# Formula for Damage Calculation Based on Distance

I am working on programming a game, and I want the damage that a player takes to be based off of the distance they are from the explosive. Consider it like a grenade. Right on the blast radius (distance of 0) I want it to be the maximum damage. At the maximum distance away where damage is still sustained, I want it to be 0 (or 1, technically, but for simplicity I guess we can say 0.

let d = distance away the explosive is from the player when it lands.

let m = max distance away for a minimum damage

let x = maximum damage possible (when d = 0)

let r = result damage done

Now I think cosine is the perfect function to use here, because cos(d = 0) would be 1. Then I can multiply that by x to get the max damage. I am stuck on how to do the minimum damage though. I need to somehow use cos(pi/2) to get 0 so that when I multiply by x I get 0 damage. But what about all the cases in between?

What would be the formula I'm looking for?

r = .....?

Ok I got what I want.

let result be the resulting damage from the shot

let m be the max distance where damage is done

let d be the distance the shot was away from the targeted player

let x be the maximum damage possible (when d = 0)

 result = sin[((m - d)/m) * (PI/2)] * x;


Works perfect!