Issue 047 - Climate - Vehicle-emissions equivalence
How many cars would produce the same carbon emissions as Indonesia's wildfires?
Reuters reported that Indonesia's unusually intense wildfire season released about 17.1 million metric tons of carbon in seven days, roughly 429% above the seasonal average.
The problem
Estimate how many average gasoline-powered U.S. cars driven for one year would produce the same amount of carbon emissions as those Indonesian fires produced in seven days.
Then estimate what fraction of the entire U.S. passenger-vehicle fleet's annual emissions that represents.
You'll need to estimate annual driving or fuel use, fuel economy, gasoline burned per car, and how much carbon is released when gasoline is burned. You can reason directly in carbon or convert through CO2.
Because Fermi problems target an order of magnitude, I normally use no more than two significant digits and write most calculations in scientific notation; the Fermi reference explains both conventions.
Before checking sources
Matt's first pass
First, I assumed there is about one household per 2.5 people in the U.S. and about 1.5 vehicles per household. Starting with a U.S. population of about 330 million, that gives about 130 million households and about 200 million vehicles.
U.S. households ~= 3.3 x 10^8 people / 2.5 people/household
~= 1.3 x 10^8 households
U.S. vehicles ~= 1.5 vehicles/household x 1.3 x 10^8 households
~= 2.0 x 10^8 vehiclesNext, I assumed the average vehicle refuels about once weekly and the average fill-up is about 14 gallons. I converted that to about 56 liters, then simplified gasoline mass to about 1 kg/L.
gasoline per car per week ~= 14 gallons ~= 56 L
gasoline mass per week ~= 56 kg
gasoline mass per year ~= 56 kg/week x 52 weeks/year
~= 2.9 x 10^3 kg/yearIf gasoline is roughly four parts carbon and one part hydrogen by mass, then the carbon component of burned fuel is about 80% of the fuel mass.
carbon per car-year ~= 0.8 x 2.9 x 10^3 kg fuel/year
~= 2.3 x 10^3 kg C/yearThe fires released about 17.1 million metric tons of carbon, or 1.71 x 10^10 kg C. Dividing by my per-car estimate:
car-years equivalent
~= 1.71 x 10^10 kg C / 2.3 x 10^3 kg C/car-year
~= 7.4 x 10^6 carsSo my first answer was about 7.4 million cars worth of annual carbon emissions. If the U.S. has about 200 million vehicles, that is about 3.7% of the fleet's annual carbon emissions.
Calibration Score
Matt's Calibration Score: 70 / 100
Higher is better: earn points for accurate pegs, sound models, correct math, and a result close to the sourced answer. The image shows percent full of it: 100 minus the Calibration Score.
Pegs: 10/30. The vehicle count was low, gasoline density was high, and weekly fuel use was high, but the carbon fraction was strong and the errors were not catastrophic.
Model: 30/30. Building annual carbon per vehicle from fuel use and dividing the fire-carbon total by that value is exactly the right model.
Math: 10/10. The arithmetic was clean given the assumptions.
Result: 20/30. The final answer was about half the corrected answer, easily within one order of magnitude.
Grounding facts
Copernicus wildfire-emissions reporting is usually given as carbon mass, not CO2 mass. To convert carbon to CO2, multiply by 44/12 ~= 3.7. So 17.1 million metric tons C is about 63 million metric tons CO2.
EPA uses about 8.89 kg CO2 per gallon of gasoline. Since carbon is 12/44 of CO2 by mass, that is about 2.4 kg carbon per gallon.
FHWA's 2024 highway table gives about 271 million light-duty vehicles, about 10,800 miles per light-duty vehicle, and about 460 gallons per light-duty vehicle per year. As a memory peg, that is roughly 10 gallons/week.
After checking sources
Check and recalibrate
Use the gasoline route first:
average gasoline per vehicle ~= 4.6 x 10^2 gallons/year
carbon per gallon gasoline ~= 2.4 kg C/gallon
carbon per vehicle-year
~= 4.6 x 10^2 gallons/year x 2.4 kg C/gallon
~= 1.1 x 10^3 kg C/yearNow compare with the wildfire estimate:
Indonesia fire carbon ~= 17.1 million metric tons C
~= 1.71 x 10^10 kg C
car-years equivalent
~= 1.71 x 10^10 kg C / 1.1 x 10^3 kg C/car-year
~= 1.6 x 10^7 carsA clean Fermi answer is therefore about 10 to 20 million average gasoline cars driven for one year. Using EPA's annual passenger-vehicle CO2 number gives the same neighborhood: about 4.3 metric tons CO2e per vehicle-year, or about 1.2 metric tons carbon per vehicle-year, which gives about 14 million vehicle-years.
For the U.S. fleet share:
fleet share ~= 1.4 x 10^7 vehicle-years / 2.7 x 10^8 vehicles
~= 5 x 10^-2
~= 5%So one week of these fires was roughly comparable to the annual carbon emissions of about 5% of the U.S. light-duty vehicle fleet.
Another useful weekly comparison: if a U.S. car burns about 10 gallons/week, it emits about 10 x 2.4 ~= 24 kg C/week. Across roughly 270 million light-duty vehicles, that is about 6 to 7 million metric tons C/week. The Indonesian fires released about 2.5 times that amount in the same week.
Post-check reflection
Matt's reflection
I'm pretty happy with this one. Vehicle count was low, mostly because I used 1.5 vehicles per household and the better fleet peg is closer to 270 million light-duty vehicles. I also simplified gasoline mass to 1 kg/L when it should be closer to 0.75 kg/L, and 10 gallons per week is an easier and better memory peg than 14 gallons per week.
The carbon fraction was good, and my final answer was about half of what it should have been, so it was well within an order of magnitude. The fleet-share estimate was also pretty close.
Ultimately, the wildfires are pumping a lot of carbon into the atmosphere: roughly the amount that 5% of the U.S. vehicle fleet emits in a year, released in a single week.
The weekly comparison is even sharper. If every U.S. passenger vehicle emits around 24 kg of carbon per week, the whole U.S. light-duty fleet emits about 6 to 7 million metric tons of carbon per week. That means the Indonesian fires put about 2.5x as much carbon into the atmosphere in a week as the entire U.S. light-duty vehicle fleet did in that same time period.
Recommended memory peg
For gasoline-car carbon problems, remember 1 gallon gasoline emits about 8.9 kg CO2, or 2.4 kg carbon. A typical U.S. light-duty vehicle burns about 500 gallons/year, so it emits about 1 metric ton of carbon per year. Also remember carbon to CO2: multiply by 44/12 ~= 3.7.
Reader results
Bars show how submitted estimates sort into the answer choices from the gut-check prompt.