People add about 11 billion tonnes of carbon to the carbon cycle each year. Where does it go? This is bookkeeping with numbers in scientific notation, and every number in it is measured independently.
Key idea
About 2.124 GtC of carbon added to the air raises its carbon dioxide by 1 ppm. Of the carbon people emit, a little under half (about 45%, the airborne fraction) stays in the air; the ocean and the land take up the rest. So $$\Delta\text{CO}_2\ (\text{ppm}) \approx \frac{\text{emissions (GtC)} \times 0.45}{2.124}$$
Why it works
Where does 2.124 come from? The atmosphere has a mass of about $5.1 \times 10^{18}$ kg, or about $1.8 \times 10^{20}$ moles of air. One ppm of that is $1.8 \times 10^{14}$ moles of CO₂, and each mole holds 12 g of carbon: about $2.1 \times 10^{15}$ g, which is 2.1 GtC. The sinks work because extra CO₂ in the air pushes more into the ocean (it dissolves) and speeds up plant growth. The Global Carbon Budget for 2013–2022 balances like this, in GtC a year: emissions from fossil fuels about 9.6 and from land-use change about 1.3; the air gained about 5.2, the ocean took about 2.8, and the land about 3.3.
Worked example: One year's rise
Emissions are 11 GtC in a year, and 45% stays in the air. By how many ppm does CO₂ rise?
- Carbon staying in the air: $11 \times 0.45 = 4.95$ GtC.
- In ppm: $4.95 \div 2.124 \approx 2.3$ ppm.
- Close to the measured rise of about 2.4 ppm a year in the 2010s.
Answer: About 2.3 ppm
Worked example: Tonnes of CO₂
Fossil-fuel emissions in 2023 were about 10.0 GtC. How many billion tonnes of CO₂ is that? (CO₂ has a mass of 44 for every 12 of carbon.)
- Each tonne of carbon becomes $44/12 \approx 3.67$ tonnes of CO₂ when it combines with oxygen.
- $10.0 \times 3.67 \approx 36.7$ billion tonnes of CO₂.
Answer: About 37 billion tonnes of CO₂
Common mistake
Assuming all emitted carbon dioxide stays in the air. Measurements show only a little under half does; the ocean and land take up the rest, which is why the yearly rise in ppm is less than half what emissions alone would give ($11 \div 2.124 \approx 5.2$ ppm). The carbon the ocean takes is not gone: it makes seawater more acidic. Check: emissions ÷ 2.124 should be roughly twice the measured yearly rise.