The power optimality performance of a piezoelectric energy harvester connected to a resistive load is studied. An analytical solution for the unimorph piezoelectric energy harvester based on the piezoelectric constitutive equations and the fundamental mechanics of materials relations is adapted to estimate the optimal power and vibration amplitude. The accuracy of the output performance in the analytical solution is identified from a coupled piezoelectric-circuit finite element analysis (FEA). The results from FEA are in agreement with numerical calculation results. Furthermore, the impact of structural damping and the electromechanical coupling on the optimal energy harvesting performance is studied. The results indicate that the electricity power output has two maximum values at lower damping ratio, and the power output exhibits only one maximum value at higher damping ratio. It is also shown that the piezoelectric materials with higher effective electromechanical coupling coefficient (EMCC) don't necessarily yield more power output.