A systematic study of the redox properties of six parent quinones has been carried out using quantum chemistry methods. The reduction of the ortho (o-) and para (p-) isomers of benzoquinone and naphthoquinone, 9,10- anthraquinone and 9,10-phenantrenequinone to the corresponding hydroquinones and semiquinone radicals was investigated at the B3LYP/6-311+G(d,p) level of theory. Thermodynamic functions in the gas-phase were calculated for all the reduction reactions. Gibbs energies of reaction and standard potentials in water for the reductions were determined using the IEF-PCM model and an empirical correction to the calculations based on the limited thermodynamic data available for the quinones. Potentials were calculated both for the direct reduction to the quinols, and for the two-step reduction via the neutral semiquinones. The calculated potentials for the 2e-, 2H+ reductions were found in good agreement with experiment and to display the same trends as gas-phase enthalpies and energies, i.e., to correlate with the number of C=C double bonds, as well as on the relative position of the C=O groups. The small deviations between experiment and theoretically predicted standard potentials were found to originate from basis set incompleteness and the shortcomings in the B3LYP exchange correlation functional rather than the models used for the thermochemical calculations or description of solvation. Accurate theoretical shifts in standard potentials for the p-/o- pairs of Q <--> HQ and HQ <--> H2Q reactions are presented and compared to experiment. Reliable standard potentials and shifts for the neutral semiquinones are predicted for the first time.