At any given cell operating condition, a fuel map can be developed to predict the effect of a fuel containing carbon, hydrogen, oxygen and inert gas atoms on the maximum cell efficiency (MCE) of solid oxide fuel cells (SOFCs). To create a fuel map, a thermodynamic model is developed to obtain the fuels that would yield identical MCE for SOFCs. These fuels make a continuous curve in the ternary coordinate system. A fuel map is established by developing continuous fuel curves for different MCEs at the same operating condition of a cell and representing them in the carbon–hydrogen–oxygen (C–H–O) ternary diagram. The graphical representation of fuel maps can be applied to predict the effect of the fuel composition and fuel processor on the MCE of SOFCs. As a general result, among the fuels that can be directly utilized in SOFCs, at the same temperature and pressure, the one located at the intersection of the H–C axis and the carbon deposition boundary (CDB) curve in the C–H–O ternary diagram provides the highest MCE. For any fuel that can be indirectly utilized in SOFCs, the steam reforming fuel processor always yields a higher MCE than auto-thermal reforming or partial oxidation fuel processors at the same anode inlet fuel temperature.