A preliminary design efficiency-optimization of an axial-flow compressor, using one-dimensional flow theory, is studied in this paper. A model for the optimum design of a compressor stage, assuming a fixed distribution of axial velocities, is presented. The absolute inlet and exit angles of the rotor are taken as design variables. Analytical relations between the isentropic efficiency and the flow coefficient, the work coefficient, the flow angles and the degree of reaction of the compressor stage are obtained. The results are universal and can be extended to the optimal design of a multi-stage compressor. Numerical examples are provided to illustrate the effects of various parameters on the optimal performance of the compressor stage. (c) 2004 Elsevier Ltd. All rights reserved.