A new theory is given which relates excess rainfall to runoff for overland flow on a plane. The theory assumes that rate of change of water flux with distance down the plane is constant at any time, but its variation with time is such that runoff from the plane is exact. It follows that mass of water is conserved for the entire runoff event, but not exactly at all times within the event. The magnitude of the error in the solution due to this approximation is investigated by comparison with the more complex exact theory. If runoff from the plane is measured, the theory allows simple direct estimation of excess rainfall as a function of time. Alternatively, if rainfall and infiltration rates are known then runoff can be calculated. This approximate theory and the exact theory are also compared by using them to estimate infiltration rate into a small planar catchment from measured rates of rainfall and runoff. The accuracy and great simplicity of the approximate theory makes it useful in practice.