Air Quality Index (AQI) Formula
Reference for the EPA AQI formula and PM2.5, PM10, ozone, CO, SO2, and NO2 breakpoints.
Explains the 0-500 scale from Good to Hazardous with health guidance.
The Formula
The AQI converts a pollutant concentration into a standardized index from 0 to 500. It uses breakpoint tables to interpolate linearly between defined AQI category boundaries.
Variables
| Symbol | Meaning |
|---|---|
| AQI | Air Quality Index value (0-500) |
| C | Measured pollutant concentration |
| C_low, C_high | Concentration breakpoints surrounding C |
| I_low, I_high | AQI breakpoints corresponding to C_low and C_high |
AQI Scale: 0-50 Good, 51-100 Moderate, 101-150 Unhealthy for Sensitive Groups, 151-200 Unhealthy, 201-300 Very Unhealthy, 301-500 Hazardous.
Example 1
PM2.5 concentration is 35.9 μg/m³. Find the AQI.
Breakpoints: C_low = 35.5, C_high = 55.4, I_low = 101, I_high = 150
AQI = ((150 - 101) / (55.4 - 35.5)) × (35.9 - 35.5) + 101
AQI = (49 / 19.9) × 0.4 + 101 = 2.462 × 0.4 + 101
AQI ≈ 102 (Unhealthy for Sensitive Groups)
Example 2
Ozone concentration is 0.060 ppm. Find the AQI.
Breakpoints: C_low = 0.055, C_high = 0.070, I_low = 51, I_high = 100
AQI = ((100 - 51) / (0.070 - 0.055)) × (0.060 - 0.055) + 51
AQI = (49 / 0.015) × 0.005 + 51 = 16.33 + 51
AQI ≈ 67 (Moderate)
When to Use It
Use the AQI formula when:
- Converting raw pollution measurements into health-relevant values
- Comparing air quality across different locations
- Deciding whether outdoor activities are safe on a given day
- Reporting air quality data to the public
Key Notes
- AQI formula: I = [(I_high − I_low)/(C_high − C_low)] × (C − C_low) + I_low: The AQI is calculated by linear interpolation between concentration breakpoints. Each pollutant (PM2.5, PM10, ozone, CO, SO₂, NO₂) gets its own AQI; the reported AQI is the highest of all individual values.
- Six AQI categories: Good (0–50): no concern; Moderate (51–100): some sensitive individuals; Unhealthy for Sensitive Groups (101–150); Unhealthy (151–200); Very Unhealthy (201–300); Hazardous (301+). Each level triggers different public health guidance.
- PM2.5 is the most common limiting pollutant: Fine particulate matter (≤2.5 µm diameter) penetrates deep into the lungs and bloodstream. In most urban and wildfire smoke events, PM2.5 drives the AQI. It is measured in µg/m³ over 24-hour averages.
- Ozone is time-of-day dependent: Ground-level ozone forms through photochemical reactions and peaks in the afternoon. The 8-hour ozone AQI often differs significantly from the 1-hour value. Ozone season varies by region and climate.
- Applications: AQI is used to trigger outdoor activity restrictions for schools, issue air quality alerts, guide HVAC filter selection (MERV ratings), inform industrial emission permit decisions, and monitor long-term pollution trends for public health research.