How Is a Dinosaur Weighed? Estimating Mass From Bones That Weigh Nothing
By the BrainSnail editorial team. How these articles are written and checked, and how to tell us when one is wrong.
Published weights for extinct animals look like measurements and are calculations resting on assumptions. Two methods dominate, they disagree with each other, and the size of that disagreement is rarely reported alongside the figure.
The two approaches
The first method scales from a measurement that correlates with mass in living animals, usually the circumference of the weight-bearing limb bones, since a leg must be thick enough to support what stands on it. Measuring that correlation across many living species gives an equation, and applying it to a fossil returns a mass. The method is quick, requires only two bones and inherits whatever scatter exists in the living sample. The second method reconstructs the volume of the animal, historically by building a scale model and measuring how much water it displaces and now by constructing a digital model from the skeleton, then multiplying by an assumed density. That approach uses the whole animal and depends entirely on how much flesh the reconstructor puts on the bones and what density they assume.
Where the uncertainty enters
Each step introduces error and several are difficult to bound:
- •Incomplete skeletons, since most specimens are partial and missing sections must be estimated from relatives
- •Soft tissue quantity, which is the largest single source of disagreement in the volume method
- •Density, which is assumed and which air sacs reduce substantially in the groups that had them
- •Scatter in the living reference sample, since animals of the same limb dimensions vary in mass
- •Whether living animals are appropriate comparisons at all for body sizes far beyond anything alive
- •Growth stage, since a specimen may not be adult and scaling assumes it is
How far apart the answers are
Published estimates for the same specimen frequently differ by a factor of two, and for the largest animals the spread has been larger still, with figures for some sauropods ranging across tens of tonnes depending on method and author. That variation is not a scandal, since it reflects genuine uncertainty rather than carelessness, and studies comparing methods on living animals of known mass find errors of a similar order, which means the fossil estimates are about as good as the techniques allow. The problem is in how the numbers travel, since a figure published with an uncertainty range is quoted without it, enters popular accounts as a fact and is then compared with figures derived by a different method for a different animal. Comparisons between species are therefore considerably less reliable than they appear.
The length problem too
Lengths are quoted more confidently than masses and are less reliable than they look, for a different set of reasons. Most large dinosaurs are known from incomplete skeletons, so the total is assembled by scaling missing sections from relatives, and a missing tail section can add or remove several metres. Vertebral counts differ between related species, which means a reconstruction that assumes a relative's count may be wrong. Historic claims for the very largest animals rest on material that has been lost, damaged or never adequately described, with one famous giant known only from drawings and measurements of bones that were destroyed. Cartilage between vertebrae added length in life that a mounted skeleton does not include. And length is a poor measure of size in any case, since an animal built long and slender and one built short and heavy can have the same figure and very different masses.
Why it matters
Mass is not an idle statistic, since a great deal else is calculated from it. Metabolic rate scales with body mass, so an energy budget rests on the estimate. Food requirements follow, and therefore conclusions about how many animals a landscape could support. Locomotion analyses depend on it, since the forces a limb must withstand and the speed an animal could reach both depend on what it weighed. Growth curves derived from bone rings plot mass against age and inherit the uncertainty. And questions about upper limits on body size, which are genuinely interesting, cannot be addressed without knowing what the largest animals actually weighed. That dependency means an error in mass propagates into a long chain of conclusions, which is a good reason for the uncertainty to travel with the number.
The takeaway
Scaling from limb bone circumference and reconstructing volume then multiplying by an assumed density are the two methods, and they disagree. Soft tissue quantity and density are the largest sources of error, and estimates for the same specimen frequently differ by a factor of two. Metabolic rate, food requirements, speed and growth curves are all calculated from mass, so the uncertainty propagates.