© The Institution of Engineering and Technology 2017.The modelling of the effective dielectric constant of a planar spoof surface plasmon polariton waveguide for X-band frequencies is presented. The waveguide has a single conductor structure that is corrugated on both sides. A methodology to extract the effective dielectric constant of waveguides with complex patterns and a novel closedform formula based on complex analysis of the structure and empirical methods are suggested. The suggested formula is a function of the corrugation depth, aperture, periodicity, thickness of the substrate material and permittivity. The worst case error between the formula and measurement result is 8.4%, which is much lower than the previously reported coplanar stripline formulation approach having an error of 14.5%.