The HD molecules are key species for the cooling of pristine gas at temperatures below 100 K. They are also known to be key tracers of H-2 in protoplanetary disks and thus, they can be used as a measure of protoplanetary disks mass. Accurate modeling of the cooling mechanism and of HD abundance in astrophysical media requires a proper modeling for its excitation by both radiative and collisional processes. Here, we report quantum time-independent calculations of collisional rate coefficients for the rotational excitation of HD by H for temperatures ranging from 10 to 1000 K. The reactive and hydrogen exchange channels are taken into account in the scattering calculations. New exact quantum results are compared to previous calculations performed neglecting reactive and exchange channels. We found that for temperatures higher than similar to 300 K, the impact of these channels on the rate coefficients cannot be neglected. Such results suggest that the new HD-H collisional data have to be used for properly modeling HD cooling function and HD abundance in all the astrophysical environments where HD plays a role, e.g. in photon-dominated regions, protoplanetary disks, early Universe chemistry, and primordial star forming regions.