I wanted to understand the relationship between particulate matter measurements (PM2.5) and the U.S. air quality index (AQI). Update: [2024-09-19] The US changed their AQI mapping in 2024, so I've updated the chart.

The formula is on wikipedia, defined as a piecewise linear function. But it's weird that the slope isn't monotonic! It started at 4.2, then drops to 2.1, but goes up to 2.5, then drops to 0.5, then goes up to 1.0, then back down to 0.66. In 2024 it changed to 5.5, drops to 1.8, goes up to 2.5, then drops to 0.7, then goes up to 1.0, then up again to 2.0. Weird!

Also see this article from smartairfilters.com that goes into more detail and also suggests using µg/m³ instead of AQI. The definition of AQI varies across countries! For example, 250 µg/m³ is considered AQI 400 in India but AQI 300 in the U.S. until 2024, and AQI 350 after 2024.