Inelastic cross sections and rate coefficients in Ca + H and Ca+ + H− collisions for all transitions between the 17 lowest covalent states plus one ionic molecular state are calculated based on the most recent ab initio adiabatic potentials for the 11 lowest molecular states, as well as on the model asymptotic potentials for higher-lying states, including the ground ionic molecular state. Nuclear dynamics is treated by the probability-current method and the multichannel formulas for the collision energy range 0.01–100 eV. The rates are computed for mutual neutralization, ion-pair formation, and (de-)excitation processes for the temperature range T=1000–10,000 K. The calculations single out the partial processes with large and moderate rate coefficients. The largest rates correspond to the mutual neutralization into the Ca(4s5s 3S), Ca(4s5p 3P), Ca(4s5s 1S), and Ca(4s5p 1P) final states; at T=6000 K the largest value is 5.50×10−8cm3 s−1 for Ca(4s5s 3S). Among the (de-)excitation processes, the largest rate coefficient corresponds to the Ca(4s5s 1S) Ca(4s5s 3S) transition; at T=6000 K, the largest rate has the value of 8.46×10−9cm3 s−1.