Radiative Forcing Calculator Formula

Understand the math behind the radiative forcing calculator. Each variable explained with a worked example.

Formulas Used

Radiative Forcing

delta_f = 5.35 * log(co2_final / co2_initial)

Variables

VariableDescriptionDefault
co2_initialInitial CO2 Concentration(ppm)280
co2_finalFinal CO2 Concentration(ppm)420

How It Works

Radiative Forcing from CO2

Radiative forcing measures the change in energy balance at the top of the atmosphere caused by a change in CO2 concentration.

Formula

Delta F = 5.35 x ln(C / C0) W/m²

Where C is the new concentration and C0 is the reference (pre-industrial) concentration. The natural logarithm reflects the diminishing absorption effect as CO2 levels rise.

Worked Example

CO2 has risen from 280 ppm (pre-industrial) to 420 ppm (current).

co2_initial = 280co2_final = 420
  1. 01Ratio = 420 / 280 = 1.5
  2. 02ln(1.5) = 0.4055
  3. 03Delta F = 5.35 x 0.4055 = 2.169 W/m²

Frequently Asked Questions

What is radiative forcing?

Radiative forcing is the difference between incoming solar energy absorbed by the Earth and energy radiated back to space, measured in watts per square meter.

Why is the relationship logarithmic?

As CO2 increases, the absorption bands become saturated. Each additional molecule of CO2 has a slightly smaller warming effect, producing a logarithmic curve.

What does 2 W/m² mean in practical terms?

A forcing of 2 W/m² roughly corresponds to about 1.5 degrees Celsius of eventual warming once the climate reaches equilibrium.

Ready to run the numbers?

Open Radiative Forcing Calculator