<p>A fast computational method for Hertzian contact theory is proposed. An incremental formula is introduced to calculate the ellipticity of the contact disk when two elastic bodies are in contact. This method, which can determine the ellipticity with good accuracy in a small number of iterations, is reported. This method is also shown to be applicable from the case of a near-perfect circle to the case where the major diameter is sufficiently long compared to the minor diameter.</p>