DDDDDDrop the Bass! (Calculating Bullet Drop)

chartA bullet’s path is not a straight line. I know most of you are saying “well, duh”. I think it’s safe to say that we all know a bullet will eventually hit the ground however the details concerning path of a fired bullet is not considered by most outside of the standard “know your target and what’s behind it” safety commandment. You know who does consider the path a bullet follows in great detail? Rifle shooters.

When you’re dealing with only a few yards, the drop of a bullet is negligible. Start traversing distances longer than 100 yards and bullet drop becomes a big deal. When you’re looking at shots near 1 mile, it’s not so much shooting the target as it is lobbing a bullet towards the target. The question is, how much do you lob said bullet? If only there was some way to know exactly or at least estimate how much you’re going to have to aim above the target so you can hopefully get that first shot on target.

The good news is, there is a way. The bad news is it involves some maths. Feel free to run screaming. I won’t blame you. As the great Jimmy Buffett once wrote: “Math Suks”. For those of you who wish to journey with me on a trigonometric adventure of algebraic bliss, buckle up.

First off, you’re going to need a bit of information before you start. The main one is going to be the muzzle velocity of the bullet. How do you figure that? Well, you could go spend some money on an chronograph and spend a great deal of time testing various ammo, recording the velocities and then averaging them and keeping them in a special journal. Personally, that sounds about as exciting to me as a root canal. The easier thing to do is to look up the ballistic information from your ammo’s manufacturer. All the major ones make the information available on their websites.

Then you’re going to need to know the bullet’s weight. This should be displayed prominently on the box/bag/case the ammo came in. It’ll usually say something like “[some number] grains”. Then, once you have all that information, plus a few standard items, you can plug the numbers into the following equation:

Bullet height H = Hi + V*sinΘ*t – ½g*t² 

where

  • V = muzzle velocity
  • Θ = angle above horizontal of the initial velocity
  • Hi = Initial height
  • t = time after firing, seconds
  • g = gravitational acceleration

Now, this is going to give you a range of values that you can then plot out on a graph and…uhm…at least I think that’s what happens. Hang on…

Ok, I don’t have a graphing calculator on me. Uhm. Oh wait, my smartphone might have…nope. Alright, you know what? As much as I love science and neat looking equations and stuff, there’s no real point to doing it this way. There are countless ballistics calculators that do all the grunt work for you and you just have to plug in a couple of easily obtained information. No maths necessary.

One of my favorite online calculators is over at Hornady. There’s also numerous apps available for your phone that can make the calculations as well. So let’s back up a bit and go through this way.

First off, one of the things that confused the heck out of me when I first saw a ballistics chart was how it showed the bullet travelling upwards first then eventually dropping. My brain, having studied physics and such for so long, said “that doesn’t look right”. You see, bullets start to drop the moment they leave the barrel. Gravity: it’s not just a good idea, it’s the law. Now, the velocity of the bullet lessens the effect on gravity but it certainly doesn’t reverse the effect and cause the bullet to rise. What causes that is the difference in height between the barrel and the (properly zeroed) scope. So it’s going to rise up to the point that the scope is zeroed then start to fall as would be expected. Essentially, you’re kind of lobbing the bullet towards your target instead of that laser straight shot we all envision.

So to use one of those calculators, you’re still going to need to know a few things before you start. There is, of course, the bullet grain and velocity. As stated before, this information is readily available online. Depending on the calculator, you might also need to know the “ballistic coefficient”. This is the ability of the round to overcome air resistance and, thanks to differences in bullet shape, is different for each bullet. Again, most manufacturers provide this number on their websites and sometimes the ammo boxes and it will be a number between 0.001 and 1.0. The last number we’ll need is the distance between the scope/sights and the barrel.

Plug those numbers into the calculator and you should be greeted with a table of numbers. Every calculator displays things a bit differently but ultimately, here is the information you’re going to find most valuable. At the range your scope is zeroed to, it’s going to have a 0 for the trajectory. This means that if your scope is zeroed at 100 yards, barring crosswind and such, your point of aim will be the point of impact. There is no bullet drop. Starting at regular intervals after that point, you’re going to see a negative trajectory. For example, say at 200 yards it shows a -4.2 for the trajectory. That means the bullet is going to drop 4.2 inches at that point. Eventually, you’re going to see a number that’s larger than you are tall. Unless you’re shooting off a cliff, that’s where the bullet is going to hit the ground.

Some calculators, like the Hornady calculator I mentioned, even shows you what adjustments you’ll have to make on your scope in order to get that “point of aim/point of impact” goodness at distances. I ran a .308 Win round through it using the ballistics data from the manufacturer. Let’s say I’m shooting at a target at 700 yards. According to the calculator, I would have make a 20.6 MOA adjustment to my scope in order to put the bullet on target. Knowing that number and how many “clicks” on your scope equates to 1 MOA, you can then set the scope accordingly. Handy information to be sure!

Keep in mind, the accuracy of the basic calculations is based off of certain “ideal” constants. Most calculators also have an advanced mode where you can enter in information like wind, altitude, temperature, and barometric pressure to really nail down some near exact numbers. The thing to ultimately remember is that these calculations, even if you enter all the information necessary, are still a “best case scenario”. They give you a starting point. It’s a relatively accurate starting point, mind you, but it’s still just a starting point. You still have to do your part. Nothing beats getting out there and shooting with this information so you can learn how your gun works compared to the calculations. In order words: get out there and practice.


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