Animal Scaling: Metabolic Rate

An elephant weighs 200 000 times as much as a mouse but uses only about 10 000 times as much energy. Kleiber’s law captures this: metabolic rate grows with mass to the power ¾.

PhysiologyAllometryKleiber

Inputs

Input examples

Basal metabolic rate: the energy an animal uses at rest. Kleiber’s constant of 70 kcal per day for a 1 kg animal fits mammals from mice to cattle.

Body mass M

Kleiber constant B₀ (kcal/day for 1 kg)

Why Bigger Animals Burn Less per Kilogram

Per kilogram of body, a shrew burns energy about 30 times faster than an elephant. If metabolism simply grew with mass, a big animal would overheat: its heat is made throughout its volume but lost only through its skin. In 1932 Max Kleiber measured animals from rats to steers and found metabolic rate grows as M^¾.

The same law reaches from mice to whales. That is why small animals must eat almost constantly, live fast, and why a cat needs proportionally more food than a horse.

¾Kleiber’s exponent

×16mass ⇒ ×8 energy

per kgfalls as M^−¼

human≈ 1700 kcal/day

Metabolic Rate vs. Body Mass

log–log

Kleiber: B ∝ M^¾

if B ∝ M (same per kg)

your animal

Result

Enter the values above

Key Relations

Kleiber’s Law

B₀ ≈ 70 kcal/day (about 3.4 W) for a 1 kg mammal. Doubling the mass raises the energy use by 2^¾ = 1.68.

Example:

Per Kilogram

Every kilogram of a big animal works more slowly, so the energy per kilogram falls as mass grows.

Power in Watts

A resting human runs at about 80 W, like an old light bulb.

Sources & Verification

References

M. Kleiber, “Body size and metabolism”, Hilgardia 6(11), 315–353 (1932).
K. Schmidt-Nielsen, Scaling: Why Is Animal Size So Important?, Cambridge University Press, 1984 — Ch. 6 (Metabolic Rate and Body Size).