A method to evaluate the polydispersed extinction efficiency rapidly is presented. The method can be used for any shape for which a monodisperse code or expression is known and any polydispersion for which a second moment inverse can be computed. Integration can be performed over any interval of the distribution function. Additionally, and if required, arbitrary accuracy can be obtained. This approach is applied to spheres and randomly oriented spheroids with nth-order log-normal and modified gamma particle distributions.