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I = Pat

I = PAT is the lettering of a formula put forward to describe the impact of human activity on the environment.

I = P × A × T

In words:

Human Impact on the environment equals the product of Population, Affluence, and Technology. This shows how the population, affluence and technology produce an impact

The equation was developed in the 1970s during the course of a debate between Barry Commoner, Paul R. Ehrlich and John Holdren. Commoner argued that environmental impacts in the United States were caused primarily by changes in its production technology following World War II, while Ehrlich and Holdren argued that all three factors were important and emphasized in particular the role of human population growth.[1][2][3]

The equation can aid in understanding some of the factors affecting Denis Hayes, Lester Brown, René Dubos, and Sidney Ripley that did not come to pass.[5] Neal Koblitz classified equations of this type as "mathematical propaganda" and criticized Ehrlich's use of them in the media (e.g. on The Tonight Show) to sway the general public.[6]

The Kaya identity is closely related to the I = PAT equation. The I = PAT equation is more general, describing an abstract "impact". The Kaya identity describes more clearly the impact of human activity on CO2 emissions.


  • Population 1
    • Environmental Impacts 1.1
  • Affluence 2
    • Environmental Impacts 2.1
  • Technology 3
    • Environmental Impacts 3.1
  • Reception 4
  • See also 5
  • References 6


Population (est.) 10,000 BC – 2000 AD.

In the I=PAT equation, the variable P represents the population of an area, such as the world. Since the rise of industrial societies, human population has been increasing exponentially. This has caused Thomas Malthus and many others to postulate that this growth would continue until checked by widespread hunger and famine (see Malthusian growth model).

The United Nations and the US Census Bureau project that world population will increase from 7.0 billion today to about 9.2 billion by 2050.[7][8] These projections take into consideration that population growth has slowed in recent years as women are having fewer children. This phenomenon is believed to be a result of demographic transition in developed nations. As a result, the UN believes that human population might stabilize around 9 billion by 2100.[1] However, since the world population is set to keep rising for the next few decades, this factor of the I=PAT equation will likely keep increasing human impact on the environment for the near future.

Environmental Impacts

Increased population increases humans' environmental impact in many ways, which include but are not limited to:

  • Increased land use - Results in habitat loss for other species.
  • Increased resource use - Results in changes in land cover
  • Increased pollution - Can cause sickness and damages ecosystems.


World GDP per capita (in 1990 Geary-Khamis dollars)

The variable A, in the I=PAT equation stands for affluence. It represents the average consumption of each person in the population. As the consumption of each person increases, the total environmental impact increases as well. A common proxy for measuring consumption is through GDP per capita. While GDP per capita measures production, it is often assumed that consumption increases when production increases. GDP per capita has been rising steadily over the last few centuries and is driving up human impact in the I=PAT equation.

Environmental Impacts

Increased consumption significantly increases human environmental impact. This is because each product consumed has wide ranging effects on the environment. For example, if the construction of a car had the following environmental impacts among others:

  • 605,664 gallons of water for parts and tires[9]
  • 682 lbs. of pollution at a mine for the lead battery.[9]
  • 2178 lbs. of discharge into water supply for the 22 lbs. of copper contained in the car.[9]

then the more cars per capita, the greater the impact. Since the ecological impacts of each product are far reaching, increases in consumption quickly result in large impacts on the environment.


The T variable in the I=PAT equation represents how resource intensive the production of affluence is; how much environmental impact is involved in creating, transporting and disposing of the goods, services and amenities used. Improvements in efficiency can reduce resource intensiveness, reducing the T multiplier. Since technology can affect environmental impact in many different ways, the unit for T is often tailored for the situation I=PAT is being applied to. For example, for a situation where the human impact on climate change is being measured, an appropriate unit for T might be greenhouse gas emissions per unit of GDP.

Environmental Impacts

Increases in efficiency can reduce overall environmental impact. However, since P has increased exponentially, and A has also increased drastically, the overall environmental impact, I, has still increased.


The I=PAT equation has been criticized for being too simplistic by assuming that P, A, and T are independent of each other. In reality, at least 7 interdependencies between P, A, and T could exist, indicating that it is more correct to rewrite the equation as I = f(P,A,T).[10] For example, a doubling of technological efficiency, or equivalently a reduction of the T-factor by 50%, does not necessarily reduce the environmental impact (I) by 50% if efficiency induced price reductions stimulate additional consumption of the resource that was supposed to be conserved, a phenomenon called the rebound effect (conservation) or Jevons Paradox. As was shown by Alcott,[10]:Fig. 5 despite significant improvements in the carbon intensity of GDP (i.e., the efficiency in carbon use) since 1980, world fossil energy consumption has increased in line with economic and population growth. Similarly, an extensive historical analysis of technological efficiency improvements has conclusively shown that energy and materials use efficiency improvements were almost always outpaced by economic growth, resulting in a net increase in resource use and associated pollution.[11][12]

As a result of the interdependencies between P, A, and T and potential rebound effects, policies aimed at decreasing environmental impacts through reductions in P, A, and T may not only be very difficult to implement (i.e., population control and material sufficiency and degrowth movements have been very controversial) but also are likely to be rather ineffective compared to rationing (i.e., quotas) or Pigouvian taxation of resource use or pollution.[10]

See also


  1. ^ a b O'Neill, B.C.; MacKellar, F.L.; Lutz, W. (2004). "Population, greenhouse gas emissions, and climate change". In Lutz, W.; Sanderson, W.C.; Scherbov, S. The End of World Population Growth in the 21st Century: New Challenges for Human Capital Formation & Sustainable Development. London: Earthscan Press. pp. 283–314. 
  2. ^  
  3. ^  
  4. ^  
  5. ^ R Bailey (2000) Earth day then and now, Reason 32(1), 18-28
  6. ^ N Koblitz (1981) "Mathematics as Propaganda", in Mathematics Tomorrow, ed. Lynn Steen, pp 111-120.
  7. ^ US Census Bureau international popopulation statistics and projections 1950 to 2050
  8. ^ United Nations population projections
  9. ^ a b c Andriantiatsaholiniaina, L. A.; Kouikoglou, V. S.; Phillis, Y. A. (2004). "Evaluating strategies for sustainable development: Fuzzy logic reasoning and sensitivity analysis".  
  10. ^ a b c Alcott, B. (2010). "Impact caps: Why population, affluence and technology strategies should be abandoned". Journal of Cleaner Production 18 (6): 552–560.  
  11. ^ Huesemann, Michael H., and Joyce A. Huesemann (2011). Technofix: Why Technology Won’t Save Us or the Environment, Chapter 5, "In Search of Solutions II: Efficiency Improvements", New Society Publishers, Gabriola Island, British Columbia, Canada, ISBN 0865717044, 464 pp.
  12. ^ Cleveland, C. J.; Ruth, M. (1998). "Indicators of Dematerialization and the Materials Intensity of Use". Journal of Industrial Ecology 2 (3): 15.  
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