Aims. Inelastic processes in low-energy Ca + H and Ca+ + H- collisions are treated for the states from the ground state up to the ionic state with the aim to provide rate coeffcients needed for non-LTE modeling of Ca in cool stellar atmospheres. Methods. The electronic molecular structure was determined using a recently proposed model approach that is based on an asymptotic method. Nonadiabatic nuclear dynamics were treated by means of multichannel formulas, based on the Landau-Zener model for nonadiabatic transition probabilities. Results. The cross sections and rate coeffcients for inelastic processes in Ca + H and Ca+ + H- collisions were calculated for all transitions between 17 low-lying covalent states plus the ionic state. It is shown that the highest rate coeffcient values correspond to the excitation, de-excitation, ion-pair formation, and mutual neutralization processes involving the Ca(4s5s 1;3S) and the ionic Ca+ + H- states. The next group with the second highest rate coeffcients includes the processes involving the Ca(4s5p 1;3P), Ca(4s4d 1;3D), and Ca(4s4p 1P) states. The processes from these two groups are likely to be important for non-LTE modeling.