How the AQI turns a concentration into one number
The Air Quality Index is a piecewise linear scale. EPA publishes a breakpoint table for each pollutant, and every row pairs a concentration range with an index range. To convert a reading, you find the row it falls in and interpolate: AQI = (Ihi - Ilo) / (Chi - Clo) x (C - Clo) + Ilo, then round to the nearest whole number.
Before any math, the concentration is truncated, not rounded: ozone to three decimals in ppm, PM2.5 and CO to one decimal, and PM10, SO2 and NO2 to whole numbers. EPA's own worked example shows why this matters. An 8-hour ozone average of 0.07853 ppm is cut to 0.078, which lands in the 0.071 to 0.085 row (AQI 101 to 150). The result is 49 / 0.014 x 0.007 + 101 = 125.5, reported as 126.
When several pollutants are measured, each gets its own sub-index and the highest one becomes the reported AQI. In the same EPA example, PM2.5 at 35.9 gives 102 and CO at 8.4 ppm gives 90, so the day is reported as AQI 126 with ozone as the main pollutant. The index is not an average, which is why one bad pollutant can push a whole city into orange.