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Sediment transport capacity for shallow overland flow was represented as a quadratic function of downslope distance using the assumption of a linear increase in overland flow discharge with downslope distance and an approximation to the Yalin equation for sediment transport capacity. The simplified equation for sediment transport applies to complex topography having uniform soil and management characteristics. The simplified equation accurately approximated the Yalin equation when calibrated using the average of the hydraulic shear stresses at the end of a constant slope reference profile and the end of the actual profile. The simplified equation is useful in deriving closed-form solutions to the governing erosion equations for steady state conditions and reduces the computational time when numerical solutions are required.