A network of rain gages provides information about rainfall at only a limited number of points within a region: some procedure must then be adopted to estimate the rainfall for other chosen points and areas within the region. Methods are presented here whereby the accuracy of rainfall estimates can be quantified so that a comparison with the requirements of users of rainfall data can be made. The calculation of the accuracy of optimal estimates based on any number and configuration of gages is described. The results can be applied to the redesign of existing networks of gages by mapping the root mean square error of point interpolation, allowing the identification of those areas where new gage sites are most needed to meet some specified criterion of accuracy. Formulae are also presented which allow the accuracy of an optimal estimate of areal rainfall to be calculated for any shape of area and any configuration of gages.