Ab initio FP-APW+lo calculations were performed for the rare earth orthoferrites RFeO3 with R=La, Nd, Sm, Gd, Dy, Lu using the well-known WIEN2k package. Ferromagnetic and antiferromagnetic alignments between the iron moments were studied using the GGA (PBE) functional for the exchange-correlation energy. Antiferromagnetic structures are energetically favoured in all cases. Except for SmFeO3, all antiferromagnetic configurations are insulators, while the ferromagnetic ones give metals except for LaFeO3 and LuFeO3. Hyperfine fields at the iron sites agree with experiment to within 25%.