Kleiber's Three-Quarters

Plate 99 speaks for itself: “An elephant burns less per gram than a mouse.”

The Physics

Across mammals, basal metabolic rate grows roughly as body mass to the three-quarters power. So the rate per kilogram falls as animals get bigger.

B = B₀ M^(3/4)

• B: basal metabolic rate, W (quoted in kcal/day)
• B₀: normalisation, kcal day⁻¹ kg⁻³ᐟ⁴
• M: body mass, kg

B₀ ≈ 70 kcal/day per kg^(3/4). So per-mass rate falls as M^(−1/4).

Honest caveat: The exponent 3/4 is empirical; fits across groups give values from about 0.67 to 0.75.

Sources

• M. Kleiber, Hilgardia 6, 315 (1932).
• C. R. White, R. S. Seymour, PNAS 100, 4046 (2003).

On the poster

Plate 099, “Kleiber's Three-Quarters”: the pixel-art plate with its slogan “An elephant burns less per gram than a mouse.”, the key equation and the facts panel shown above. Pixelated Physics. Physics. Personified.