What is Kleiber's law in simple terms?

Larger animals use more energy in total but less per kilogram of body mass, and the relationship follows roughly the 3/4 power of body mass.

Has the reason for the 3/4 exponent been settled?

Explanations such as distribution network models have been proposed, but whether the exponent is really 3/4, 2/3 or varies across groups is still debated.

Kleiber's Law

🔬 Natural Sciences By CampusDown Wiki Editorial Team Last updated October 26, 2026

Kleiber's law is the empirical rule that an animal's basal metabolic rate scales with roughly the 3/4 power of its body mass. An animal sixteen times heavier has a metabolic rate about eight times, not sixteen times, higher, so larger animals use less energy per unit of body mass. The Swiss-born American animal nutritionist Max Kleiber proposed it in 1932.

Contents

1. Origins and the surface law
2. Allometry and theoretical explanations
3. The exponent debate and assessment
4. FAQ
5. References

Origins and the surface law

Measuring metabolism in dogs, the nineteenth-century German physiologist Max Rubner (1883) proposed a surface law: because heat is lost through the body surface, metabolic rate should be proportional to surface area, and hence to the 2/3 power of body mass. Max Kleiber (1932) collected data on mammals of many sizes, analyzed them on logarithmic axes and found a slope of about 0.74, greater than 2/3, which he summarized as 3/4. Brody (1945) obtained similar results with his mouse-to-elephant curve. Hemmingsen (1960) argued that the relationship extends broadly to unicellular organisms and plants, and Kleiber's book The Fire of Life (1961) presented the law as a foundation of animal energetics.

Allometry and theoretical explanations

Kleiber's law is a leading example of allometry, the study of how biological traits change as power functions of body size. Schmidt-Nielsen (1984) and Calder (1984) showed that life-history traits such as heart rate, lifespan and growth rate also tend to follow powers of body mass in multiples of one quarter. West, Brown and Enquist (1997) derived the 3/4 exponent mathematically from the assumption that space-filling, branching distribution networks such as blood vessels and plant vascular systems are designed to minimize energy loss. Building on this, Brown et al. (2004) proposed a metabolic theory of ecology, under which individual metabolic rate and temperature help explain population growth, community structure and ecosystem nutrient cycling. The law is closely linked to life history theory.

The exponent debate and assessment

Whether the 3/4 exponent is universal is contested. Reanalyzing the data, Dodds, Rothman and Weitz (2001) argued that there is little basis for rejecting an exponent of 2/3, and White and Seymour (2003) reported an exponent close to 2/3 in mammal data controlled for body temperature and digestive state. Glazier (2005) showed that the exponent varies roughly between 2/3 and 1 across animal groups and activity levels and stressed the need for theories that explain this variation rather than a single law. West (2017) sought similar scaling laws in social systems such as cities and companies, work that connects to research on Zipf's law and power laws.

FAQ

What is Kleiber's law in simple terms?: Larger animals use more energy in total but less per kilogram of body mass, and the relationship follows roughly the 3/4 power of body mass.
Has the reason for the 3/4 exponent been settled?: Explanations such as distribution network models have been proposed, but whether the exponent is really 3/4, 2/3 or varies across groups is still debated.

Sources reviewed: 2026-10-26

References

Kleiber, M. (1932). Body size and metabolism. Hilgardia, 6(11), 315–353.
Kleiber, M. (1961). The Fire of Life: An Introduction to Animal Energetics. New York: Wiley.
Rubner, M. (1883). Über den Einfluss der Körpergrösse auf Stoff- und Kraftwechsel. Zeitschrift für Biologie, 19, 535–562.
Brody, S. (1945). Bioenergetics and Growth. New York: Reinhold.
Hemmingsen, A. M. (1960). Energy metabolism as related to body size and respiratory surfaces, and its evolution. Reports of the Steno Memorial Hospital, 9, 1–110.
Schmidt-Nielsen, K. (1984). Scaling: Why Is Animal Size So Important? Cambridge: Cambridge University Press.
Calder, W. A. (1984). Size, Function, and Life History. Cambridge, MA: Harvard University Press.
West, G. B., Brown, J. H., & Enquist, B. J. (1997). A general model for the origin of allometric scaling laws in biology. Science, 276(5309), 122–126.
Dodds, P. S., Rothman, D. H., & Weitz, J. S. (2001). Re-examination of the “3/4-law” of metabolism. Journal of Theoretical Biology, 209(1), 9–27.
White, C. R., & Seymour, R. S. (2003). Mammalian basal metabolic rate is proportional to body mass2/3. PNAS, 100(7), 4046–4049.
Brown, J. H., Gillooly, J. F., Allen, A. P., Savage, V. M., & West, G. B. (2004). Toward a metabolic theory of ecology. Ecology, 85(7), 1771–1789.
Glazier, D. S. (2005). Beyond the ‘3/4-power law’: Variation in the intra- and interspecific scaling of metabolic rate in animals. Biological Reviews, 80(4), 611–662.
West, G. (2017). Scale: The Universal Laws of Growth, Innovation, Sustainability, and the Pace of Life. New York: Penguin Press.

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This article was last updated on October 26, 2026. It is based on widely recognized original works and textbooks; when citing it in a paper, please check the original sources listed in the references.