Abstract This paper improves previously published models by the authors for a single solid oxide fuel cell (SOFC), and introduces a procedure to optimize its external configuration and operating conditions, so that the net power is maximized. The previous models are hereby improved to include: i) a constant offset overpotential in total potential drop; ii) heat generation associated with all the potential losses; iii) temperature-dependent thermo-physical properties of fuel and air, and iv) pumping power to maximize fuel cell performance. The thermodynamic model is derived from physical laws (e.g., the first law of thermodynamics, Fick's law, Fourier's law) to obtain the temperature and pressure spatial distribution in the SOFC. The electrochemical model is validated by direct comparison with experimental data from the Pacific Northwest National Laboratory (PNNL), and allows for the computation of the SOFC voltage, current, and power output. Based on the simulation results, the structural design, the active three phase boundaries regions at the electrodes and the fuel utilization factor, and their impact on the SOFC performance are discussed. Subjected to fixed total volume, the optimal geometric and operating parameters are pursued so that the net power of the SOFC is maximized through a 4-way-optimization procedure. The method used is general and the numerically obtained maxima are sharp, taking into account that up to a 631% single SOFC performance variation was observed within the studied parameters' range. The fixed volume constraint was then relaxed, and the effect of total volume variation on performance was investigated, delivering the general optimal parameters for the 4-way maximized SOFC net power output within the studied total dimensionless fuel cell volume range. These findings show the potential to use the model as a tool for future SOFC design, simulation and optimization.