Based on the concept of the converter fed machine (CFM), an optimal machine design can be considered as the best match of the machine topology, the power electronic converter and the performance specification. To compare power production potential of axial flux machines with various topologies, different waveforms of back emf and current, general purpose sizing and power density equations for such machines are needed. In this paper, a general approach is presented to develop and to interpret these equations. Sample applications of the sizing and power density equations are utilized to compare the axial flux toroidal permanent magnet (AFTPM) machine and the axial flux two-stator permanent magnet (AF2SPM) machine.