Want to know how it works?
Multiply the product of the weight of the pellet (in grains) times the square of the velocity and divide that number by 450240. That last number is a constant created by multiplying two times the acceleration of gravity by 7,000 - the number of grains in a pound. The number I am using for the acceleration of gravity is 32.16 f.p.s. That number is obsolete, but the number that replaces it, 32.174 feet per second (f.p.s.) below the 50th latitude, does not change the energy calculation significantly.
Here's how the formula works. Suppose we shoot an 8-grain pellet at 800 (f.p.s.). The energy would be 8 times the square of the number 800, which is 640,000. So, it's 8 times 640,000 - which is 5,120,000. Now, divide that number by the constant 450240 and you get 11.371712. There may be even more digits out to the right of the decimal point, but that's where my small calculator stops, so that's my answer. I'm going to round off the number to two decimal places anyway, so I write it down as 11.37 foot-pounds.
The problem above looks like this when written in mathematical notation: