Climate Model Interpreter Calculator
Temperature and radiative forcing from greenhouse gas concentrations using Myhre et al. formulas.
About this calculator
This calculator applies the standard radiative forcing formulas climate scientists use to translate greenhouse gas concentrations into a warming estimate. CO2's forcing follows the well-established logarithmic relationship from Myhre, Highwood, Shine & Stordal, "New estimates of radiative forcing due to well mixed greenhouse gases," Geophysical Research Letters, 1998, ΔF = 5.35 × ln(C/C₀) — logarithmic because each additional CO2 molecule contributes progressively less extra warming as the atmosphere becomes more saturated at CO2's absorption wavelengths. Methane and nitrous oxide instead follow square-root relationships (simplified versions of the same paper's formulas), reflecting their different absorption behavior.
The three gases' forcings are summed, then converted to a temperature response using the climate sensitivity parameter λ = ECS / F₂ₓ, where F₂ₓ (≈3.7 W/m²) is the forcing produced by doubling CO2 and ECS is the equilibrium climate sensitivity you set — IPCC AR6 Working Group I's best estimate, from its 2021 Physical Science Basis report, is 3°C per doubling, with a likely uncertainty range of roughly 2.5-4°C. The equilibrium warming figure is what temperatures would eventually reach if forcing held steady long enough for the whole climate system, oceans included, to catch up; because the deep ocean absorbs heat slowly, only about 60% of that warming shows up in the near term (the transient response), with the remainder as "committed" warming still working its way through the system over decades. This calculation deliberately omits other forcings — aerosols, land-use change, and non-CO2/CH4/N2O gases — so it will read lower than full climate-model output; use it to build intuition about how concentration changes translate into forcing and temperature, not as a substitute for a coupled climate model.
Inputs
Results
Equilibrium warming (°C)
2.42
Figures current as of 2021. Sources: Myhre, G., Highwood, E.J., Shine, K.P., Stordal, F. New estimates of radiative forcing due to well mixed greenhouse gases. Geophysical Research Letters. 1998;25(14):2715-2718., IPCC. Climate Change 2021: The Physical Science Basis. Working Group I Contribution to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change. Cambridge University Press, 2021.
How to Use This Calculator
- Enter current CO₂ concentration (ppm), pre-industrial CO₂ baseline, and equilibrium climate sensitivity (°C/doubling).
- Add CH₄ (ppb), N₂O (ppb), and their pre-industrial baselines.
- Review Equilibrium Warming (°C), Transient Warming (°C), and Total Radiative Forcing (W/m²).
- Compare equilibrium vs. transient warming — the committed warming is often larger than what we currently observe.
How the result changes with Pre-industrial CO2 (ppm)
| Pre-industrial CO2 (ppm) | Equilibrium warming (°C) |
|---|---|
| 180 | 4.34 |
| 210 | 3.67 |
| 400 | 0.88 |
What each input means
- CO2 concentration (ppm)
- Atmospheric CO2 in parts per million. Current level ~420 ppm (2024).
- Pre-industrial CO2 (ppm)
- Pre-industrial CO2 baseline, typically 280 ppm.
- Climate sensitivity (°C/doubling)
- Equilibrium climate sensitivity. IPCC AR6 best estimate is 3°C.
- CH4 concentration (ppb)
- Atmospheric methane in parts per billion. Current ~1,900 ppb.
- Pre-industrial CH4 (ppb)
- Pre-industrial methane baseline, typically 722 ppb.
- N2O concentration (ppb)
- Atmospheric nitrous oxide. Current ~335 ppb.
- Pre-industrial N2O (ppb)
- Pre-industrial N2O baseline, typically 270 ppb.
What each result means
- Equilibrium warming (°C)
- Long-term temperature rise once the climate system fully equilibrates.
- Transient warming (°C)
- Near-term warming accounting for ocean thermal inertia (~60% of equilibrium).
- Total radiative forcing (W/m²)
- Net energy imbalance from all specified greenhouse gases.
- CO2 forcing (W/m²)
- Radiative forcing from CO2 using ΔF = 5.35 × ln(C/C₀).
- CH4 forcing (W/m²)
- Radiative forcing from methane.
- N2O forcing (W/m²)
- Radiative forcing from nitrous oxide.
- Committed warming remaining (°C)
- Additional warming locked in but not yet realized due to ocean lag.
- CO2 × pre-industrial
- Current CO2 as a multiple of pre-industrial levels.
How this is calculated
Worked example, using the default values
- Identify Input Parameters4 parametersCO2 concentration (ppm) = 420, Pre-industrial CO2 (ppm) = 280, Climate sensitivity (°C/doubling) = 3, CH4 concentration (ppb) = 1900 = 7 input(s) provided
- Calculate Equilibrium warmingEquilibrium warming = lambda * totalForcing2.42 = 2.42
- Calculate Transient warmingTransient warming = equilibriumWarming * 0.61.45 = 1.45
- Calculate Total radiative forcingTotal radiative forcing = forcingCO2 + forcingCH4 + forcingN2O2.996 = 2.996
Figures and sources
- CO2/CH4/N2O radiative forcing formulas (1998) — Myhre, G., Highwood, E.J., Shine, K.P., Stordal, F. New estimates of radiative forcing due to well mixed greenhouse gases. Geophysical Research Letters. 1998;25(14):2715-2718.
- Equilibrium climate sensitivity best estimate (3°C, likely range 2.5-4°C) (2021) — IPCC. Climate Change 2021: The Physical Science Basis. Working Group I Contribution to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change. Cambridge University Press, 2021.
Engine last updated . Checked against 2 independently-derived tests — how we verify calculators. Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.
Frequently Asked Questions
Why does CO2 use a logarithmic formula while methane and N2O use square roots?
Each gas has its own absorption behavior in the atmosphere's infrared spectrum. CO2 already absorbs strongly across its main wavelengths, so each additional molecule adds progressively less forcing — a logarithmic (diminishing-returns) relationship, ΔF = 5.35 × ln(C/C₀). Methane and nitrous oxide are far less concentrated and haven't saturated their absorption bands the same way, so the formulas this calculator uses — from Myhre, Highwood, Shine & Stordal, Geophysical Research Letters, 1998 — model their forcing with square-root terms instead.
What does the equilibrium climate sensitivity (ECS) input actually control?
ECS sets how much eventual warming results from a doubling of CO2, and the calculator converts it into a sensitivity parameter λ = ECS / F₂ₓ (F₂ₓ ≈ 3.7 W/m² is the forcing from doubling CO2). That λ is then multiplied by the total radiative forcing from all three gases to get equilibrium warming, so raising ECS scales every temperature output proportionally — try the IPCC AR6 Working Group I best-estimate range of roughly 2.5-4°C (central estimate 3°C, from the 2021 Physical Science Basis report) to see how much that uncertainty matters.
Why is transient warming lower than equilibrium warming?
The deep ocean absorbs heat slowly, so the full temperature response to a given forcing doesn't show up immediately even if that forcing holds steady. This calculator applies a simplified 60% factor to equilibrium warming to estimate the transient (near-term) response, with the remaining 40% reported separately as "committed warming remaining" — warming that's already locked in by the current forcing but hasn't been realized yet.
Why might this calculator's warming estimate be lower than a full climate model's?
It only sums forcing from CO2, methane, and nitrous oxide. Real climate models also account for aerosols, land-use change, and other minor greenhouse gases, some of which offset warming (aerosols tend to cool) and some of which add to it. That narrower scope makes this a tool for building intuition about concentration-to-temperature relationships, not a stand-in for coupled climate model output.
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