A model is presented for breakage of single particles as a function of the impact energy. The model is based on a hazard function for test particles in impact energy in order to takes explicit cognizance of the distribution of feed particles in their resistance to breakage as well as the weakening of particles under repeated impacts. With this approach, it is possible to simulate the size spectra of progeny particles produced in impact grinding as a function of the impact energy employed, interrelate quantitatively the so-called t-family of curves, compute the primary, energy-free breakage distribution function, and predict the optimum level of impact energy for a given size reduction task. Extensive published data of Pauw and Mare on single-particle impact grinding are in agreement with the model.