Kaya Identity Calculator (CO₂ from population, GDP, energy and carbon intensity)

Understanding the Kaya identity calculator — concept and principle

This calculator applies the Kaya identity, which splits energy-related CO₂ emissions into population, GDP per person, energy intensity of the economy and carbon intensity of energy. It shows the emissions, the intermediate totals, and projects emissions forward using a growth rate for each factor. It is used in climate policy teaching and scenario thinking.

Emissions are a product of four factors, so their yearly growth rates roughly add up.

How it is calculated

CO₂ = P × (GDP/P) × (E/GDP) × (CO₂/E)

Growth: (1 + g_CO₂) = (1 + g_P)(1 + g_GDP/P)(1 + g_E/GDP)(1 + g_CO₂/E)

Emissions after n years = CO₂ × (1 + g_CO₂)ⁿ

Population in millions, GDP per person in USD/yr, energy intensity in MJ per USD, carbon intensity in g CO₂ per MJ.

The principle

The identity is simply a chain of fractions in which everything cancels except CO₂, so it is always true. Its value lies in separating the drivers: more people and higher incomes push emissions up, while using less energy per unit of GDP and less carbon per unit of energy pull them down. Because the factors multiply, their growth rates combine multiplicatively, which for small rates is close to adding them. The identity was introduced by Yoichi Kaya in 1990 and is used in IPCC reports.

Worked example

Default inputs: 8,100 million people, 13,000 USD per person, 5.9 MJ/USD, 60 g CO₂/MJ; growth +0.9%, +1.8%, −1.5%, −0.5% per year; 10 years.

GDP = 8.1 × 10⁹ × 13,000 = 105.3 trillion USD.
Energy = 105.3 × 10¹² × 5.9 MJ = 621 EJ/yr.
CO₂ = 621 × 10¹² MJ × 60 g = 37.28 Gt/yr; per person 4.6 t; per GDP 0.354 kg/USD.
Growth = 1.009 × 1.018 × 0.985 × 0.995 − 1 = 0.67%/yr (the simple sum is 0.7%).
After 10 years = 37.28 × 1.006696¹⁰ = 39.85 Gt/yr.

Each point is the calculator re-run with only “Population (millions)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Population (millions)	Energy-related CO₂ emissions (Gt/yr)
2,025	9.32
4,050	18.64
6,075	27.96
8,100	37.28
10,125	46.6
12,150	55.91
16,200	74.55

How to read the result

The defaults are round, illustrative world-scale numbers. To bring emissions down, the combined decline in energy intensity and carbon intensity must outpace growth in population and income. The IPCC Fourth Assessment Report shows that from 1970 to 2004, falls in energy intensity offset only part of the rise from population and income.

Common mistakes

Treating the identity as a model that explains causes; it only decomposes.
Adding growth rates when they are large, instead of multiplying.
Mixing primary and final energy in the energy intensity.
Using these defaults as real statistics for a specific country.

Keep in mind: The projection holds all four growth rates constant, which real economies do not. Use official statistics (for example IEA or World Bank) for real analysis.

Frequently asked questions

Is the Kaya identity a model?

No. It is an exact identity that helps organise the drivers of emissions.

Why are the growth rates multiplied?

Because emissions are the product of the four factors.

Does it include non-energy emissions?

No. It covers CO₂ from energy use only.

Which factor is easiest to change?

Policies usually target energy intensity (efficiency) and carbon intensity (cleaner energy).

Sources: IPCC Fourth Assessment Report, Working Group III (2007), section 1.3.1.2 "Intensities"

Checked 9 Nov 2026. IPCC Fourth Assessment Report, Working Group III (2007), §1.3.1.2 “Intensities”: Kaya identity (Kaya, 1990) and the 1970–2004 decomposition (population +1.6%/yr, GDP per capita +1.8%/yr, energy intensity −1.2%/yr, carbon intensity −0.2%/yr).

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