A novel approach to calculate the performance map of a centrifugal compressor stage is presented. At the design point four nondimensional parameters (the flow coefficient φ, the work coefficient λ, the tip-speed Mach number M, and the efficiency η) characterize the performance. In the new method the performance of the whole map is also based on these four parameters through physically based algebraic equations which require little prior knowledge of the detailed geometry. The variable empirical coefficients in the parameterized equations can be calibrated to match the performance maps of a wide range of stage types, including turbocharger and process compressor impellers with vaned and vaneless diffusers. The examples provided show that the efficiency and the pressure ratio performance maps of turbochargers with vaneless diffusers can be predicted to within ±2% in this way. More uncertainty is present in the prediction of the surge line, as this is very variable from stage to stage. During the preliminary design the method provides a useful reference performance map based on earlier experience for comparison with objectives at different speeds and flows.