Radiation of sound from planar vibrating panels has been extensively studied for years. In most of these investigations, the total sound power is approximately obtained from the modal radiation efficiencies without considering the contributions from modal cross couplings. The primary reason for doing this is perhaps that the inclusion of cross-coupling terms may result in a tremendous increase in computational load, particularly when a large number of structural modes is involved. In a recent paper [R. D. Snyder and N. Tanaka, J. Acoust. Soc. Am. 97, 1702--1709 (1995)], an approximate estimate of the cross-coupling terms from the modal radiation efficiencies was discussed. It is, however, valid only in a low-frequency range and deteriorates rapidly as frequency increases. In this paper, the effect of modal cross couplings on the total sound power radiated from a simply supported rectangular panel is discussed. A formula is derived for an accurate and efficient calculation of the cross-coupling terms which allows for effortlessly including the effects of the modal cross couplings in the total sound power calculation. In addition, the present formulation is valid in the whole frequency range. Results are presented.