# Carbon dioxide equivalent

Carbon dioxide equivalent (CDE) and equivalent carbon dioxide (CO
2
e
and CO
2
eq
) are two related but distinct measures for describing how much global warming a given type and amount of greenhouse gas may cause, using the functionally equivalent amount or concentration of carbon dioxide (CO
2
) as the reference.

## Global warming potential

Carbon dioxide equivalency is a quantity that describes, for a given mixture and amount of greenhouse gas, the amount of CO
2
that would have the same global warming potential (GWP), when measured over a specified timescale (generally, 100 years). Carbon dioxide equivalency thus reflects the time-integrated radiative forcing of a quantity of emissions or rate of greenhouse gas emission—a flow into the atmosphere—rather than the instantaneous value of the radiative forcing of the stock (concentration) of greenhouse gases in the atmosphere described by CO
2
e.

The carbon dioxide equivalency for a gas is obtained by multiplying the mass and the GWP of the gas. The following units are commonly used:

• By the UN climate change panel IPCC: n×109 tonnes of CO2 equivalent (GtCO2eq).
• In industry: million metric tonnes of carbon dioxide equivalents (MMTCDE).
• For vehicles: g of carbon dioxide equivalents / km (gCDE/km).

For example, the GWP for methane over 100 years is 34 and for nitrous oxide 298. This means that emissions of 1 million metric tonnes of methane and nitrous oxide respectively is equivalent to emissions of 34 and 298 million metric tonnes of carbon dioxide.

## Equivalent carbon dioxide

Equivalent CO
2
(CO
2
e) is the concentration of CO
2
that would cause the same level of radiative forcing as a given type and concentration of greenhouse gas. Examples of such greenhouse gases are methane, perfluorocarbons, and nitrous oxide. CO
2
e is expressed as parts per million by volume, ppmv.

CO
2
e calculation examples:
• The radiative forcing for pure CO
2
is approximated by $RF=\alpha \ln(C/C_{0})$ where C is the present concentration, $\alpha$ is a constant, 5.35, and $C_{0}$ is the pre-industrial concentration, 280 ppm. Hence the value of CO
2
e for an arbitrary gas mixture with a known radiative forcing is given by $C_{0}\exp(RF/\alpha )$ in ppmv.
• To calculate the radiative forcing for a 1998 gas mixture, IPCC 2001 gives the radiative forcing (relative to 1750) of various gases as: CO
2
=1.46 (corresponding to a concentration of 365 ppmv), CH4=0.48, N2O=0.15 and other minor gases =0.01 W/m2. The sum of these is 2.10 W/m2. Inserting this to the above formula, we obtain CO
2
e = 412 ppmv.
• To calculate the CO
2
e of the additional radiative forcing calculated from April 2016's updated data: ∑ RF(GHGs) = 3.3793, thus CO
2
e = 280 e3.3793/5.35 ppmv = 526.6 ppmv.