is within your default range, also called your Battle Sight Zero or BSZ. Bullets travel in arcs, not lines, and the Battle Sight Zero is the maximum range at a given sight setting which a center hold sight picture will produce a hit – anything closer than that will be shot, anything beyond that range will not be. To engage targets beyond your BSZ, you need to either adjust your sights or hold over your target a given amount. Naturally, adjusting the sights is more precise.

The BSZ extends if you raise your rear sight and drops if you lower it, so you usually keep the sights set at a given range. If you can calculate the range to target quickly, you can determine if you need to adjust your sights, then take the shot, confident that you will hit the target. On the M14, the BSZ is designed to be 300 yards (275 meters) with 147 grain ball ammo.

Let’s take a real-world example. The front sight width for the nearest AR at hand is 0.067″, and it has a 20″ sight radius. This gives a sight width of 11.5 MOA. Suppose I’m shooting at a 20″ steel target at unknown range. I can tell from my sight picture that the target is half the width of the sight, so about 345-350 yards, which is about the maximum effective range of the rifle. Suppose I wait until the target is the full width of the front sight. This puts the range at about 175 yards, half the distance. The problem scales linearly.

Notice that I say “about” a lot. I’m rounding to take into effect the error in target size estimation. The exact numbers are more precise than most people can accurately determine and shoot, including myself.

The wonderful thing about the AR platform is that there are a zillion different parts that are easy for anyone to swap out, including the front sight. My job now is to find a sight with a width such that a 20 inch target at 250 yards appears the same width as the front sight.

Which would mean the front sight needs to be how wide? Anyone? Anyone?

Bueller?

^{*}Both formulae are taken from Boston’s Gun Bible, chapter 18. If you don’t have this great book, or if you have an old one, click the link and get yourself an updated copy.

Very, very good info, VAR. This is good stuff. I am familiar with using a scope to estimate range, but for some reason, the thought of using the front sight never occurred to me.

Thanks for the tip.

I can’t trackback for some reason, but I’ll link to this…

Oh, and

about.0465.Someone check my math.

AP

0.047 inches?

They talked about this stuff at the last Appleseed shoot I went to. Thanks for adding a little math to explain things.

Pretty cool stuff!

Sight radius shouldn’t be measured from rear to front sight for purposes of this discussion – it should be measured from eye to front sight. A front sight 20 inches away from your eye will have half the MOA of the same sight 10 inches away from your eye, regardless of the sight radius (rear to front) of the rifle, so the R radius in the first equation should be distance from eye to front sight.

In some rifles, one can simply take the actual rifle’s sight radius and add an inch or two for eye relief from the rear sight (M1, M14, AR, and others with a rear aperture close to the eye), but for other rifles (AKs and other ramped rear-sights come to mind), the sight radius should be measured from the eye to the front sight.

Your math is right, Arctic.

AlexSpartan, you bring up a good point, mathematically speaking. The rear sight gets the barrel aligned, but optically it doesn’t affect the problem’s solution significantly unless the sight to sight radius is drastically different.

For example, with an extra three inches on the sight radius in the AR problem above, it only changes the apparent width from 11.5 MOA to 10 MOA. Most people won’t be able to tell the difference. But with an AK style rifle, the difference would be almost twice as large (just guessing on that, as I don’t have an AK handy).

Right. Just something to consider, although I’m not sure this method really needs to be done with the AK, at least in 7.62×39. Past 300 meters or so, the round drops off sharply and becomes rather anemic, having the energy of a handgun round at that distance, besides the fact that AK47s just aren’t accurate past 300-400 meters (but, they are accurate enough – minute of man.) For other ramped rear-sighted rifles where the rear sight is placed far away from the eye, such as Mosin-Nagants, Mausers, etc., sight radius must be measured from the eye for the most accurate range estimation using the front sight.

20 inches at 250 yards is 8 minutes (2.5 inches equals 1 moa at 250 yards).

A 20 inch sight radius on an M16 style AR means an 8 moa gives (20″x2Pi)/(360×60) x 8moa = 0.047. Not trying to be johnny come lately with the math, just always work through a problem myself.

If you have a different sight distance between rear and front sights that makes it a different angular measurement.

However, you can use ANY front sight post as a measuring tool, all you need to do is figure out the width in terms of MOA. So a common width like 0.072 on a 20 inch sight radius would be 0.072(360×60) / (20x2Pi) = 12.37 MOA. That works out to any chest size target wider than the post is less than 200 yards, and any thinner is beyond. Any chest size target between half the blade width and full is between 200 and 400 (roughly), between a quarter and a half between 400 and 600.

So as long as you do the math for the sight post you have it will work fine for ranging.

Good information gentlemen. The formula I use is slightly different. W / (D / 3600) = MOA. W = front sight width, D = distance of your eye from front sight. Answers are roughly the same, I feel this formula is easy to remember. There is an easier way. Place a 1 inch grid target at 10, 25, 50, or 100 yards away. See how many inches are covered by your front sight and multiply that number by 10 for 10 yards, 4 for 25 yards, 2 for 50 yards, and obviously at 100 yards no math needed. For example: at 25 yards, your sight spans 2 inches – 8 MOA; at 50 yards your sight spans 4.5 inches – 9 MOA; at 100 yards your sight spans 11 inches – 11 MOA. This is the best way, most of us are estimating how far our eye is from the front sight and we can’t be sure of the front sight width. I hope this helps.