Radiative properties of particulate matter must be calculated accurately and in an expeditious way, in order to ensure both correct radiative transfer predictions and computational efficiency, requiring practicable computation time expenditure. The influence of large particles in radiative transfer is of major importance, placing an increased emphasis on the asymptotic solutions applicable to those particles. For large particles the scattering is: highly anisotropic, causing the asymmetry factor to assume a very significant role. In the present work, an efficient method for the calculation of the asymptotic limits of both scattering: efficiency and asymmetry factor for spherical particles is presented. The results are presented in simple and closed form expressions that exhibit a high degree of accuracy. This allow's fur a simultaneously accurate and expeditious evaluation of the referred parameters for large particles.