Calculating the volume of ceramic vessels found whole or in fragments on archaeological sites is a key analytical endeavour that can have implications for economic and social activity, including storage and feasting. Established methods for estimating volumes are mostly based on the assumption that vessel shapes approximate to a circular form in plan-view. This new study shows that such an assumption may not be warranted and that methods that assume circularity produce less accurate volumetric estimates than approaches which accept that a less regular elliptical shape may be closer to reality. Statistical analysis allows the accuracy of the different methods to be compared and evaluated.