What it does
Body mass of an extinct animal is usually estimated from a bone measurement (a limb bone circumference, a tooth length, a skull length) through an allometric equation fitted to living animals: log M = a + b·log X. This tool lets you build that equation from your own reference data and use it honestly:
- Fit the line by least squares on log₁₀ X and log₁₀ M, with the standard errors of a and b, r², and the standard error of estimate (SEE) on the log scale.
- Error measures used in the body mass literature: %PE, the average absolute error of the reference predictions as a percentage of the prediction, and %SEE, 100 × (10^SEE − 1).
- Bias correction: back-transforming from logs gives the median, not the mean, mass. Pick the smearing factor (the average of 10^residual over the references) or the QMLE factor from the SEE, or none.
- Prediction intervals for each fossil (90, 95 or 99 %), and a warning when a fossil lies outside the range of the references, where the estimate is an extrapolation.
- Type an equation instead: enter a and b from a paper (log₁₀ or ln, with any correction factor it gives). The tool does not include any published equations; use the source’s own error figures with the result.
How to use it
Paste the reference specimens as three columns: name, X, mass (or open a CSV or Excel file). Use the same measurement and units for the fossils, as two columns: name and X. Any units work, as long as they match; type them in so the tables and plot are labelled.
Worked example
The page opens with made-up reference data: 12 invented specimens with X from 49 to 304 mm and masses from 18 to 1350 kg. The fit is log₁₀ M = −2.8593 + 2.4384 log₁₀ X (r² = 0.9928, SEE = 0.0592), with %SEE 14.6 % and %PE 10.4 %. The smearing factor is 1.0078.
For the three made-up fossils, with smearing and 95 % intervals:
- Fossil A, X = 160 mm: 330 kg (238.5 to 449.4 kg).
- Fossil B, X = 65 mm: 36.69 kg (26.02 to 50.94 kg).
- Fossil C, X = 410 mm: 3273 kg (2282 to 4622 kg), flagged as outside the reference range.
Good practice
- Choose references that share the fossil’s body plan and way of moving; a single equation across very different animals adds large errors.
- Report the interval, not only the point estimate, and say which correction you used.
- Ordinary least squares is the usual choice for prediction. Reduced major axis lines describe scaling, but are not meant for predicting one variable from the other.
FAQ
Why is the interval not symmetric? It is symmetric on the log scale, so in kilograms it stretches further upwards.
Is my data uploaded? No. Everything runs in your browser and works offline.
Where the numbers come from
- Ordinary least squares on log10-transformed data with the standard prediction interval; %PE and %SEE as defined by R. J. Smith (1984, American Journal of Physiology 246: R152-R160); smearing estimate of N. Duan (1983, Journal of the American Statistical Association 78: 605-610); the QMLE factor exp((ln 10 · SEE)² / 2). No published regression coefficients are included.
- Checked against statsmodels (OLS parameters, standard errors, r², SEE, and 90 % and 95 % prediction and confidence intervals at three X values) and numpy (%PE, %SEE, smearing and QMLE factors).
- The example reference specimens and fossils are made up for this tool; they are not real animals.
Standard scientific values, such as constants, atomic weights and melting points, are facts found in every textbook; we name where ours were checked. If you are an author or publisher and want a value, a credit or a table changed or removed, tell us and we will act quickly.
Last updated 2026-11-09.