"A falling climber gathers energy as long as he/she gathers speed. When the rope slows his descent, this energy is absorbed, by the deformation of his body, by stretching of the climbing rope, by the friction of the rope sliding over carabiners and perhaps through belayers hands, and by movement of the belayer and perhaps some of the anchors. Rope stretch and slide are desireable as long as the climber doesn't hit anythingand the rope doesn't cut on a sharp edge. Within narrow limits movement of  the belayer is ok, even desireable. Movement of anchors is frightening, if not dangerous." (Michael Loughman) 
  
 Think of how a spring works and you will understand the main priniciple of physics behind a force generated by a fall. Yes there is a formula for calculating these forces,

F = W * K * (Xfall/ Xstop)  + W 

I know it doesn't make much sense like that, however, W is the climbers wieght, K is the spring constant, ranging from 1 to 2, and X fall, is pure falling distance, while Xstop, is the distance the rope was stretched by the climber.