This report deals with material properties which determine dielectric strength rather than phenomena that occur during breakdown. We propose that the determining factors are the same for liquids and polymers. We report dielectric strengths calculated from measured breakdown potentials and sample thicknesses for liquids, ionic solutions, and epoxy polymers doped with ionizable materials. The breakdown field (in liquids and polymers) is hypothesized to be that which generates some critical current density value in the dielectric. The reasons for this value being critical and characteristic of the material are unknown; however, the ionic current density that the measured breakdown field produces can be calculated from the Onsager theory of high-field electrolytic conduction, and this ionic current density is assumed to be the critical threshold quantity involved. Because of field effects on the dissociative ionization and conductivity of electrolytes in organic systems, the breakdown field varies with concentration and solute species, but the ionic current density associated with the breakdown field is essentially constant for a wide range of species and molar concentrations in a given solvent.