In this paper, a simple formulation for current application for the axial compressive strength determination of hot rolled circular hollow steel sections, with sinusoidal form initial crookedness and values of the central deflection between 1/2,000 and 1/500 of the length, is proposed. In order to validate the analysis, several numerical models were generated by finite element method, considering members with 1/1,000 of the length initial crookedness, and the results were compared with the values obtained by EN 1993-1-1:2005. Using the methodology of modeling validated, many other members with initial crookedness of 1/2,000, 1/1,500, 1/750 e 1/500 of the length were analyzed, allowing to obtain the values of the reduction factor, , as a function of the reduced slenderness parameter, ̅. The values of of members with initial crookedness between these two limits were evaluated by polynomial interpolation.