To calculate shell material relative to internal volume at each point in morphospace, we follow Raup and assume that shell thickness is a fixed fraction of radius, namely thickness/radius = 0.077, as measured by [47]. Interestingly, this ratio is close to the optimal ratio of thickness/radius =0.07 from calculations of mechanical strength in tube-like bones [4]. We improve slightly on Chamberlin and Raup’s original calculation [48] by numerically evaluating the necessary integrals rather than using the analytical approximations of [49] (see Methods), yielding corrections of about 10%.