Volume calculations based on a digital elevation model (DEM) are widely used instead of traditional handmade cross-sectioning methods on contour maps. Cross sections can be derived from a DEM performed in a computer, when the cross-sectioning method is preferred. Although many studies have been performed on the accuracy of DEM, accuracy of volume calculation based on a DEM is still unfamiliar to users. Therefore, in the concept of this study, accuracies of the DEM based volume calculations are tested on four selected theoretical surfaces for various data patterns. Volume calculations with triangular prisms, rectangular prisms, and cross sections are applied. Rational true errors are derived for the DEM based volume calculations.