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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 (I) on the environment equals the product of population (P), affluence (A: consumption per capita) and technology (T: environmental impact per unit of consumption).

This describes how our growing population, affluence, and technology contribute toward our environmental 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 population growth.[1] (PR Ehrlich, JP Holdren, Impact of population growth,Science, 1971)

The equation can aid in understanding some of the factors affecting human impacts on the environment.



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, such as ecologist Garrett Hardin,[2] to postulate that this growth would continue until checked by widespread hunger and famine.

However, in recent years population growth has slowed 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 our 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 - Causes climate change, sickens people 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 as 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[3]
  • 682 lbs. of pollution at a mine for the lead battery.[3]
  • 2178 lbs. of discharge into water supply for the 22 lbs. of copper contained in the car.[3]

then the more cars per capita, the greater the impact. Since the ecological impacts of each product are so 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, with P increasing exponentially, T would have to decrease drastically (doubling efficiency each time the population doubles) just to maintain the same impact with the same affluence. Over the last few years, data from the UN World Bank has shown that T has decreased and that it is likely to continue to do so in the future.[4] However, since P has increased exponentially, and A has also increased drastically, the overall environmental impact, I, has still increased.

See also


  1. ^ a b O'Neill et al. 2004. Population, Greenhouse Gas Emissions and Climate Change. Essay in book: Lutz W. et al. (editors). 2004. The End of Population Growth in the 21st Century London: Earthscan
  2. ^ Hardin, Garrett. "The Tragedy of the Commons". Science 162, Dec. 13, 1968. 1243-1248.
  3. ^ a b c Andriantiatsaholiniaina, L.A., V.S. Kouikoglou and Y.A. Phillis. 2004. Evaluating strategies for sustainable development: fuzzy logic reasoning and sensitivity analysis Ecological Economics 48: 149 - 172.
  4. ^ World Bank "World Development Indicators 2003"


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