The aim of this work was to establish a mathematical model based on Tafel equation to quantitatively relate the maximum volumetric power (P-V,P-max) as well as the internal resistance (R-int) in a microbial fuel cell (MFC) with the specific surface area of the graphite anodes (A'(S)), and either their conductance C or electrolytic conductivity sigma of the material. The anodic chambers of the cells were packed with different anodic materials (graphite rods (GR), triangles of graphite (GT) and graphite flakes (GF), in order of increasing A'(S)). The R-int decreased and the P-V,P-max increased for cells equipped with GR, GT and GF anodes. There was a correspondence of either the decrease of R-int or the increase of P-V,P-max with the increase of the log of A'(S) of the graphite anodic materials. The fitting of the models was characterized in terms of determination coefficient R-2, the p value, and the Ranking. The best fitting model for P-V,P-max was P-V,P-max = a'(0) + a'(1) x log A'(S); with R-2 = 0.8872, p = 0.005, and Ranking = 100%. The inclusion of C as second fitting variable slightly improved the R-2; however, the term with C did not have a theoretical origin. For Ria the best fitting model was R-int = b'(0) +b'(1) x log A'(S). The model of P-V,P-max was validated with independent results from literature with satisfactory fitting results (R-2 = 0.8704; p = 0.0022; Ranking = 100%). Copyright (c) 2015, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.