This paper discusses the accuracy of spatial data estimated by areal interpolation, a process of transferring data from one zonal system to another. A stochastic model is proposed which represents areal interpolations in diverse geographic situations. The model is used to examine the relationship between estimation accuracy and the spatial distribution of estimation error from a theoretical viewpoint. The analysis shows that the uniformity in error distribution improves the accuracy of areal interpolation. Four areal interpolation methods are then assessed through numerical examinations. From this it is found that the accuracy of simple interpolation methods heavily depends on the appropriateness of their hypothetical distributions, whereas the accuracy of intelligent methods depends on the fitness of the range of supplementary data for that of true distribution.