Reversible potentials, U-o, have been calculated based on reaction energies, E, for the intermediate steps in the outer-sphere oxygen reduction reaction to water. The working formula is U-o = (-E-r eV(-1) + c) V, where U-o is the reversible potential and the reference energy of the electron is -4.6 eV on the physical (vacuum) or 0 V on the hydrogen scale. Results using a 6-31G** basis in the B3LYP hybrid density functional theory are shown to be comparable to ab initio MP2 results obtained previously for acid solution with c = 0.49 for the former and 0.50 for the latter. Both methods are shown to work for basic solution but, unlike in acid, the c values are different, 0.58 for B3LYP and 0.76 for MP2, reflecting differences in the two computational methods in treating anions.