How is AQI Calculated? Formulas, Sub-Index Methods, and Worked Examples

How exactly is India's Air Quality Index (AQI) calculated? Learn the 3 methods — the average formula, the 3-pollutant API, and the sub-index method — with the CPCB approach explained step by step.

Here, we walk through all three calculation methods clearly.

If you're new to the topic, start with what AQI is and what the 0–500 scale means before diving into the formulas below

The Core Concept: Sub-Indices

Before calculating a final AQI, a sub-index is calculated for each individual pollutant. Each sub-index represents that pollutant's concentration relative to its air quality standard — a kind of "how bad is this pollutant right now?" score.

The final AQI is the worst (maximum) sub-index value across all pollutants measured. This ensures the AQI always reflects the most harmful pollutant present — not an average that could mask a dangerous spike.

AQI = max(Sub-index₁, Sub-index₂, ..., Sub-indexₙ)

The standards used as denominators in these formulas are drawn from India's National Ambient Air Quality Standards (NAAQS) — the legal concentration limits set by CPCB for 12 pollutants.

Method 1 — The Averaging Formula (n Pollutants)

When n major pollutants are being tracked, the Air Pollution Index (API) is the average of each pollutant's concentration expressed as a percentage of its standard:

Where:

• Cᵢ = Measured concentration of pollutant i

• Sᵢ = Air quality standard for pollutant i

• I = Air Pollution Index

Interpretation: A value of 100 means the pollutant is exactly at its standard limit. Values above 100 mean the standard is being exceeded.

Example

Pollutant	Measured (Cᵢ)	Standard (Sᵢ)	Cᵢ/Sᵢ × 100
SO₂	40 µg/m³	80 µg/m³	50
NO₂	60 µg/m³	80 µg/m³	75
PM10	90 µg/m³	100 µg/m³	90

I = (50 + 75 + 90) / 3 = 71.7

Method 2 — The 3-Pollutant API Formula

When exactly three major pollutants (A, B, C) are considered, the formula is:

Where:

• Cᵢ = Concentration of pollutant i

• Sᵢ = Ambient air quality standard for pollutant i

This is mathematically identical to Method 1 with n = 3, but is commonly presented separately in exam syllabi since three-pollutant scenarios are the most frequently tested.

Method 3 — The Sub-Index Table Method (5 Parameters)

This method uses a lookup table to assign sub-index values to five measured parameters. Each parameter's reading falls within a range, and a corresponding sub-index (Aᵢ) is assigned.

One of those five parameters is visibility — because air pollution directly reduces how far you can see through light scattering and absorption. Read more about how air pollution affects visibility and what COH measures.

Sub-Index Table

CO (ppm)	NO₂ (ppm)	Oxidant (ppm)	COH (units)	Visibility (km)	Sub-Index (Aᵢ)
0 – 1	0 – 0.005	0 – 0.005	0 – 0.5	12 – 24	2
1 – 2	0.005 – 0.01	0.005 – 0.01	0.5 – 1.0	8 – 12	4
2 – 4	0.01 – 0.02	0.01 – 0.04	1 – 2	6 – 8	8
4 – 6	0.02 – 0.06	0.04 – 0.06	2 – 3	4 – 6	12
6 – 8	0.06 – 0.10	0.06 – 0.09	3 – 4	2 – 4	16
8 – 35	0.10 – 0.20	0.09 – 0.10	4 – 5	0 – 2	20

COH = Coefficient of Haze — a measure of particulate matter collected on a filter.

The final API is the sum of sub-indices for all five parameters:

Example

Parameter	Measured Value	Sub-Index (Aᵢ)
CO	3 ppm	8
NO₂	0.05 ppm	12
Oxidant	0.07 ppm	16
COH	1.5 units	8
Visibility	5 km	12

API = 8 + 12 + 16 + 8 + 12 = 56

According to India's AQI scale, a value of 56 falls in the Satisfactory category.

How CPCB Calculates the Final AQI (Official Method)

India's Central Pollution Control Board (CPCB) follows this procedure for the official national AQI:

1. Measure concentrations of up to 8 pollutants at a monitoring station

2. Calculate sub-indices for each pollutant using 24-hour mean values (8-hourly for CO and O₃)

3. The worst (highest) sub-index = Final AQI for that monitoring location

Minimum data requirements:

• At least 3 pollutants must be measured

• At least one of those three must be PM2.5 or PM10

• At least 16 hours of data is needed to compute a valid sub-index

If these conditions aren't met, AQI is not reported — though individual pollutant sub-indices may still be published.

The Final AQI Formula

When multiple calculation methods are in play, the final AQI is taken as:

AQI = max(Method 1 AQI, Method 2 AQI, ..., Method n AQI)

This maximum operator ensures the reported AQI always reflects the most conservative (worst-case) assessment of air quality.

Limitations of AQI Calculation

Even with a robust formula, the AQI has real-world limitations:

• Manual data entry at some stations introduces human error

• Data may vary across time and measurement tools, giving inconsistent values

• Power cuts and maintenance failures at monitoring stations can disrupt data

• Calibration errors in sensors lead to inaccurate sub-indices

Exam Tip

Focus on:

• Being able to apply Method 1 (the averaging formula) with given Cᵢ and Sᵢ values

• Understanding the sub-index concept and the maximum operator rule

• The data sufficiency requirement (3 pollutants, one must be PM₂.₅ or PM₁₀, 16 hrs minimum)

Further Reading

On this blog:

• What is AQI? India's Air Quality Index (0–500) Scale Fully Explained

• How Does Air Pollution Affect Visibility? The Science of Haze and AQI

External resources:

• US EPA — AQI Basics: How AQI Works

• CPCB National Air Quality Index Portal