Transient Climate Response (TCR) Calculator
Calculate the warming realized at the time of CO2 doubling using Transient Climate Response (TCR), and compare it against the larger, slower ECS-based equilibrium warming.
📈 What is Transient Climate Response (TCR)?
Transient Climate Response (TCR) is the global mean surface warming realized at the exact moment atmospheric CO2 concentration reaches double its starting value, under an idealized scenario where CO2 rises gradually at about 1 percent per year. It is a "realized now" measure of warming, capturing what the climate system has actually delivered at the surface by the time of doubling, rather than the larger warming still working its way through the ocean.
Climate scientists use TCR to project near-term and mid-century warming under realistic, gradually rising emissions pathways, to compare climate models against each other on a common, well-defined metric, to translate a projected future CO2 concentration into an expected near-term temperature response, and to explain why the climate keeps warming for decades after emissions level off. It appears throughout the IPCC assessment reports alongside its slower-responding companion metric, Equilibrium Climate Sensitivity (ECS).
The most important and most commonly confused distinction in climate science is TCR versus ECS. TCR is always smaller than ECS. Equilibrium Climate Sensitivity is the eventual warming once the entire climate system, including the deep ocean, has fully caught up to a doubled and then held-fixed CO2 level, a process that takes centuries. TCR captures only the warming realized by the time of doubling itself, before that slow ocean response has finished. IPCC AR6 puts TCR's best estimate at about 1.8 degrees Celsius, versus about 3.0 degrees Celsius for ECS, roughly 60 percent larger.
This calculator lets you compute TCR-based warming directly from any CO2 concentration change, and, unlike a TCR-only calculator, shows the ECS-based equilibrium warming for the identical CO2 change side by side, so the size of the gap between "warming realized so far" and "warming still to come" is concrete rather than abstract.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — Present-Day CO2 vs Pre-industrial
TCR = 1.8°C, ECS = 3.0°C, C0 = 280 ppm (pre-industrial), C = 421 ppm (mid-2020s level)
Example 2 — A Full CO2 Doubling at Best-Estimate Values
TCR = 1.8°C, ECS = 3.0°C, C0 = 280 ppm (pre-industrial), C = 560 ppm (double pre-industrial)
Example 3 — IPCC AR6 Lower-Bound Likely Range at Doubling
TCR = 1.4°C (likely-range lower bound), ECS = 2.5°C (likely-range lower bound), C0 = 280 ppm, C = 560 ppm
❓ Frequently Asked Questions
🔗 Related Calculators
What is Transient Climate Response (TCR)?
Transient Climate Response is the global mean surface warming realized at the moment atmospheric CO2 concentration reaches double its starting value, under a scenario where CO2 rises gradually at about 1% per year. It captures the warming the climate system has actually delivered by that point, not the larger warming still to come as the ocean keeps absorbing heat.
How is TCR different from ECS (Equilibrium Climate Sensitivity)?
TCR is the warming realized at the time of CO2 doubling, while ECS is the eventual warming once the entire climate system, including the deep ocean, reaches a new equilibrium after CO2 doubles and then stays fixed. ECS is always larger than TCR because the ocean takes centuries to fully respond to a forcing change; IPCC AR6 estimates put TCR's best estimate at about 1.8 degrees Celsius versus ECS's best estimate of about 3.0 degrees Celsius.
What formula does this calculator use?
It uses dT = TCR x ln(C / C0) / ln(2), where C is the current or target CO2 concentration in ppm, C0 is a reference concentration (typically 280 ppm, the pre-industrial level), and TCR is in degrees Celsius. The same formula with ECS substituted for TCR gives the eventual equilibrium warming for comparison.
Why does the formula use a logarithm of the CO2 ratio?
CO2's warming effect is logarithmic rather than linear because its main infrared absorption bands are already partly saturated at current concentrations, so each further increase in concentration produces a smaller additional forcing. Scaling TCR or ECS by ln(C/C0) divided by ln(2) means the formula returns exactly TCR (or ECS) at a full doubling, and scales proportionally for partial or multiple doublings.
What is the IPCC AR6 best estimate and likely range for TCR?
IPCC AR6 gives a best estimate for TCR of about 1.8 degrees Celsius, with a likely (66% confidence) range of 1.4 to 2.2 degrees Celsius. This calculator defaults to 1.8 degrees Celsius but lets you test the full likely range.
Why is TCR always smaller than ECS?
The ocean has enormous heat capacity and mixes slowly, so when CO2 rises it takes centuries for the deep ocean to fully absorb its share of the resulting energy imbalance. TCR captures only the warming realized by the time of doubling itself, while ECS captures the full eventual warming once that ocean heat uptake process is complete, which is mathematically and physically always a larger number.
Does this calculator account for other greenhouse gases besides CO2?
No. Like the standard TCR and ECS definitions, this calculator isolates the CO2-driven warming component using the logarithmic CO2-to-forcing relationship. Real-world observed and projected warming also includes methane, nitrous oxide, aerosols, and other forcings, each with different behavior.
What does the gap between the TCR-based and ECS-based results mean?
That gap represents warming that is already committed by a given CO2 level and its associated forcing, but has not yet fully appeared at the surface because the ocean has not finished responding. Climate scientists sometimes call this committed or pipeline warming, and it is one reason observed warming can continue to rise even if CO2 concentration were held constant.
Can I use this calculator for CO2 levels that aren't exactly double the reference?
Yes. The formula works for any ratio of C to C0, not just a factor of 2. Enter any reference concentration C0 and any current or target concentration C, and the calculator scales the TCR-based and ECS-based warming proportionally using the logarithmic relationship, exact at a doubling and interpolated smoothly elsewhere.
Is TCR-based warming the same as what we are currently observing?
It is a reasonable approximation for the type of gradual, steadily rising CO2 pathway TCR was designed to represent, but actual observed historical warming also reflects other forcings (methane, aerosols, solar and volcanic variability) and a CO2 growth rate that has not been a constant 1% per year throughout the industrial era, so real observed warming will not match the TCR-only calculation exactly.
Where do the default TCR and ECS values come from?
Both default to the IPCC AR6 Working Group I best estimates: 1.8 degrees Celsius for TCR and 3.0 degrees Celsius for ECS. Both parameters carry meaningful scientific uncertainty and are reported as likely ranges (1.4 to 2.2 degrees Celsius for TCR, 2.5 to 4.0 degrees Celsius for ECS) rather than single fixed numbers, so treat any single-number output here as a central estimate, not an exact prediction.
Why does the calculator let me edit ECS if this is a TCR calculator?
Editing ECS alongside TCR makes the distinction between the two concrete: for the same CO2 change, you can see exactly how much larger the eventual equilibrium warming is compared to the warming already realized. This side-by-side view is the clearest way to understand why TCR and ECS are two genuinely different, commonly confused climate metrics.