What this calculator does
The Kaya identity splits total CO₂ emissions into four factors multiplied together: how many people there are, how much output each produces, how much energy that output takes, and how much carbon that energy carries. It is an identity rather than a model, meaning it is true by construction, because the units cancel to leave emissions.
Its value is in showing where change can come from. Emissions fall only if one factor falls faster than the others rise, and since population and income per head are both generally rising, that leaves energy intensity and carbon intensity to do the work. Halving carbon intensity halves emissions, holding everything else fixed.
The formula
The four inputs are multiplied together. Population times GDP per capita gives total output. Multiplying by energy intensity, the energy needed per unit of output, gives total energy. Multiplying by carbon intensity, the CO₂ released per unit of energy, gives total emissions. The result is converted to gigatonnes a year and divided back by population for the per capita figure.
| Term | Meaning |
|---|---|
| P | Population. |
| GDP per capita | Economic output per person, the income factor. |
| Energy intensity | Energy used per unit of GDP, in megajoules per dollar. Falls as an economy becomes more efficient or shifts away from heavy industry. |
| Carbon intensity | CO₂ released per unit of energy, in kilograms per megajoule. Falls as generation shifts away from fossil fuels. |
The inputs explained
| Field | What to enter |
|---|---|
| Population | Population, global or for a single country. |
| GDP per capita ($/person) | GDP per capita in dollars. Use the same basis, nominal or purchasing-power, consistently. |
| Energy intensity of GDP (MJ/$) | Energy intensity in megajoules per dollar of GDP. |
| Carbon intensity of energy (kg CO₂/MJ) | Carbon intensity in kilograms of CO₂ per megajoule of energy. |
When to use it
Testing what a decarbonisation target requires
Setting the emissions figure you want and working backwards shows what carbon intensity would have to fall to, which is usually a more concrete statement of a target than a percentage.
Comparing two countries
Two countries with similar emissions can arrive there very differently, one through a large population at low income and another through high income at low carbon intensity. The decomposition makes that visible.
Understanding why efficiency gains get absorbed
A fall in energy intensity offset by a rise in income per head leaves emissions flat. Running both changes together shows how large an efficiency gain has to be to actually reduce the total.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How much does carbon intensity move total emissions?
The other three factors held fixed while the carbon intensity of energy falls.
| Carbon intensity | CO₂ emissions | Emissions per capita | Energy use per capita |
|---|---|---|---|
| 0.02 kg CO₂/MJ | 9.60 Gt/year | 1.20 t/person/year | 60.0 GJ/person/year |
| 0.04 kg CO₂/MJ | 19.20 Gt/year | 2.40 t/person/year | 60.0 GJ/person/year |
| 0.06 kg CO₂/MJ | 28.80 Gt/year | 3.60 t/person/year | 60.0 GJ/person/year |
| 0.08 kg CO₂/MJ | 38.40 Gt/year | 4.80 t/person/year | 60.0 GJ/person/year |
Questions
Is the Kaya identity a model or a fact?
A fact, in the sense that it is an accounting identity. The units cancel, so the product of the four factors is emissions by definition and cannot be wrong. What it does not do is say anything about how the factors influence each other, which is where the actual difficulty lies.
Which factor matters most?
Arithmetically all four are equal, since a 10% change in any of them moves emissions by 10%. In practice they differ enormously in how easily they can be changed. Population and income per head are not policy levers in any acceptable sense, which leaves energy intensity and carbon intensity carrying the whole burden.
What does carbon intensity of energy actually mean?
How much CO₂ is released per unit of energy delivered. Coal is the highest of the common sources, gas roughly half of coal, and nuclear and renewables close to zero in operation. Shifting the mix is what moves this number, which is why it is the factor most directly targeted by energy policy.
Can I use this for one country rather than globally?
Yes, the identity holds at any scale. Be careful with energy and carbon intensity for a single country, though, since emissions embodied in imported goods are counted where they were produced rather than where they are consumed, which can flatter a country that has moved its heavy industry offshore.
For the output of a single renewable installation, see the wind turbine power calculator or the hydroelectric power calculator.