The validity of the numerical results obtained in Part 1 is examined via some typical examples. The results indicate that the numerical results can be applied to the particle size distribution transformation within the practically tolerated error. On this basis an equation was derived to calculate analytically the mean diameters of a powder. The verification and application of this equation are demonstrated by a typical example. It is shown that the Hatch-Choate relationship used in the transformation of particle size distributions expressed by the log-normal distribution is only a special (extreme) case of the present numerical results. Although the numerical simulation cannot always provide a consistent transformation, this approach can greatly facilitate the application of the S(B) distribution function in powder technology by simplifying the transformation between particle size distributions and the calculation of mean diameters.