FPS is a unit of speed (feet per second) which, in airsoft, usually refers to the speed of a BB as it leaves the barrel of an airsoft gun.
A Joule is a unit of kinetic energy. The faster and heavier an object is, the more kinetic energy it has. For example, a BB might leave the barrel with 0.3J of energy.
Kinetic Energy is calculated as Mass multiplied by Velocity squared and then halved. Algebraically this is shown as
KE = 0.5 x M x V²
However, this is assuming that you are using standard units, which would be kilograms and metres-per-second. As we are using grams and feet-per-second we must modify the formula.
KE = 0.5 x (M / 1000) x (V / 3.2808399)²
So, a 0.20g BB shot with a speed of 300FPS has a kinetic energy of 0.836127 Joules.
Kinetic Energy Calculator