Formula & Calculator
Air Quality Index (AQI) Linear Interpolation
Converts a measured pollutant concentration into the standardized Air Quality Index scale using linear interpolation between breakpoints.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| AQI | Air quality index | |
| C | Measured pollutant concentration | |
| C_lo | Lower breakpoint concentration | |
| C_hi | Upper breakpoint concentration | |
| AQI_lo | AQI value at lower breakpoint | |
| AQI_hi | AQI value at upper breakpoint |
What it means
The Air Quality Index (AQI) is a standardised system to report daily air quality. For each pollutant, the concentration is converted to an AQI value using a piecewise linear function defined by breakpoints. This formula linearly interpolates between two adjacent breakpoints. If the concentration C falls between C_lo and C_hi, the corresponding AQI is computed using the given formula. This method is used by environmental agencies (e.g., EPA) to provide a simple and understandable index for the public. The AQI ranges from 0 to 500, with higher values indicating worse air quality. Example: For ozone, if C=80 ppb, and the breakpoints are C_lo=65 (AQI_lo=100) and C_hi=85 (AQI_hi=150), then AQI = ((150-100)/(85-65)) × (80-65) + 100 = (50/20) × 15 + 100 = 2.5 × 15 + 100 = 137.5, which rounds to 138. This informs the public about health risks.
Worked example
Air Quality Index Interpolation – Two Examples
Real‑World| Parameter | Value |
|---|---|
| C | 20 |
| C_lo | 12.1 |
| C_hi | 35.4 |
| AQI_lo | 51 |
| AQI_hi | 100 |
| Parameter | Value |
|---|---|
| C | 80 |
| C_lo | 55.5 |
| C_hi | 150.4 |
| AQI_lo | 151 |
| AQI_hi | 200 |
Common mistakes
- Concentration C: The measured pollutant concentration – must lie between C_lo and C_hi.
- AQI_hi and AQI_lo: The AQI values corresponding to the upper and lower breakpoints for that concentration range – use EPA or local tables.
- Interpolation: Linear interpolation assumes a straight line between breakpoints – reasonable for AQI.
- Rounding: AQI is typically rounded to the nearest integer.
- Multiple pollutants: The overall AQI is the maximum of individual pollutant indices – not the sum.
Applications
The air quality index (AQI) is determined by linear interpolation between breakpoints for each pollutant (e.g., PM₂.₅, O₃, NO₂), using pollutant concentration (C) and the corresponding high and low AQI and concentration values. This linear scaling allows for standardised communication of air pollution levels to the public, indicating health implications and recommended actions. Environmental regulators and health agencies use AQI to issue daily forecasts, to issue alerts during episodes of high pollution, and to evaluate compliance with standards. By applying this interpolation, professionals can convert measured concentrations into an intuitive index that guides community behaviour, such as limiting outdoor activity during poor air quality days.
- Public communication of air quality through daily AQI reports
- Alert systems for ozone, particulate matter, and other pollutants
- Health risk communication and advice for sensitive groups
- Compliance assessment with National Ambient Air Quality Standards (NAAQS)
- Real‑time air quality monitoring and data visualisation