A universal modeling method, developed at the Peter the Great St. Petersburg Polytechnic University and successfully used in design practice, uses a flow rate coefficient, a loading factor and compressibility criteria as gas-dynamic design parameters. The main design constraint for the impeller is the hub ratio. The algorithm previously used for initial design of impellers is based on generalizing the design experience and separate calculated experiments. In some cases, significant correction of the dimensions and shape of the impeller is required in subsequent stages of design. To approximate the initial design to the final design, we performed optimal design of 124 radial and axial-radial impellers with flow rate coefficients of 0.015 to 0.15, loading factors of 0.40 to 0.70, hub ratios of 0.25 to 0.40. Geometric parameters are approximated by algebraic formulae and supplemented with recommendations to apply classic formulae of the impeller’s inlet dimensions, which together form the proposed method of initial design.