The second stage of evaporation from a bare soil has been described in terms of the desorptivity, a parameter related to the soil's hydraulic properties. Several formulas for desorptivity dependence on the soil water diffusivity have been proposed, but to date have not achieved the accuracy established for the sorptivity (i.e., <1% absolute relative error), the equivalent parameter for infiltration. A new formula is derived in the present study using a weighted residual approach. Comparison with precise numerical solutions for exponential and power law diffusivity functions shows that the new result has an absolute relative error less than 1%.