Rate coefficients for inelastic Na+H collisions are calculated for all transitions between the ten levels up to and including the ionic state (ion-pair production), namely Na(3s,3p,4s,3d,4p,5s,4d,4f,5p)+H(1s) and Na++H-. The calculations are based on recent full quantum scattering cross-section calculations. The data are needed for non-LTE applications in cool astrophysical environments, especially cool stellar atmospheres, and are presented for a temperature range of 500-8000 K. From consideration of the sensitivity of the cross-sections to input quantum chemical data and the results of different methods for the scattering calculations, a measure of the possible uncertainties in the rate coefficients is estimated.