By Kevin Thompson

The Challenge of Scaling: Lessons From Biology and Physics


Scaling is a near-universal goal for mission-driven organizations.

What do you do with an idea?

Sometimes nothing. And, sometimes, an idea gets turned into something extraordinary.

Social intrapreneurs and entrepreneurs start with ideas responding to societal, environmental, governance, policy, and financial challenges. For these innovators, ideas become products, services, and organizations with positive societal impact.

Along the way, these organizations face a moment of truth—if only we could scale.

Scaling is a near-universal goal for mission-driven organizations because these organizations often—and naturally—believe that a larger organization with more people and a greater number of resources can proportionally, or even exponentially, drive impact and outcomes.

But, why is it so hard to scale How do organizations sustain scaling? Why do so many organizations get stuck?

Some Help From Biology and Physics

To answer these questions and explore solutions to some of the challenges social enterprises face while trying to scale, we begin in a unique and unexpected place: biology and physics.

First, let’s consider a pattern and phenomena to scaling so common it has a name: the sigmoid or “S” curve.

The “S” curve embodies the experience of empires, relationships, and corporations (Handy, 1994). The horizontal dimension represents time, moving left to right, and the vertical dimension represents growth, impact or scale.

The beginning starts with ideas, possibilities, and hypotheses that are tested and evaluated. This is the learning phase. Then scaling and unbounded potential as progress rises during the growth phase. Then a period of plateau and decay in the decline phase. The challenge: can you transition during decline to a new model that starts with learning and builds to a new wave of growth?


The “S” curve also shows up in biology in a predictable, consistent, and quantifiable way.

But, why should we care? By understanding scaling laws and patterns of scaling the natural world has evolved we can reflect on our scaling expectations for the ideas, organizations, and movements we are trying to build.

A Little Bit of Science

Two fundamental features of life are that biological diversity is largely a matter of size and that in order to achieve diversity, organisms must adjust their structure and function to compensate for the geometric, physical, and biological consequences of being different sizes (Brown and West, 2000).  The same is true for organizations made up of people—a failure to adjust and compensate invariably leads to a failure to scale. Growth is complex.

In science, the study of the relationship between body size and shape, anatomy, physiology, and behavior is called allometry. Allometry helps explain how an organism can change proportions as it grows while maintaining an approximate shape.

Consider how analogous allometry is to a growing and scaling organization where the people, programs, products, processes, and resources change proportions but the mission and purpose (i.e., the shape) manage to stay approximately the same.

Through the study of allometry, scientists have observed strikingly consistent patterns for how organisms adjust and compensate as they grow in relation to the system they’re in. The natural system is analogous to an organization operating within a market.

Max Kleiber of the University of California Davis helped articulate this in Kleiber’s Law, a quantitative insight that an animal’s metabolic rate scales to the ¾ power of the animal’s mass (Kleiber, 1932).

A power law is like an exponent, where, in this instance, 1¾ means that for each three-unit growth in metabolic rate, an animal increases its mass by four units. Scientists call this observation sublinear scaling, as ¾ is a number less than one.

Turns out, quarter power laws have extraordinary regularity and are observable just about anywhere you look. From the relationship between a tree’s root system and canopy to the ratio of white and gray matter in the human brain, scaling is repeatedly represented by a quarter power law (West, 2018).

Of Elephants and Mice

To put this into context, consider larger-bodied species such as elephants, who have lower metabolic rates and heartbeats compared to smaller-bodied species such as mice—this is called, unsurprisingly, the “mouse-to-elephant curve” (Willmer, 2009).  The below graphic plots a range of animals all governed by the ¾ power law of metabolic rate to mass.

Source: Schmidt-Nielson, K. 1984. Scaling: Why Is Animal Size So Important? New York: Cambridge University Press.

Think of Kleiber’s Law as an explanation for how nature governs itself: as you get bigger, you slow down. If elephants had the metabolism, heart rate, and speed-relative-to-size of mice, they would run amok and destroy the vegetation they depend on for food. Kleiber’s Law also demonstrates and explains how growth and scaling in nature follows the sigmoid curve.

So, why does this matter to a social enterprise organization trying to scale?

Let’s consider the implications of quarter power laws:

  1. Economies of scale. Each time you double in size, you save 25 percent in the energy required to maintain that size.
  2. Slower pace of life. The organizational “circulatory system” requires resources to travel longer distances, putting downward pressure on speed.
  3. Sigmoidal growth. All organisms grow until they reach a stable, mature size. Human beings reach their full adult size about twenty years after birth yet continue to survive for decades before decline and death.
  4. Finite lifespans. All mammals have about 1.5 billion heartbeats in their lifetimes. A canary weighing twenty grams has a heart rate of 1,000 beats per minute, compared to seventy to eighty beats per minute for a human being (Levine, 1997, and Zhang, 2009).

Quarter Power Laws: A Cautionary Tale

Successful capital campaigns and large grants for social enterprises are rightly celebrated and produce growth capital, but too much funding and too many resources that can’t be metabolized can produce an unsustainable and inefficient organization. This problem is especially acute with overly charismatic leaders who attract large philanthropic funders or organizations who get one-time large grants.

The traditional organizational response to growth—creating more structure, siloed functions, and control systems—usually slows down the distribution of resources and, in turn, organizational metabolism. If organizational metabolism is too slow for organizational size, parts of the organization begin to atrophy. Slowing down with size is natural but slowing down too much can cause the organization lose advantage in its market.

For philanthropic funders of social enterprises, it’s important to maintain a healthy suspicion of grantee proposals that defy scaling laws of nature. If increased size and growth are paired with an acceleration of execution in a 1:1 linear trajectory or higher, question the grantee’s ability to both metabolize the funding and have a distribution system that moves resources faster as it gets larger. Sometimes solutions come from technology or process innovation, but eventually the reality of the “S” curve will apply pressure.



Brody, S. and Henry A. Lardy. 1946. “Bioenergetics and Growth.” The Journal of Physical Chemistry 50,  no. 2: 168-169.

Handy, C. 1994. The Age of Paradox. Harvard Business School Press,  50-58.

Hudson, L.N., Nick J. B. Isaac, and Daniel C. Reuman. 2013. “The relationship between body mass and field metabolic rate among individual birds and mammals.” Journal of Animal Ecology 82, no. 5 (September): 1009-1020.

Kleiber M. 1932. “Body size and metabolism.” Hilgardia 6, no. 11: 315-353.

Levine, H.J. 1997.  “Rest heart rate and life expectancy.” Journal of the American College of Cardiology 30, no. 4 (October): 1104-6. Review.

Mackenzie, D. 1999. “New Clues to Why Size Equals Destiny.” Biophysics 284 (June): 1607-1609.

West, G. 2017. Scale: The Universal Laws of Life, Growth and Death in Organisms, Cities and Companies. London: Weidenfeld & Nicolson.

Willmer, Pat, Graham Stone, and Ian Johnston. 2004. Environmental Physiology of Animals. Wiley-Blackwell.

Zhang, G.Q. and W. Zhang. 2009. “Heart rate, lifespan and mortality risk.” Aging Research Reviews 8, no. 1: 52-60.

About the author

Kevin Thompson empowers individuals, teams, and organizations in the public, private, and social sectors.

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