Kleiber's Law: Metabolic Scaling Across Body Sizes

Organism

Body mass 70 kg

Ambient temperature 20 °C

Show naive surface-area law (M^2/3)

Jump to a species

Live readouts

Basal metabolic rate

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Specific rate

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Pulse rate

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How it works

Basal metabolic rate does not scale in proportion to body mass — it scales with mass raised to roughly the 3/4 power, an empirical relationship known as Kleiber's Law (1932):

BMR = a · M^0.75        (mammals, a ≈ 70 kcal/day)
BMR = a · M^0.72        (birds,   a ≈ 78 kcal/day)
SMR(T) = a · M^0.76 · Q10^((T-20)/10)   (ectotherms, a ≈ 4.9)

Dividing by mass gives the mass-specific metabolic rate a·M^(b-1) — since b−1 is negative, every kilogram of a shrew burns far more energy per day than a kilogram of an elephant. That single exponent explains why small endotherms must eat almost continuously while large ones can survive on relative scraps.

Body mass slider — logarithmic, spans roughly 5 g to 6 t; moves the glowing marker along the log-mass axis and re-evaluates BMR from the active taxon's power law.
Mammal / Bird / Ectotherm — swaps the (a, b) coefficients above. Only ectotherms answer to the temperature slider: mammals and birds are homeotherms, so their internal metabolic machinery is buffered against ambient temperature by thermoregulation.
Ambient temperature — for ectotherms, metabolic rate follows a Q10 = 2.5 relationship: roughly a 2.5× change in rate per 10 °C, referenced to 20 °C. This is why a lizard's energy budget swings with the weather while a mammal's does not.
Pulse rate — the glow/heartbeat animation frequency is driven by the classic allometric heart-rate relation HR ≈ 241·M^-0.25 bpm for mammals (Stahl, 1967), an analogous form for birds, and a temperature-scaled analogue for ectotherms — visualising that smaller, faster-burning bodies literally pulse faster.
Surface-area law toggle — overlays the older (and wrong) 19th-century hypothesis that metabolism should track body surface area, M^0.667. Kleiber's actual M^0.75 line sits visibly above it at large body sizes, which is the historical reason the 3/4 exponent was considered surprising.

The eight preset spheres are real reference species positioned by their true mass and metabolic rate on a log–log axis — together they trace the same curve as the formula, exactly as Kleiber's original mouse-to-elephant plot did.

Mammal Bird Ectotherm Your organism

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