Body mass is an important determinant of most biological functions, and knowing the mass of extinct animals is essential in order to learn about their biology. It was the aim of this paper to develop a method of mass estimation which would make it possible to determine allometric length-mass relationships for the different groups of dinosaurs. Mass is calculated from graphical reconstructions of fossils, or from photos of skeletal mounts or live animals. Body shape of animals is described by high order polynomial equations. Integration of the polynomial gives body mass of a ‘round’ animal, which is then corrected for animal width by intersection with a second equation (Y = 1 − ax2). The method was validated by predicting body mass of extant animals of known mass and with complex body shapes (kangaroos, emu, elephant, giraffe, rhinoceros). Body mass increased allometrically with total length in all groups of dinosaurs (Ankylosauria, Ceratopsia, Ornithopoda, Prosauropoda, Sauropoda, Stegosauria and Theropoda), but 95% confidence intervals were very large for Ankylosauria and Stegosauria so that, for those groups, the resulting regression equations have little predicting power. Scaling exponents were least for the Sauropoda which may have grown less massive to function at their great body size. Scaling exponents were greatest for the Theropoda, but it was speculated that small coelurosaurs, as the precursors of birds, may have grown less massive compared to other theropods. Mass estimated by the ‘polynomial’ method presented here did not differ significantly from mass estimates in the literature where these were available.