This article presents a simple and unique method for predicting the friction factor for the fully developed, laminar flow of power-law fluids in ducts with a rectangular cross-section by means of an engineering calculation for rapid equipment design. The relationship between friction factor f and the Reynolds number defined by Metzner-Reed (Re-MR) for a rectangular cross-section was investigated and rearranged with very good engineering accuracy using the results of very simple correlations based on the application of the well-known and long-established coefficient for Newtonian fluid flow. The investigated value of the flow index was up to 2, and the aspect ratio ranged from 0 to 1, with calculation error not higher than 3.5%. The proposed method was compared with conventional methods from the literature, and was validated by means of numerical computations, and also with experimental data from the literature. The product of friction factor and Re-MR is a linear function of geometrical parameter C and flow behavior index n and also the proposed method predicts the friction factor as accurately as conventional and traditional methods.