Mother Pelican
A Journal of Solidarity and Sustainability

Vol. 9, No. 4, April 2013
Luis T. Gutiérrez, Editor
Home Page


Thermodynamic Footprint

Paul Chefurka
Approaching the Limits to Growth

This article was originally published in
Approaching the Limits to Growth, 12 March 2013

This article introduces the concept of the Thermodynamic Footprint or TF. At the end I briefly discuss a follow-on concept, a measure I call the Human Thermodynamic Equivalent or HTE.

This article introduces the concept of the Thermodynamic Footprint or TF. At the end I briefly discuss a follow-on concept, a measure I call the Human Thermodynamic Equivalent or HTE.

This work has two purposes: to measure the impact we are having on the planet, and to measure the change in our impact over time. I believe that our energy use is the best available proxy for the impact we are having on the planet because energy is essential for all human activity.  It is through energy expenditure that we alter the planet's physical, biological and chemical makeup - through mining, manufacturing, construction, habitat alterations, and the generation of wastes such as carbon dioxide and other pollution.

Unlike the "carbon footprint" that it may superficially resemble, the TF is really a measure of overall human activity.  By implication it measures our impact on the environment, since all human activity has some impact on the planet.  As a result it has quite a different intention than the existing measures of carbon footprint or ecological footprint.  This difference in intention has a direct bearing on discussions of our growing population and consumption.


The Thermodynamic Footprint is the ratio of all the energy a person normally uses in their life, over just  the amount of energy they generate within their bodies from food.  The "energy we normally use" includes food, fossil fuels and non-fuel generated electricity from hydro, nuclear and renewable power.  It includes both our own direct energy use and our individual share of all the energy society uses to create and maintain the world we live in.

The result is a number that describes how many peoples' worth of environmental impact an individual creates. If someone uses no additional energy beyond food, their TF value would be 1.0. If their TF is 2.0, it means that person has twice the thermodynamic impact on their environment as an "unaided" person.  Someone with a TF of 10 has the same impact as ten unaided people.

How is the TF Calculated?

The TF calculation begins with the amount of fuel-sourced CO2 produced by one person in a day.  This can be for an specific individual, or an average per-capita share for a nation, or the world as a whole.  That number is divided by the ~1.4 kg/day of CO2 an average person working normally generates from burning food. That ratio is then adjusted upwards to account for any added use of hydro and nuclear electricity, since in the final analysis all the extra energy we use creates environmental impact.

Some Initial Assumptions

The main assumption is that all energy use creates an environmental or ecological  impact.  While we are used to thinking of the impact of the energy sources themselves (for example, the CO2 and other pollution from burning fossil fuels; radioactive contamination from nuclear reactors; the mountaintop damage of coal mining; etc.) the impact of energy goes far beyond those initial effects.  Energy enables all human activities, from agriculture to city-building, from dredging waterways to digging mines.  Every human activity carries with it a web of direct and indirect environmental impacts that are independent of the source of energy used in the activity.

Using CO2 emissions from breathing and fuel use in this way requires the following assumptions:
  1. The CO2 in our breath (endosomatic CO2 "from within the body") represents the basic thermodynamic state of one human being.
  2. The CO2 we generate by burning fossil fuels (exosomatic CO2 "from outside the body") can be thought of as a mechanical extension of our breathing, since it results in the same thermodynamic outcome: work.
  3. The generation of ~1.4 kg/day of exosomatic CO2 represents a similar amount of impact to the planet as one human being doing average physical work. (Note that this doesn't fully account for the CO2 produced by the land use changes required for food production, though our other energy use swamps that effect today.)
  4. Exosomatic CO2 emissions from fuel use represent a reasonable initial proxy for all human planetary impact.  This is because all our impact is driven by energy, and 87% of our energy comes from fossil fuels.
What about other forms of energy?

Humans were already using a substantial amount of exosomatic energy well before 1800. Even before the discovery of agriculture some 8,000 years ago, our ancestors were already using firewood and other biofuels, oxen, horses, donkeys, mules, yaks, dogs etc. to do some of the work that had to be done.  If we count all of the energy and CO2 produced by biomass fuels and and draft animals, that would seem to add quite a lot to the human footprint.

However, I deliberately omit these sources of energy and CO2 from the calculation and focus solely on our use of stored energy sources.  I have several reasons for this decision.
  • Those pre-industrial CO2 sources are all the direct result of the real-time flows of energy that originate with photosynthesis - whether directly in the case of biomass or indirectly in the case of animals.  As a result, the amount of work they can provide isn't a major contributor to planetary damage - certainly not compared to our drawdown of stored energy stocks such as fossil fuels.
  • Humanity has always had animals and biomass as part of our heritage.  In the past we have generally employed them in direct proportion to our numbers. I assume that even today their contribution remains approximately proportional to our population.  Where this may not be so for modern humans, as with the expansion of our use of food animals like cattle and pigs, that expansion is enabled by the use of fossil fuels and electricity. As a result, the damage it represents is already accounted for under the assessment of that energy.
  • I am using the CO2 production of human beings as a baseline for the minimal level of human activity.  This approach allows a simple comparison between unaided human activity and the activity that has been enabled by our use of stored energy. Our use of stored energy far outstrips any other work-producing factor in human society.
For example, the calculation for the year 1800 represents the human human muscle power of approximately one billion people, with a small addition for coal - the only stored energy source in use at the time.  1800 marks the point when the human "energetic exoskeleton" began to draw down the stored reserves of planetary energy in a big way.

