A method was developed to determine the initial peripheral contact angle of sessile drops on solid surfaces from the rate of drop evaporation for the case where theta(i) < 90 degrees. The constant drop contact radius. the initial weight, and the weight decrease with time should be measured at the ambient temperature for this purpose. When water drops are considered, the relative humidity should also be known. The peripheral contact angle so obtained is regarded as the average 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 can be eliminated. The application of this method requires the use of the product of the vapor diffusion coefficient with the vapor pressure at the drop surface temperature. This product can be found experimentally by following the evaporation of fully spherical liquid drops.