The hard-sphere transition predicted by computer experiments is theoretically studied with the aid of the expandable-lattice theory of liquid-solid transitions developed in previous two papers. The freezing and melting points are thus given in the mean energy approximation by P/kTρc = 2.3577, ρf/ρc = 0.6819, ρm/ρc = 0.9053, where ρc is the closest-packed density √2/r03, r0 being the core diameter.