Air Quality Index Interpolation (EPA Equation 1)

Every pollutant page for the US Air Quality Index does one thing: it finds the band of the EPA's breakpoint table that holds the reading, then slides along a straight line inside that band. This page is that step on its own, written as the EPA prints it in equation 1, with the breakpoints left for you to supply. That makes it the page to use when no dedicated pollutant page exists, such as the 1-hour ozone table or the 24-hour sulphur dioxide table, and for any other national index that uses the same method.

The terms split into two groups. $BP_{Lo}$ and $BP_{Hi}$ are the concentrations at the two ends of the band, and $I_{Lo}$ and $I_{Hi}$ are the index values those ends stand for. $C$ is the reading, which must lie between the two breakpoints; if it does not, you have picked the wrong band. The fraction $\frac{I_{Hi}-I_{Lo}}{BP_{Hi}-BP_{Lo}}$ is a slope: index points gained per unit of concentration inside this one band. Multiply it by how far the reading has climbed above the lower breakpoint, $C-BP_{Lo}$, then add $I_{Lo}$. Each band has its own slope, so the whole index is a chain of straight segments, not one line. Keep $C$ in the unit of the table you are reading, truncated the way that table says.

The EPA's own examples show the pattern. An 8-hour ozone of 0.078 ppm sits between 0.071 and 0.085, in the band that runs from 101 to 150. That band holds 49 index points across 0.014 ppm, and the reading is 0.007 ppm above the bottom, so $49/0.014\times0.007+101=125.5$, which the EPA reports as 126. PM2.5 of 35.9 between 35.5 and 55.4 gives 101.984925, reported as 102. Carbon monoxide of 8.4 ppm between 4.5 and 9.4, in the 51 to 100 band, gives 90. Each reported value is the line rounded to a whole number.

The relation also runs backwards. Given an index it returns the concentration, so the 125.5 from the ozone example hands back 0.078 ppm, and it can solve for a breakpoint or an index value when the other terms are known. Because the page gives the continuous line, expect the last digit to differ from a published figure where the EPA rounds. The equation is equation 1 of the EPA's Technical Assistance Document for the Reporting of Daily Air Quality (EPA-403/B-26-003, May 2026), and Table 6 of the same document lists the breakpoints to use; it is a US federal work in the public domain.