In this paper, we develop a three-dimensional conductivity model for the active material in the electrodes of a lead-acid battery. We use the model to investigate the influence that this conductivity has on battery capacity. Previous computer models used for this purpose were two-dimensional. Our three-dimensional model allows electrons to move out of a two-dimensional layer to another layer in order to find conductive pathways to an edge thereby allowing the reaction to occur. By using a number of two-dimensional layers, the actual changes in conductivity taking place in the plates can be more accurately modeled. Because of the many layers of our three-dimensional model, the total number of conductive paths is much greater than the previous two-dimensional models. We extend the two-dimensional models to three-dimensions, and compare the model capacity results with those predicted by the Percolation Theory and Effective Medium Theory. We find that the results of the three-dimensional model closely match the predictions of these theories.