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The IPAT Equation


What is the IPAT Equation, or I = P X A X T?

One of the earliest attempts to describe the role of multiple factors in determining environmental degradation was the IPAT equation1. It describes the multiplicative contribution of population (P), affluence (A) and technology (T) to environmental impact (I). Environmental impact (I) may be expressed in terms of resource depletion or waste accumulation; population (P) refers to the size of the human population; affluence (A) refers to the level of consumption by that population; and technology (T) refers to the processes used to obtain resources and transform them into useful goods and wastes. The formula was originally used to emphasize the contribution of a growing global population on the environment, at a time when world population was roughly half of what it is now. It continues to be used with reference to population policy.


New Insights

In addition to highlighting the contribution of population to environmental problems, IPAT made two other significant contributions. It drew attention to the fact that environmental problems involved more than pollution, and that they were driven by multiple factors acting together to produce a compounding effect. Subsequent research using IPAT indicates that the assumption of a simple multiplicative relationship among the main factors generally does not hold – doubling population, for example, does not necessarily lead to a doubling of impact. Approaches which allow for different weighting to be assigned to each factor have been more successful in accounting for impact2.


Attempts to strengthen the predictive power of the equation have been made in terms of incorporating a variety of social, political and technical factors3. Some of these studies4 enhance the equation’s usefulness for policy development by indicating the variable contribution of different factors, who is responsible for various factors and therefore where resources might best be directed to reduce impact most effectively. However, making the formula more complex also makes it more difficult to apply.



To date, IPAT applications have been limited to evaluation of a single variable measure of environmental impact, such as air pollution. For example, the Intergovernmental Panel on Climate Change has applied IPAT to studies of CO2 levels5. The equation is helpful, to a limited extent, in assessing the contribution of different PAT factors to greenhouse gas (GHG) emissions. The report suggests that levels of GHG emissions for affluent countries increase with increases in affluence, while both population and level of affluence can be significant factors in GHG emission trends in poorer countries. Various applications have found that different types of impacts (eg whether CO2 or SO2 levels are being considered) relate differently to changes in population, affluence and technology6.


Relation to Sustainable Scale

From a scale perspective, the IPAT equation does not help us to identify sustainable limits regarding either individual or composite environmental impacts. It does assist in our understanding of the general factors that increase or decrease environmental impact, but not the level of impact that exceeds sustainable scale. However, by highlighting the complex interplay among a variety of factors in creating an impact, the IPAT equation also demonstrates that there are multiple ways of reducing undesirable effects. It has been noted, for example, that different nations might focus on different factors to reduce their overall impact: more affluent countries could contribute most by reducing their level of consumption (A); many poorer countries could contribute most by reducing their population (P); and the former socialist countries could make the greatest contribution by making their technologies more efficient (T). While there is some truth to this observation, it is also true that opportunities exist in most nations to make improvements in all three factors.


In Summary

The IPAT equation made a contribution to understanding the multiple causes of environmental impact, and it continues to be developed as a method for improving our understanding of these issues. It has not helped in identifying sustainable scale, but it is a useful framework to assist in thinking about ways of reducing environmental impacts by reducing various types of throughput.




1Commoner, Barry. “The Environmental Cost of Economic Growth.” in Population, Resources and the Environment. Washington, DC: Government Printing Office Pp. 339-63, 1972.


 Ehrlich, Paul R. and John P. Holdren. “Impact of Population Growth.” Science 171 (1971): 1212-17.


2Chertow, M. R. “The IPAT Equation and Its Variants; Changing Views of Technology and Environmental Impact,” Journal of Industrial Ecology, 4.4 (2001): 13-29. accessed at: http://mitpress.mit.edu/journals/pdf/jiec_4_4_13_0.pdf


 York, R., E.A. Rosa and T. Dietz. “STIRPAT, IPAT and ImPACT: analytic tools for unpacking the driving forces of environmental impacts.” Ecological Economics, 46.3 (2003): 351-365. 


3Fischer-Kowalski, M. and C. Amann. "Beyond IPAT and Kuznets curves: Globalization as a vital factor in analysing the environmental impact of socio-economic metabolism." Population Environment 23.1 (2001): 7-47.


 Waggoner, P. E. and J. H. Ausubel. “A framework for sustainability science: a renovated IPAT identity.” Proc National Academy of Science, 99.12 (2002):7860-5. accessed at: http://phe.rockefeller.edu/ImPACT/ImPACT.pdf


4Dietz, T. and E. A. Rosa. “Rethinking the Environmental Impacts of population, Affluence and Technology.” Human Ecology Review, 1.1 (1994).


5IPCC. Special Report on Emissions Scenarios: a special report of Working Group III of the Intergovernmental Panel on Climate Change. Cambridge, UK: Cambridge University Press, 2001. http://www.grida.no/climate/ipcc/emission/050.htm


6Cole, M. A. and E. Neumayer. "Examining the impact of demographic factors on air pollution," Population Environment 26.1 (2004): 5-21.


 Olson, Robert.  "Alternative Images of a Sustainable Future," Futures 26.2 (1994): 156- 169,

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