The terrigeneous sediment budget of passive margin basins records variations in continental relief triggered by either deformation or climate. Consequently, it becomes a major challenge to determine sediment accumulation histories in a large number of basins found in various geodynamic contexts. In this study, we developed a GIS-based method to determine the sediment budget at the scale of a whole basin (from the upstream continental onlap to the most distal deepest marine deposits) and the associated uncertainties. The volume of sediments preserved in the basin for each time interval was estimated by interpolation between cross-sections and then corrected from in situ production and porosity to obtain terrigeneous solid volumes. This approach was validated by applying it to Namibia–South African passive margin basins for which independent data are available. We determined by a statistical approach the variances associated with each parameter of the method: the geometrical extrapolation of the section (8–43%), the uncertainties on seismic velocities for the depth conversion (2–10%), on the absolute ages of stratigraphic horizons (0.2–12%), on the carbonate content (0.2–46%) and on remaining porosities estimation (3–5%). Our estimates of the accumulated volumes were validated by comparison with previous estimates at a lower temporal resolution in the same area. We discussed variations in accumulation rates observed in terms of relief variations triggered by climate and/or deformation. The high accumulation rates determined for the Lower Cretaceous, progressively decreasing to a minimum in the Mid-Cretaceous, are consistent with the progressive relaxation of a rift-related relief. The following increase to an Upper Cretaceous maximum is consistent with a major relief reorganization driven either by an uplift and/or a change to more humid climate conditions. The lower accumulation rate in the Cenozoic suggests a relief reorganization of lesser amplitude over that period.