A circle-ellipse engine includes a stationary circular outer housing having a fixed elliptical inner cam surface, and a separate internal round rotor partitioned into equal segments that are populated by identical movable radial vanes. During rotation, the end of the vanes are positioned a precise, constant distance from the elliptical inner cam surface of the housing. During rotation, a variable height cavity is created representing the difference between the major and minor axes of the elliptical inner cam surface and the rotor face. During each rotation, aspirated air is continuously drawn into combustion chambers, compressed, mixed with fuel, ignited, and exhaust gas products are expelled.