Forçante radiativa GHG

ΔF = 5.35 × ln(C/C₀) W/m².
Created by
Renato Passos, Eng. de Software
Reviewed by
Renato Passos, Eng. de Software

Last updated: Apr 18, 2026

ΔF (W/m²)
2,17

Formula

5.35 × ln(C/C₀)

About this calculator

The GHG radiative forcing calculator estimates the energy imbalance (ΔF) in the climate system caused by changes in atmospheric CO₂ concentrations. It uses the formula ΔF = 5.35 × ln(C/C₀), where C is current CO₂ concentration and C₀ is the reference value. This logarithmic relationship reflects how each additional molecule of CO₂ contributes diminishing warming, a key principle in climate science.

The equation is derived from IPCC studies showing that climate warming grows logarithmically with CO₂. For instance, doubling CO₂ from 280 ppm to 560 ppm causes a ΔF of ~3.7 W/m², while doubling it again to 1120 ppm adds only ~2.2 W/m². This diminishing return effect is critical for understanding long-term climate impacts of emissions.

This tool is valuable for scientists, engineers, and environmental managers assessing historical emissions or forecasting scenarios. However, the formula applies specifically to CO₂. Other greenhouse gases (like CH₄ or N₂O) require different equations due to varying radiative efficiencies and atmospheric lifetimes. Always validate results with comprehensive climate models for real-world applications.

Before using the calculator, ensure C and C₀ values are in compatible units (e.g., ppm or ppb). Note that ΔF is a theoretical estimate and does not account for complex climate feedbacks like albedo changes or emissivity shifts. Combine this tool with advanced climate models for holistic analyses.

Frequently asked questions

What is radiative forcing?

It's the difference between incoming solar energy and outgoing thermal energy, measured in W/m². It represents the climate system's energy imbalance caused by greenhouse gases.

Why does the formula use a natural logarithm?

Each additional CO₂ molecule contributes less to warming than the previous one. The logarithm captures this diminishing return effect, validated by IPCC studies.

Can I use this calculator for gases other than CO₂?

No. This formula is CO₂-specific. Methane (CH₄) and nitrous oxide (N₂O) require different equations due to their unique radiative properties.

How should I interpret the ΔF result?

A positive ΔF indicates additional warming. For example, ΔF = 3.7 W/m² corresponds to roughly 1°C of global average warming after decades of climate adjustment.

Do I need historical CO₂ data to use this tool?

Yes. Compare current concentration (C) with a reference value (C₀), typically pre-industrial levels (280 ppm) or a specific year of interest.

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