A simple method for predicting the primary normal stress function, 8, from viscosity data is proposed. A relation between 8 and the viscosity function, 7, based on the Goddard-Miller rheological equation of state, is given. An easy-to-use generalized chart for estimating 8 from 7 is presented; in order to use this chart, viscosity data must be available from the zero-shearrate value to the “power law region.” The method was applied to six polymer melts, three polymer solutions, and an aluminum soap solution for which 8 had been measured experimentally. Even though 8 varied by a factor of 103 over the examined range of shear rate, the theory and experiment seldom differed by more than a factor of 2. The generalized chart for 8 was combined with Tanner’s theory to prepare a graph which may be used to estimate jet swell from viscosity data. Comparison with experimental data of jet swell for 4 polymer melts shows good agreement.