The 6-th updated version of the universal modeling method for centrifugal compressor stage calculation is presented, adjusted for modeling 3D impeller performances. The developed mathematical model was identified by the results of model tests and CFD-calculations. The efficiency definition error at a design point was 0,39 %. The efficiency definition error at five flow rate points (except a point of the maximum flow rate) was 0,88 %. The centrifugal compressor stage was optimized by a new mathematical model. As a result of the optimization, stage efficiency increased by 1%. The optimization results have been verified by CFD-calculations in the NUMECA FINE/TURBO program. Design recommendations for 3D impeller design are offered.