Predicting the accuracy of GPS is of great interest to researchers. Today, empirical formulas that predict the GPS accuracy from local to regional scales are available for the scientific and surveying communities. Hence, it is a useful survey planning tool for field works for various geodetic applications. Research results in this area indicate that the GPS accuracy is a function of the length of the observing session over local to medium scales (i.e. between 10 and 300 km) whereas the accuracy is a function of both the session length and inter-station distance over regional scales (i.e. between 300 and 3000 km). In this study, we introduce a new constraint, i.e. the inter-station height difference that needs to be taken into account in GPS positioning accuracy studies. We use previously published least squares (LS) functional models and model the GPS accuracy taking inter-station height differences into account. Our results indicate that the accuracy of GPS is degraded in the presence of large height differences as the duration of the observing session gets shorter. This needs to be taken into account in accuracy computations. The prediction of the vertical positioning accuracy has been improved by about 20 % for 6 h sessions by combining the standard deviations predicted from regional GPS accuracy studies with the ones derived here.