Data Sources

The datra sources are national CO2 and energy consumption data taken from the BP Statistical Review of World Energy 2012, as well as global carbon emissions going back to 1751 provided by the U.S. Department of Energy's Carbon Dioxide Information Analysis Center.

Preliminary Results

First, here is the Thermodynamic Footprint of a single "average" world citizen at various times since 1800:


  • In 1800 the average individual TF was just over 1, since not much fossil fuel or electricity was in use yet.
  • By 1900 the average TF was about 4, meaning that each person had the same impact as four "unassisted" people.
  • By 2010 the TF of an "average" world citizen was about 12.
  • Each person alive today puts the same load on the planet as 12 people did 200 years ago.
The next graph compares the current individual Thermodynamic Footprints for various nations:


  • The average TF of an American is about 38, while that of an average Bangladeshi is just under 2. There are no big surprises there.
The next graph is probably the most interesting. By multiplying the average global TF figure by the world population, we can find the  "Thermodynamic Population Equivalent" of the world over time.  This value reflects both our increasing energy consumption and our growing world population.  It is a measure of the increasing planetary impact of the growth in our technology, activity and numbers.


  • In 1800 the actual world population was just under 1 billion, and the "thermodynamic population" was just over a billion.
  • By 2010, the world's numeric population was 6.85 billion, while the "thermodynamic population" had ballooned to the equivalent of 80 billion people.

This calculation demonstrates the amount of damage that our technological activity is causing to the planet.  This activity, driven by the energy we use in our daily lives, causes as much damage to the planetary systems we depend on as 80 billion people would if they were living in their raw human state, as hunter-gatherers.

There is potentially much more to be discovered here, but one thing jumps out at me immediately. TF seems like a very good proxy for the elusive "AT" term in the infamous I=PAT equation.  By using it that way we can deduce that humanity today is having about 80 times the impact on the planet that we had 200 years ago.

We estimate that there were about 10 million people living on the planet just before the invention of agriculture 8,000 years ago.  Modern human civilization is today having about 8,000 times the impact on the planet as did our ancestors of that time.

The Human Thermodynamic Equivalent

This measure has some similarity to the concept of the "energy slave".  Each of us represents the operation of some quantity of exosomatic energy within our environment.  That energy repesents the work of a number of "human equivalents".  The number in question is directly given by our Thermodynamic Footprint.

One Human Thermodynamic Equivalent or "HTE" is represented by the production of 1.4 kg of CO2 per day, or equivalently 140 watts of power, from exosomatic sources.

As a sidebar, this definition allows us to verify the original TF calculation in another way: by considering the amount of power generated in the world from all sources.  This is estimated to be around 14 terawatts (with some imprecision due to the efficiency differences of various fuel uses).  If there are currently 7 billion people in the world, each producing an average of 140 watts, the total power production of human bodies is about 1 terawatt.  Compared to the 14 terawatts of power consumed in the world today, this gives an average individual TF of 14 - quite close to the value of 12 that was calculated above using global CO2 emissions and adjusting for hydro and nuclear power production.  the difference is progbably due to the fact that the 14 TW estimate includes biomass power production, while the TF does not.

There are about 80 billion Human Thermodynamic Equivalents at work in the world today.  We can get a feeling for what this means to the planet if we look at the average human population density. This is estimated at 50 people per square kilometer, or 135 per square mile, calculated over the world's entire land area excluding Antarctica.  If we consider the HTE, however, the density changes to 600 per square kilometer, or 1600 per square mile.  This is similar to having the population density of Taiwan living and working on each and every square mile of land surface on the entire planet - including all the plains, steppes, tundra, taiga, swamps, forests, deserts and mountain ranges - except for Antarctica.

Of course, our activity is not spread out evenly across the planet. Some areas have very little human activity, while others have quite a lot.  If we estimate that half of all the world's land is used by humans in one way or another, this brings the average HTE density of the areas that are subject to human impact up to 3200 human equivalents per square mile.  This is somewhat higher than the population density of Bangladesh.

In the face of this degree of pressure, it is no wonder that our activity is damaging the world's atmosphere, geology, water chemistry and living ecology as profoundly as it is today.  The 64 trillion dollar question is, "How close are we to the point where the Earth's systems can no longer cope with these changes, and finally force us to cease and desist?"


Paul Chefurka is a Computer Scientist with a lifelong interest in environmental issues. He has spent over twenty years working in Research and Development in the Ottawa telecommunications industry, and is currently Project Manager at Canadian Coast Guard and the Canadian Department of Fisheries and Oceans. His personal web site, Approaching the Limits provides open access to his writings and is a valuable resource for study and reflection on many dimensions of the impending ecological crisis.

|Back to TITLE|

Page 1      Page 2      Page 3      Page 4      Page 5      Page 6      Page 7      Page 8      Page 9

Supplement 1      Supplement 2      Supplement 3      Supplement 4      Supplement 5      Supplement 6

PelicanWeb Home Page

Bookmark and Share

"No power is strong enough to be lasting
if it labors under the weight of fear."

— Cicero


Write to the Editor
Send email to Subscribe
Send email to Unsubscribe
Link to the Google Groups Website
Link to the PelicanWeb Home Page

Creative Commons License
ISSN 2165-9672

Page 3      



Subscribe to the
Mother Pelican Journal
via the Solidarity-Sustainability Group

Enter your email address: