Air Quality Index Calculation Formula Calculator
Use the U.S. EPA style breakpoint interpolation formula to estimate AQI from a measured pollutant concentration. Select a pollutant, enter the measured concentration, and calculate the AQI category, breakpoint range, and health meaning.
Expert guide to the air quality index calculation formula
The air quality index, usually shortened to AQI, is one of the most widely used public communication tools in environmental health. It converts a measured concentration of a pollutant into a simple index value that the public can understand quickly. Instead of asking people to interpret whether 27 micrograms per cubic meter of PM2.5 or 0.072 parts per million of ozone is dangerous, the AQI expresses conditions on a scale that maps directly to health categories such as Good, Moderate, Unhealthy for Sensitive Groups, and Unhealthy.
In the United States, the AQI system is managed through methods published by the U.S. Environmental Protection Agency. If you want the official technical background, two excellent starting points are the EPA’s AQI technical assistance resources at epa.gov and the public facing guidance from airnow.gov. For health interpretation, the Centers for Disease Control and Prevention also explains why poor air quality can worsen respiratory and cardiovascular symptoms at cdc.gov.
What the AQI formula actually does
The AQI formula is a linear interpolation formula. That means it does not simply label a concentration as safe or unsafe. Instead, it places the measured value within a pollutant-specific concentration range called a breakpoint interval. Every breakpoint interval corresponds to a numeric AQI band. Once the correct interval is identified, the formula estimates the exact AQI value between the lower and upper AQI endpoints.
The standard formula is:
AQI = ((Ihigh – Ilow) / (BPhigh – BPlow)) × (Cp – BPlow) + Ilow
- Cp = the observed pollutant concentration, after applying the pollutant’s required truncation rule.
- BPlow = the lower concentration breakpoint for the interval containing Cp.
- BPhigh = the upper concentration breakpoint for the interval containing Cp.
- Ilow = the AQI value associated with BPlow.
- Ihigh = the AQI value associated with BPhigh.
This is why AQI calculation is not one universal equation with one set of constants. The formula stays the same, but the breakpoint table changes by pollutant. PM2.5, PM10, ozone, carbon monoxide, sulfur dioxide, and nitrogen dioxide each have different concentration thresholds because they affect health differently and are measured in different units and averaging periods.
Why breakpoint tables matter so much
If someone says, “I know the AQI formula, so I can calculate AQI from any concentration,” that is only partly true. The formula is only half the job. The other half is choosing the correct breakpoint row. For example, a PM2.5 concentration of 10.0 micrograms per cubic meter falls into the Good category, but 40.0 falls into Unhealthy for Sensitive Groups. You must identify the row that contains the measured value before applying the interpolation formula.
Breakpoints are designed so the AQI communicates public health risk in a consistent way. An AQI of 150 always means the upper end of the Unhealthy for Sensitive Groups category, even though the corresponding pollutant concentration is different for ozone versus PM2.5. This makes AQI suitable for public alerts, school activity decisions, outdoor work guidance, and personal health planning.
| AQI range | Category | General color convention | Public health meaning |
|---|---|---|---|
| 0 to 50 | Good | Green | Air pollution poses little or no risk for most people. |
| 51 to 100 | Moderate | Yellow | Acceptable for most, though unusually sensitive individuals may notice effects. |
| 101 to 150 | Unhealthy for Sensitive Groups | Orange | Children, older adults, and people with heart or lung disease may be affected sooner. |
| 151 to 200 | Unhealthy | Red | Some members of the general public may experience health effects; sensitive groups face greater risk. |
| 201 to 300 | Very Unhealthy | Purple | Health alert conditions. The risk of effects increases for everyone. |
| 301 to 500 | Hazardous | Maroon | Emergency conditions. The entire population is more likely to be affected. |
Step by step example using PM2.5
Suppose your measured 24-hour PM2.5 concentration is 37.8 micrograms per cubic meter. For PM2.5, EPA procedures use one decimal place truncation, so 37.8 remains 37.8. Now look at the PM2.5 breakpoint table. That concentration lies in the interval from 35.5 to 55.4, which corresponds to AQI 101 to 150.
- Set Cp = 37.8.
- Set BPlow = 35.5 and BPhigh = 55.4.
- Set Ilow = 101 and Ihigh = 150.
- Compute the slope: (150 – 101) / (55.4 – 35.5) = 49 / 19.9.
- Compute the concentration offset: 37.8 – 35.5 = 2.3.
- Multiply the slope by the offset and add Ilow.
The resulting AQI is a little above 106, which rounds to about 107. That means the PM2.5 level falls in the Unhealthy for Sensitive Groups category. This is an important reminder that AQI categories are not abstract labels. A concentration increase of only a few micrograms can move conditions into a category where schools, athletes, outdoor workers, and people with asthma should take precautions.
