Abstract This paper presents a transformation between compressible and incompressible two-dimensional and axisymmetric boundary-layer flows. The transformation may be used to predict local skin-friction coefficients for laminar and for turbulent flows, in zero as well as in favorable pressure gradient, and also for conditions with surface heat transfer through the use of the reference temperature. Application is limited, in the present version, to Prandtl number in the order of unity. The final form of the transformation involves a factor to be determined by comparison with experiment, and in the present case this is done for a particular range of data on air. Accordingly, quantitative application of the results will have greatest assurance for air over this same range, pending further data on other fields and ranges of flow conditions. Sample computations illustrate the application of the transformation to (1) turbulent flow of air along an insulated flat plate with free stream Mach number of 3.7, and (2) laminar boundary layer of air along a sphere with free stream Mach number of 2.855. These cases demonstrate good agreement between predicted and measured skin-friction coefficients as affected by aerodynamic heating.