The restitution coefficient, used up to now to describe binary inelastic collisions between macroscopic bodies, is interpreted here as a measure of the limiting value of the recoil angle in binary inelastic collisions at microscopic scale. The description of inelastic collisions in terms of this new quantity enables us to dramatically simplify several basic equations for the kinematics of binary inelastic collisions. As an application, the hard sphere cross section when elastic and inelastic processes are correlated is also shown.