A new method for analyzing uniaxial torque data has been developed. Based upon the well-known 45-degrees method, the present technique analyzes data taken at any angle and provides for determination of K2 in addition to M and K1. Constant angle torque data is fit to a uniaxial model via a least squares method at many angles, wherein each angle data set provides an independent measure of M, K1 and K2. Mean values and uncertainties are obtained by combining results from all angles. The procedure is tested on 1) simulated torque data generated from known M, K1 and K2 values with subsequent introduction of normally distributed "noise"; and 2) a Fe/Cu multilayer sample. Confidence intervals associated with the extracted values are also presented.