The crystal structure of cefradine dihydrate, C16H19N3O4S·2H2O, is considered in the pharmaceutical sciences to be the epitome of an isolated-site hydrate. The structure from single-crystal X-ray data was described in 1976, but atomic coordinates were not published. The atomic coordinates are determined here by combining the information available from the published single-crystal data with a dispersion-corrected density functional theory (DFT-D) method that has been validated to reproduce molecular crystal structures very accurately. Additional proof for the correctness of the structure comes from comparison with cefaclor dihydrate, C15H14ClN3O4S·2H2O, which is isomorphous and for which more complete single-crystal data are available. H-atom positions have not previously been published for either compound. The DFT-D calculations confirm that both cefradine and cefaclor are present in the zwitterionic form in the two dihydrate structures. A potential ambiguity concerning the orientation of the cyclohexadienyl ring in cefradine dihydrate is also clarified, and on the basis of the calculated energies it is shown that disorder should not be expected at room temperature. The DFT-D methods can be applied to recover full structural data in cases where only partial information is available, and where it may not be possible or desirable to obtain new experimental data.