Abstract The approximate kinematic overland flow equation for parallel-sided planar surfaces proposed by Rose et al. has been generalized to a form that includes a water surface profile shape factor. Rose's equation assumes that transient water surface profiles can be approximated by the shape of the steady-state water surface profile using the steady-state shape factor (= 0.625). As a further development of his approach shape factors have been derived for rectangular, triangular and parabolic profiles. The rectangular profile approximates the actual profile during the early part of the overland flow hydrograph rise, while the steady-state profile approximates the profile near the hydrograph peak (or steady-state runoff). The water surface profile approaches a triangular or parabolic shape during the latter stages of the hydrograph recession. Use of the appropriate shape factor during the relevant portion of the hydrograph rise and fall allows improved predictions with Rose's approximate theory. Rose's theory has also been generalized for application to converging and diverging planar surfaces. This complete theory incorporates a brink depth convergence factor and a water surface profile factor that allows the predictions from an equivalent parallel-sided planar surface to be corrected to account for the effects of convergence or divergence on the overland flow hydrograph. These factors can be calculated directly from the physical characteristics of the overland flow plane.