This week, Volkswagen admitted that it had secretly rigged as many as 11 million diesel cars worldwide so that their pollution controls only worked when they were being tested by regulators. The rest of the time, while the cars were actually being driven, they emitted smog-forming nitrogen oxides at 15 to 35 times higher than the US legal limit.

So how much extra pollution is Volkswagen's deception responsible for? And, since we know air pollution is harmful, how many additional deaths could those extra emissions cause? What follows is a very rough, back-of-the-envelope estimate based on what we know so far. (Spoiler: the premature death numbers range from single digits to hundreds per year. Like I said, it's rough.)

1) How much extra pollution do Volkswagen's cars cause? By my calculations, Volkswagen's 482,000 problematic US cars are currently emitting between 5,800 to 14,200 additional tons of nitrogen oxide pollution (NOx) each year, assuming the cars are driven the US average.* This is over and above the pollution the cars would have emitted if Volkswagen had adhered to the legal limit.

Extrapolating that to 11 million cars around the world, and assuming the rest of the cars are driven the European average, we get somewhere between 86,800 and 212,500 additional tons of NOx emissions per year.**

Now, there are lots of assumptions and simplifications embedded in those estimates, particularly around how many miles VW's cars are actually driven. But that's ... potentially a large amount of extra NOx pollution. At the high end globally, it's 20 times what a typical coal plant without emission controls puts out in a year.

2) How many deaths might that extra pollution cause? We know NOx pollution is harmful — current emissions from all the world's cars, trucks, factories, and power plants already cause various health ailments and contribute to thousands of deaths each year. What we're interested in is the additional toll caused by Volkswagen's illegal pollution.

This is a bit trickier to calculate. Certain types of nitrogen oxides are harmful both both because they can irritate the lungs and because they can help form damaging particulate pollution and smog. Higher smog levels have been linked to respiratory illnesses, increased asthma attacks, and even premature deaths (especially among the sick or elderly). The complicated part is that the exact levels of smog formation can vary from place to place, depending on sunlight, temperature, local winds, and other factors. What's more, the exact harm can depend on where the pollution occurs, how dense the area is, and so on.

Still, we can get ballpark figures using data from the Environmental Protection Agency, which calculates that every ton of NOx from vehicles in the United States leads to somewhere between 0.00085 and 0.0019 premature deaths. (Note that this only includes impacts from particulate formation, not smog effects, which are harder to quantify. See p. 40 of this report.)

Using these figures, the extra pollution from Volkswagen's US cars can be expected to lead to an additional 5 to 27 premature deaths per year. If we extrapolated worldwide to all 11 million vehicles, that would come to somewhere between 74 and 404 premature deaths each year.***

Again, this is a back-of-the-envelope exercise, not a peer-reviewed scientific analysis. Criticisms and refinements are welcome. But the broader point is that air pollution can cause real harm, up to and including killing people. The United States and Europe have been trying to limit that health damage over the last 50 years by putting pollution limits in place. And, by evading those limits, Volkswagen's actions had tangible consequences.

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(As counterpoint, Volkswagen's cheating might have been mildly helpful for global warming efforts. The company appears to have rigged the cars so that they would get slightly better fuel economy. And NOx emissions can have an indirect cooling effect. That said, this effect is likely to be smaller in the grand scheme of things. And this really isn't the way to go about solving climate change...)

Footnotes and updates:

* Here's how I estimate US pollution: the current Tier2-Bin5 lifetime standard for NOx emissions in the United States is 0.07 grams per mile driven. Testing by the ICCT has said Volkswagen's 482,000 clean diesel cars in the United States were emitting NOx at 15 to 35 times that standard, depending on how they were driven. And the average US car is driven 11,244 miles in a year. So multiply those numbers together, subtract out the "legal" pollution, convert to tons, and you get your range of additional pollution caused by VW's cars.

(Note that this estimate is for the current fleet. VW's cars obviously weren't sold all at once, so the pollution impact gets smaller the further back you go in the past.)

** For the global figures, I'm assuming the pollution controls in the remaining 10.5 million Volkswagen diesel cars with a Type EA 189 engine worked the same way and produced similar levels of additional pollution. I've updated this section by also assuming the rest of the cars were driven the European average of around 7,170 miles per year (since most of them were likely in Europe). That lowered the global pollution estimates from an earlier version.

*** This global estimate of health impacts might well be low, since a simple extrapolation from US data isn't ideal. The World Health Organization's research suggests that NOx pollution can have even higher mortality effects in some parts of Europe (due to higher population density), but we'd really have to know where the rest of Volkswagen's 11 million problematic diesel cars are being driven to get any more precise.

Further reading: Volkswagen's appalling clean diesel scandal, explained