This paper analyses the accuracy of count data transferred from a zonal system to an incompatible zone through the areal weighting interpolation method. To treat a variety of situations in a theoretical framework, stochastic models representing areal weighting interpolation are developed. The relationship between the accuracy of estimates and the size of source zones is analytically investigated by use of a proposed model. The results strongly suggested that smaller zones give better estimates on a wide range of zonal systems. The effect of the shape of source zones and the target zone on estimation accuracy is also numerically examined, and is also found to be significant.