Pollutant specific details you should never ignore
One common mistake is assuming all pollutants are entered in the same units. They are not. PM2.5 and PM10 are typically expressed in micrograms per cubic meter. Ozone and carbon monoxide often use parts per million. Sulfur dioxide and nitrogen dioxide are commonly handled in parts per billion for AQI breakpoints. Another frequent mistake is using the wrong averaging time. Ozone has both 8-hour and 1-hour frameworks in regulatory contexts, but the public AQI calculation usually relies on the appropriate official breakpoint scheme, and not every category is available in every averaging period.
Truncation is another technical point that matters. The EPA does not always round the observed concentration before applying the AQI formula. Instead, it often truncates to a fixed number of decimal places depending on the pollutant. In practical terms, truncation means dropping extra digits rather than rounding them up. For PM2.5 you generally truncate to one decimal place. For PM10, sulfur dioxide, and nitrogen dioxide, the public AQI calculation typically uses integer handling. Ozone uses three decimals in ppm. Carbon monoxide uses one decimal in ppm. If your goal is official or audit quality reporting, using the right preprocessing rule is essential.
Comparison table: AQI communication bands versus WHO guideline values
People often compare AQI breakpoints with health guideline concentrations from other organizations. That comparison can be useful, but the numbers should not be treated as interchangeable because they reflect different policy and health communication goals. The table below shows selected World Health Organization 2021 guideline values, which are concentration based, not AQI based.
| Pollutant | WHO guideline statistic | Guideline value | Typical AQI calculator unit |
|---|---|---|---|
| PM2.5 | 24-hour mean | 15 micrograms per cubic meter | micrograms per cubic meter |
| PM10 | 24-hour mean | 45 micrograms per cubic meter | micrograms per cubic meter |
| Ozone | Peak season 8-hour daily maximum | 60 micrograms per cubic meter | often converted to ppm for AQI tables |
| Nitrogen dioxide | 24-hour mean | 25 micrograms per cubic meter | often expressed as ppb in AQI systems |
| Sulfur dioxide | 24-hour mean | 40 micrograms per cubic meter | often expressed as ppb in AQI systems |
| Carbon monoxide | 24-hour mean | 4 milligrams per cubic meter | often expressed as ppm in AQI systems |
How official AQI reporting usually works in practice
Real monitoring networks do not usually stop after calculating one pollutant. They calculate a sub-index for each pollutant with available data, then report the highest resulting AQI as the day’s or hour’s headline AQI, depending on the reporting framework. That pollutant becomes the “dominant pollutant” for communication purposes. If PM2.5 calculates to 122, ozone calculates to 88, and carbon monoxide calculates to 27, the reported AQI is 122 and the dominant pollutant is PM2.5.
This matters because the AQI number alone does not tell the entire story. A city with AQI 120 due to ozone may present different practical advice than a city with AQI 120 due to smoke related PM2.5. The headline health category is similar, but exposure reduction strategies differ. For ozone, people might shift outdoor exertion to earlier hours. For wildfire smoke, people may close windows, use filtration, and wear a well-fitted respirator in high smoke conditions.
Common errors when using an AQI calculator
- Entering the wrong unit, such as ppb instead of ppm.
- Using a concentration from the wrong averaging period.
- Rounding when the procedure requires truncation.
- Applying the formula without first choosing the correct breakpoint interval.
- Assuming AQI values from different countries are always directly comparable.
- Ignoring that the reported AQI is usually the maximum of several pollutant sub-indices.
How to interpret the result responsibly
If your calculated AQI lands in the Good or Moderate range, that does not mean zero health risk for every person. People with asthma, chronic obstructive pulmonary disease, coronary disease, or unusual sensitivity may notice symptoms earlier. Once the AQI passes 100, targeted precautions become more important. Sensitive individuals may need to reduce prolonged outdoor exertion, monitor symptoms, or use cleaner indoor air strategies. As the AQI enters Unhealthy, Very Unhealthy, or Hazardous ranges, broader population level protective behavior is warranted.
Another best practice is to interpret the AQI in context. Short spikes, long duration events, temperature, humidity, wildfire smoke composition, local traffic corridors, and indoor infiltration can all change the real world exposure picture. The AQI is a strong and useful screening tool, but it is not a substitute for all exposure science.
When this calculator is most useful
This calculator is helpful when you have a single pollutant concentration and want to understand its AQI equivalent quickly. It is especially useful for:
- Students learning environmental health or atmospheric science.
- Community groups reviewing local monitor data.
- Writers and analysts translating technical pollution values into public health language.
- Professionals building dashboards that need a quick AQI estimation method.
- Individuals checking how a sensor reading compares with common AQI categories.
Bottom line
The air quality index calculation formula is simple in appearance but precise in application. To calculate AQI correctly, you need four things: the right pollutant, the right unit, the right breakpoint interval, and the right concentration preprocessing rule. Once those are in place, the interpolation formula transforms a raw concentration into a public health index that can guide decisions in homes, schools, workplaces, and cities. A good AQI calculator should therefore do more than output a number. It should show the category, breakpoint math, and context. That is exactly what the calculator above is designed to do.