Allometric Scaling Calculator
Estimate basal metabolic rate from body mass using Kleiber's law.
Compare BMR across animal sizes and see how the 3/4 power law scales from mice to elephants.
In 1932, biologist Max Kleiber observed that metabolic rate does not scale linearly with body mass. Instead, across all mammals and birds, it follows a 3/4 power law now known as Kleiber’s law.
The formula:
BMR (kcal/day) = 70 x M^0.75
where M is body mass in kilograms. In watts: BMR = 3.45 x M^0.75.
This 3/4 exponent was controversial for decades. Simple geometry predicts a 2/3 exponent because surface area scales as M^(2/3) and metabolic rate was thought to track heat loss. Kleiber’s empirical 3/4 has since been confirmed by data from shrews to blue whales.
What it means in practice. A mouse at 25 grams needs about 3.5 kcal/day per gram of body mass. An elephant at 4,000 kg needs about 0.076 kcal/day per gram. Larger animals are metabolically cheaper per unit mass, which is one reason larger animals can sustain longer fasts and live longer lives.
Field metabolic rate (FMR) for active free-living animals is roughly 3-5 times BMR depending on activity level and species. Hibernating animals may drop to 2-5% of BMR.
Limitations. Kleiber’s law is an empirical average. Individual variation is substantial. The law applies well to endotherms (mammals, birds). Ectotherms (reptiles, fish) have lower BMRs at the same body mass and are more temperature-dependent. This calculator uses the mammalian equation.