The calculation of dielectric constant from the frequency of a cylindrical resonant-mode dielectrometer is affected by the extension of the substrate into the gap beyond the cavity radius. An analysis of this gap effect is used to develop a correction calculation. As verification, we present measurements that cover a range of specimen thickness to cavity diameter ratios up to 0.1875 and dielectric constants from 1 to 154. Also included are measurements of sapphire, considered a standard dielectric. The algorithm developed results in a systematic error in the dielectric constant of less than one percent.