A method was developed to determine the initial peripheral contact angle of sessile drops on solid surfaces from the rate of drop evaporation by using the published precise data of Rowan et al. The constant drop contact radius throughout this stage of evaporation, the initial weight (or volume), the weight decrease by time, and the experiment temperature should be measured for this purpose. When water drops are considered, the relative humidity should also be known. The drop profile data are not required in the calculations. The peripheral contact angle so obtained may be regarded as the mean of all the various contact angles existing along the circumference of the drop. Thus, each determination yields an average result not unduly influenced by irregularities at a given point on the surface. In addition, the error in personal judgment involved in drawing the tangent to the curved drop profile at the point of contact. is eliminated. The application of this method requires the use of the product of the vapor diffusion coefficient of the evaporating liquid with the vapor pressure at the drop surface which can be found directly by experiment by following the evaporation of fully spherical liquid drops. The other alternative method is the measurement of the drop surface temperature in order to find Delta p(v) and then to estimate the product D Delta p(v).