A simple analysis technique to extract the complex dispersion characteristics of thin periodic 2-D Fabry-Pérot leaky wave antennas (LWA) is presented. The analysis is based on a two-stage process that dispenses with the need for root-finding in the complex plane. Firstly, full-wave MoM together with reciprocity is employed for the estimation of the LWA radiation patterns at different frequencies from which the phase constant is calculated. Employing array theory the phase constant is subsequently used to estimate the radiation patterns for different values of the leakage rate. The correct value for the leakage rate is identified by matching the corresponding radiation pattern to that obtained using the full-wave method. To demonstrate this technique, we present results for half-wavelength and sub-wavelength profile LWAs. Unlike the transverse equivalent network method, the proposed technique maintains its accuracy even for antennas with low profile.