The concepts of fluid dynamic and thermodynamic similarity are introduced. The key nondimensional parameters of relevance to radial compressors, such as flow coefficient, work coefficient, pressure coefficient and the blade tip-speed Mach number are explained. The appropriate nondimensional parameters allow the preliminary design of a new machine to be based on features of an existing machine, even one designed for a different size, a different fluid, other flow conditions or rotational speed. Its performance can also be estimated from that of a similar machine, even though it may be larger or smaller. The principle of similarity and the associated nondimensional parameters provide an invaluable aid to the design and testing of all turbomachinery and to the proper understanding of their performance maps and stage characteristics. A good grasp of these is an excellent basis for rationalising compressor performance in different applications. Deviations from similarity in real machines are considered leading to performance corrections for changes in Reynolds number and isentropic exponent.