**Carteach0** put up a post where he asked the question, “How far (in thousandths of an inch) must the muzzle deflect to change the point of impact 1moa at 100 yards?” I answered in text in his comments, but it seemed like such an interesting question I wanted to explore it here.

He was considering the full length of the rifle, but I think you could consider the problem from the rear sight forward, as it would be the same whether there is a stock mounted on the rifle or not. On most rifles the rear sight sits over the chamber, the front sight is close to the muzzle. To eliminate all other variables, assume no wind and that perfect ammo is being used, so that if the rifle doesn’t move, every round would impact the same hole. With that, here goes my thoughts on the topic.

Imagine a line that begins at the center of the rear sight, passes over the tip of the front sight, and impacts the target in the center. How much does the front sight move to move the impact point one inch? In my calculation, I assumed my rifle had a sight radius of 16 inches. I used **this on-line calculator** to solve the angles. Essentially you are solving for a long skinny triangle. Two sides are 3600 inches, the third side is one inch. That makes the small angle 0.0159 degrees. A movement of 0.0159 degrees moves the bullet impact 1 inch. If your sight radius is 16 inches, that means your front sight has to move 0.0044 inches to move the bullet impact 1 inch.

It puts the whole “sight picture / sight alignment” issue in a new light.

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Man! And people give me grief for being a math nerd for trying to figure out how high a bullet will travel when fired straight up.

How high a bullet would go is a much harder problem, as are velocity, elevation and arc calculations with target shooting. It would depend on the initial velocity and the ballistic coefficient of the bullet. Since it is continuously slowing down due to gravity and it is possible to know the initial velocity, the additional slowing caused by the air is the part of the equation that makes this tricky.

There are calculation programs that take a lot of the mystery out. If you zero a rifle at 300 yards, how does the bullet travel before dropping back down to the target? It’s really the same problem; initial velocity, ballistic coefficient, and gravity, with velocity changing over time. In this case, gravity isn’t slowing the bullet as much as it is causing it to drop, the amount of drop over a certain distance is related to the (continuously diminishing) velocity.