CO₂ Radiative Forcing and Climate Sensitivity Calculator
The extra heating a change in carbon dioxide concentration puts on the climate, in W/m², and the warming it commits to once the climate settles, for a chosen climate sensitivity.
Results
The dashed line marks the value you entered.
What this tool does
The warming effect of CO₂ grows with the logarithm of its concentration: ΔF = 5.35 ln(C ÷ C₀) W/m², so each doubling adds the same 3.7 W/m² whatever the starting level. Climate sensitivity — the eventual warming for one doubling — has a best estimate near 3 °C, with a likely range of about 2.5 to 4 °C in the IPCC's latest assessment. Going from 280 ppm to 420 ppm is about 0.58 of a doubling. The result is the equilibrium warming: oceans take decades to catch up, and other gases and aerosols also matter, so the warming seen to date is not the same number.
Formula
ΔF = 5.35 ln(C ÷ C₀) W/m² · ΔT = S × log₂(C ÷ C₀) (equilibrium)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
c0 | CO₂ concentration at the start (about 280 ppm before industry) | ppm |
cf | CO₂ concentration at the end | ppm |
cs | Climate sensitivity per doubling of CO₂ (best estimate about 3 °C) | °C |
DF | Extra heating of the climate (radiative forcing) | W/m² |
DT | Eventual warming once the climate settles | °C |
ND | Doublings of CO₂ | — |
F2 | Forcing from one doubling | W/m² |
LA | Sensitivity per W/m² | °C |
Worked example
- CO₂ concentration at the start (about 280 ppm before industry)280 ppm
- CO₂ concentration at the end420 ppm
- Climate sensitivity per doubling of CO₂ (best estimate about 3 °C)3 °C
- Extra heating of the climate (radiative forcing)2.17 W/m²
- Eventual warming once the climate settles1.75 °C
- Doublings of CO₂0.585
- Forcing from one doubling3.71 W/m²
- Sensitivity per W/m²0.809 °C
Limitations
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.
- The default values are typical reference figures, not measurements of your situation. Replace them with your own data whenever you have it.