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Kaya Identity Calculator

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The IPAT equationThe Kaya identityWhich are the applications of the Kaya identity?How to calculate the Kaya identityHow to use our Kaya identity calculatorWhy is the Kaya identity important?FAQs

Humanity's impact on the climate is taking its toll on our planet: learn how scientists measure it with our Kaya identity calculator.

The identity needs only a few factors, but it can open your eye to the reality of the situation we are living in: how the wellbeing of a country affects its impact and how clean energy sources are fundamental for a better future. Are you interested? Keep reading to learn:

  • What the Kaya identity is;
  • What the differences with the IPAT equation are;
  • How to calculate the Kaya identity; and
  • What factors the Kaya identity uses and where to find them.

The IPAT equation

In 1967, a group of scientists proposed an equation to calculate the impact of the human population on the planet: what they came up with was the IPAT equation:

I=PATI= P\cdot A\cdot T


  • PP is the human population;
  • AA the affluence; and
  • TT the technology.

Yes, yes: we know: how can one even begin to determine those quantities?

For starters, affluence is the consumption per individual, measured by energy consumption, for example. Technology is quantified by the cleanliness of an industrialized society per unit of consumption.

Those are not useful indicators for scientists — they are too vague and badly defined. The energy economist Yoichi Kaya decided to redesign the equation to make it concrete.

The Kaya identity

Kaya brought a lot of much-appreciated science into the IPAT equation, while keeping it a simple multiplication. His equation substitutes the factors with well-established and measurable quantities, which leave little space for ambiguity.

Here is the Kaya identity:

F=PGPEGFEF= P\cdot \frac{G}{P}\cdot\frac{E}{G}\cdot\frac{F}{E}

Let's check out the factors of the Kaya identity:

  • PP is again the human population;
  • FF is the value of global anthropogenic CO₂ emissions (but not the one you emit by breathing, though it's not negligible as you can see at our CO₂ breathing emission calculator);
  • GG is the GDP; and
  • EE the energy consumption.

Which are the applications of the Kaya identity?

The Kaya identity has extensive uses in the field of climate modeling since it allows for projections of the human impact in terms of equivalent emissions of greenhouse gases (for example, you can learn why it's better to take the bike with our car vs bike calculator).

The IPCC (Intergovernmental Panel on Climate Change) uses the Kaya identity in its reports: we are sure you heard of them. Their sixth report made the headlines in August 2021 because it finally confirmed — scientifically — the connection between human activities and climate change.

How to calculate the Kaya identity

Calculating the Kaya identity is extremely easy: that's why it has so much importance! The message it bears doesn't hide behind complex layers of math.

You can either use the factors of the Kaya identity in the form we showed before, or the result of their ratios:

  • G/PG/P is the GPD per capita;
  • E/GE/G is the energy intensity of the GDP (a measure of how energetically inefficient a country is);
  • F/EF/E is the carbon emitted in energy production (a measure of the carbon footprint, for example the one associated with aerial traffic. You can learn more at Omni's flight carbon footprint calculator).

How to use our Kaya identity calculator

Our Kaya identity calculator allows you to easily compute the environmental impact of a human population.

The factors of the Kaya identity vary quickly: the population keeps growing, the GDP is fairly variable, and the methods of energy production change by the day. We decided not to include a set of given values, but to leave some references where you can find useful data.

🙋 We set the default values of our calculator to the ones of the whole planet in the year 2014!

You can retrieve the value of gross domestic product per capita of a country (or the world) from this table. The values are in dollars and are updated fairly often. You can find the corresponding values for the population on this page of the world bank website. Plug these values in.

The data for the energy intensity of the GDP can be found on this page of Our World in Data. The units are kWh\text{kWh} per dollar. Insert this value in the field for "Energy intensity of the GDP".

Finally, in this report by the EEA, you can find the values of carbon dioxide equivalent emissions for European countries, while, on this page by EIA, you can find the same values for the US (you have to compute the ratio!). Plug the value in the "Energy carbon footprint" field. Note that the measurement units are in CO2eq. / kWh\text{g}\ \text{CO}_{2}\text{eq.}\ /\ \text{kWh}.

Remember to be consistent with the measurement units!

Why is the Kaya identity important?

Our world is changing, and humanity is the cause. The sea level is rising, the temperature grows from year to year. Major disasters hit regularly. Something has to change if we still want to be welcome on Earth. The Kaya identity helps understand why we need to change, but doesn't give direction on how to do that. Get in touch with organizations interested in climate, think of your daily actions and reduce your impact on the planet — it will be grateful!

We created some other calculators that can help you with this mission: try our wind turbine calculator, solar panel calculator, and hydroelectric power calculator!


What is the Kaya identity?

The Kaya identity measures the human impact on Earth's environment. By multiplying a set of factors, we can quantify the carbon dioxide emissions of a population.

The Kaya identity has extensive use in modeling future climate change scenarios, due to the easy connection to parameters associated with humanity's economic development.

What is the formula of the Kaya identity?

The Kaya identity's formula is straightforward:

F = P × (G/P) × (E/G) × (F/E)


  • F is the CO₂ emissions;
  • P is the population;
  • G is the GDP; and
  • E is the energy consumption.

What are IPAT and Kaya identity?

Both the IPAT (from the initials of "impact", "population", "affluence", and "technology") and the Kaya identities are simple equations that model the projected trend of carbon dioxide emissions and human impact on the planet as functions of various parameters connected to the technological and social development of a society.

What is the energy intensity of the GDP?

The energy intensity of the GDP, one of the factors of the Kaya identity, is a measure of how efficiently a country utilizes energy. It is defined as the ratio between energy consumption and GDP.

Higher energy intensity of the GDP is associated with societies that "waste" their energy consumption without converting it efficiently into higher economic throughput.

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