An analytic semi-empirical approximation to the extinction efficiency Q(ext) for randomly oriented spheroids that is based on an extension of the anomalous diffraction formula is given and compared with the extended boundary condition method or T-matrix method. With this formula Q(ext) can be evaluated over 10(4) times faster than by previous methods. This approximation has been verified for complex refractive indices m = n - ik, where 1 ≤ n ≤ ∞ and 0 ≤k ≤ ∞, and aspect ratios from 0.2-5. We believe that the approximation is uniformly valid over all size parameters and aspect ratios. It has the correct Rayleigh, refractive-index, and large-particle asymptotic behaviors. The accuracy and limitations of this formula are discussed.