Equilibrium Climate Sensitivity (ECS) Calculator

ECS is the expected long-term global mean surface warming, in degrees C, after the climate system reaches a new equilibrium following a doubling of atmospheric CO2 concentration. It captures the full response of the climate system, including slow feedbacks like deep ocean heat uptake, not just the immediate warming.

IPCC AR6 (2021) states a likely range of 2.5 to 4 degrees C, with a best estimate of about 3 degrees C. This is narrower than the long-standing 1.5 to 4.5 degree C range used since the 1970s, reflecting improved evidence from paleoclimate data, historical warming, and climate model ensembles.

Delta T_eq = ECS x ln(C / C0) / ln(2), where C0 is a baseline CO2 concentration and C is the current or target concentration. This is the standard simplified logarithmic relationship, referenced to a full CO2 doubling (ratio of 2), used throughout introductory and applied climate science.

A CO2 doubling means the atmospheric CO2 concentration becomes twice a chosen baseline, most often the pre-industrial value of about 280 ppm, giving about 560 ppm. Climate scientists use doubling as the standard reference point because radiative forcing from CO2 follows a logarithmic relationship, so a doubling always produces the same forcing increase (about 3.7 W/m squared) regardless of the starting concentration.

ECS is the full equilibrium warming after the climate system fully adjusts, which can take centuries because of ocean thermal inertia. TCR is the warming realized at the moment CO2 reaches double its baseline under a gradual 1 percent per year increase, before the ocean has caught up, and is always smaller than ECS, typically by roughly 30 to 40 percent.

When C equals C0, the ratio C / C0 is exactly 1, and the natural logarithm of 1 is 0. In Find Warming mode this correctly gives zero warming; in Find ECS mode it would require dividing by zero to solve for ECS, which is mathematically undefined, so the calculator asks for a different concentration value.

You can enter observed warming as the equilibrium warming input, but the result will be an overestimate of the true long-term ECS, because observed warming so far is transient (TCR-like), not equilibrium warming. The climate system has not yet fully responded to today's CO2 level due to ocean thermal inertia, so use this mode with that caveat in mind.

The forcing from a CO2 doubling (about 3.7 W/m squared) is well constrained by physics, but ECS also depends on feedback processes, cloud response, water vapor, ice-albedo changes, and ocean heat uptake, which are harder to measure precisely and vary across climate models and paleoclimate reconstructions, producing the IPCC's stated range rather than a single exact number.

No. ECS is explicitly a long-term equilibrium concept; it can take centuries for the full ECS-implied warming to be realized because the deep ocean absorbs heat slowly. The related but distinct transient climate response (TCR) describes warming realized on a shorter, multi-decade timescale.

A common convention is C0 = 280 ppm (the pre-industrial baseline) and C = a current or future scenario concentration, such as roughly 420 ppm for the mid-2020s or 560 ppm for a full doubling. You can also use any two concentrations relevant to a specific comparison you are making.

Yes, in structure. The commonly cited CO2 radiative forcing formula, Delta F = 5.35 x ln(C / C0), and this ECS-based warming formula both use the same logarithmic dependence on the CO2 concentration ratio, because equilibrium warming is proportional to radiative forcing through the climate sensitivity parameter.