A combination of fundamental measure density functional theory and Monte Carlo computer simulation is used to determine the orientation-resolved interfacial tension and stiffness for the equilibrium hard-sphere crystal-fluid interface. Microscopic density functional theory is in quantitative agreement with simulations and predicts a tension of with a small anisotropy of about and stiffnesses with, e.g., for the (001) orientation and for the (111) orientation. Here is denoting the thermal energy and the hard-sphere diameter. We compare our results with existing experimental findings.