How Is AQI Calculated? The EPA Formula Explained Step by Step

The Air Quality Index is not something an instrument measures. Your sensor measures a concentration, like 28 µg/m³ of PM2.5. The AQI is a number the EPA calculates from that concentration using a fixed formula and a published lookup table. Once you have seen the formula once, the whole thing stops being mysterious.

This guide walks through the exact equation the US EPA uses, the current (2024) breakpoint table, and a full worked example you can reproduce with a calculator. If you just want the answer for a specific reading, our AQI calculator and converter does every step below automatically.

The one formula behind every AQI value

The US AQI uses piecewise-linear interpolation. That phrase sounds heavy, but it describes something simple: the EPA has drawn a series of straight-line segments, and your concentration falls on one of them. The equation for the segment is:

I = (I_high − I_low) / (C_high − C_low) × (C − C_low) + I_low

Where:

• C is your measured (and truncated) pollutant concentration
• C_low / C_high are the low and high concentration bounds of the band C falls into
• I_low / I_high are the AQI values that correspond to those bounds
• I is the resulting AQI, rounded to a whole number

That is the entire calculation. Everything else is just knowing which band to use and how to prepare the concentration first.

Step 1: Truncate the concentration

Before you plug anything in, the EPA truncates the concentration to a fixed number of decimal places, it does not round. For PM2.5, that means one decimal place. A reading of 28.67 µg/m³ becomes 28.6, not 28.7. For PM10 and most gases, the concentration is truncated to a whole number.

This matters because using the raw, un-truncated value can push you into the wrong band at the edges.

Step 2: Find the band in the breakpoint table

The EPA publishes a table of breakpoints for each pollutant. Here is the PM2.5 table using the 2024 updated breakpoints (this is the current, post-revision table, where the "Good" band now tops out at 9.0 µg/m³ instead of the old 12.0):

Your truncated concentration falls inside exactly one row. That row gives you all four of the values the formula needs: C_low, C_high, I_low and I_high.

Step 3: Plug in and solve

Let's do a real one. Suppose your monitor reads 28.6 µg/m³ of PM2.5.

That falls in the 9.1 – 35.4 band, so:

• C = 28.6
• C_low = 9.1, C_high = 35.4
• I_low = 51, I_high = 100

Now substitute:

I = (100 − 51) / (35.4 − 9.1) × (28.6 − 9.1) + 51

I = (49 / 26.3) × (19.5) + 51

I = 1.863 × 19.5 + 51

I = 36.3 + 51 = 87.3

Rounded, that is an AQI of 87, which sits in the Moderate (yellow) category. That is the whole calculation, start to finish.

Step 4: If you measure several pollutants, take the worst

When a monitoring station tracks multiple pollutants (PM2.5, PM10, ozone, and so on), it calculates a separate AQI for each one. The reported AQI is simply the highest of them. The pollutant responsible for that highest value is called the "responsible pollutant" or the "primary pollutant" for that hour. The AQI never averages pollutants together; it always reports the worst offender.

Why the number jumps unevenly

One thing that surprises people: the AQI is not proportional to the concentration. Going from 9 to 35 µg/m³ moves you across 49 AQI points, but going from 55 to 125 µg/m³, a far larger jump in actual particles, also only spans about 49 points. That is deliberate. The bands are compressed at the healthy end so that small changes in clean-ish air are visible, and stretched at the dangerous end where the health message ("stay inside") is the same across a wide range.

This is also why you cannot simply divide AQI by a constant to recover the concentration, you have to invert the specific segment. It is the reason a tool like our AQI to cigarettes calculator converts AQI back to PM2.5 first, using these same breakpoints in reverse, before doing anything else.

Other countries calculate it differently

The formula above is the US EPA method. The EU's EAQI does not interpolate at all, it classifies a concentration directly into one of six bands. The UK's DAQI is a 1-to-10 scale with its own thresholds. So the same air earns different index numbers depending on which country is grading it. If you want to see one reading land on all of them at once, that is exactly what the AQI converter is for.

The bottom line

Calculating the AQI is a four-step routine: truncate the concentration, find its band in the breakpoint table, apply the linear-interpolation formula, and, if you have several pollutants, report the highest result. The math is deliberately simple; the design work is all in the breakpoints, which were chosen to make health advice legible rather than to be proportional to particle counts.

If you would rather not do it by hand, enter any concentration into the Partycle AQI calculator and watch every step happen live, including on the US, EU and UK scales side by side.

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Sources

• US EPA. "Technical Assistance Document for the Reporting of Daily Air Quality: the Air Quality Index (AQI)." The source of the interpolation formula and breakpoint methodology. airnow.gov
• US EPA (2024). "PM NAAQS Air Quality Index fact sheet." Updated PM2.5 breakpoints used in the table above. epa.gov
• US EPA AirNow. "AQI Basics." Plain-language overview of categories and the responsible-pollutant rule. airnow.gov/aqi/aqi-basics