Kleiber's Law Calculator: Basal Metabolic Rate from Body Mass

How it works

BMR (kcal/day) = K × M^b, with M in kg and b ≈ 0.75; BMR (W) = kcal/day × 4,184 ÷ 86,400; mass-specific rate = BMR ÷ M ∝ M^(b − 1); O₂ (mL/h) ≈ W × 3,600 ÷ 20.1

Max Kleiber showed in 1932 that the resting metabolic rate of mammals rises with body mass to about the ¾ power, not in direct proportion. For placental mammals the classic fit is 70 kcal per day × M^0.75 (about 3.4 W for a 1 kg animal). Because the exponent is below 1, each kilogram of a small animal burns far more energy than a kilogram of a large one: a mouse uses roughly 12 times more energy per gram than a cow. Doubling body mass raises the total rate by only 2^0.75 − 1 ≈ 68%. The coefficient K depends on the group. Marsupials run at about 49 kcal/day (Dawson and Hulbert), passerine birds at about 129 and non-passerine birds at about 78 (Lasiewski and Dawson, whose exponent was 0.72), while reptiles, which do not keep a high body temperature, sit far lower and change with temperature. Choose Custom to enter your own K. The exponent itself is still debated: 0.67 (surface-area scaling) fits some narrow groups and small birds, 0.75 fits mammals across many orders of magnitude, and modern analyses find values between about 0.68 and 0.76. The calculator gives the rate in watts, kcal and kJ per day, oxygen use (at 20.1 J per mL O₂, a mixed diet), the rate per kilogram, a daily energy figure at a chosen multiple of BMR (field metabolic rates of free-living animals are typically 2 to 4 × BMR), and a comparison with a second animal. It describes averages across species: individuals and species can differ from the line by 50% or more, and it is not a feeding or drug-dosing guide.

Worked example

A 4.5 kg cat as a placental mammal with b = 0.75: 4.5^0.75 = 3.090, so BMR = 70 × 3.090 = 216 kcal a day (905 kJ). In watts that is 216.3 × 4,184 ÷ 86,400 = 10.5 W, or 2.33 W per kg, and about 1,876 mL of oxygen per hour. At 3 × BMR a free-living cat would need about 649 kcal a day. A 70 kg human comes out at 70 × 70^0.75 = 1,694 kcal (82.0 W), so the cat uses 12.8% of a human’s total but 1.99 times as much per kilogram.

Sources: Kleiber’s law (overview, exponents and history) – Wikipedia · Lasiewski & Dawson (1967) bird coefficients, as given in a Memorial University physiology lab · Forbes N. A., Avian Therapeutics (WSAVA 2014): K = 70 placental, 129 passerine, 78 non-passerine

Frequently asked questions