AQI Calculation Guide: From PM$_{2.5}$ Concentration to Air Quality Index
Courtesy of airnow.gov
This guide explains how PM$_{2.5}$ concentration becomes an AQI number. It compares the US EPA breakpoint method, Vietnam’s updated (2019) calculation, and why the same AQI number means different PM$_{2.5}$ levels in different countries.
What is AQI?
AQI (Air Quality Index) is a single number representing outdoor air quality derived from six pollutants: PM$_{10}$, PM$_{2.5}$, NO2, CO, SO2, and O3. The reported AQI is the maximum of the individual index values calculated for each pollutant.
Key concepts:
- Each country defines its own permissible concentrations — stricter standards yield higher AQI for the same air
- Two calculation approaches exist: breakpoint interpolation (US EPA, Vietnam post-2019) and linear ratio (Australia, Vietnam pre-2019)
- Different averaging periods produce different numbers from the same raw data — instant, hourly, daily, and NowCast concentrations are all distinct
PM$_{2.5}$ particles are small enough to penetrate deep into the lungs. Courtesy of EPA.
PM$_{2.5}$ Standards by Country
| WHO 2005 | WHO 2021 | US EPA | China | Japan | Australia | Vietnam | |
|---|---|---|---|---|---|---|---|
| 24-hour mean ($\mu g/m^3$) | 25 | 15 | 35.4 | 75 | 35 | 25 | 50 |
| Annual mean ($\mu g/m^3$) | 10 | 5 | 12 | 35 | 15 | 8 | 25 |
WHO revised its guidelines substantially downward in 2021, roughly halving both thresholds. No major national regulatory standard has yet been updated to match the 2021 values — the US EPA 2024 revision tightened the annual standard to 9 µg/m$^3$ but left the 24-hour standard unchanged. Australia retains the strictest annual standard among national regulators (8 µg/m$^3$). Vietnam’s standard is moderate relative to its economic status — stricter than China’s for the 24-hour average.
Concentration Types
Before calculating AQI, you need the right concentration value:
| Type | Definition | Use |
|---|---|---|
| Instant | Single sensor reading (per second to minute) | Raw data only |
| Hourly | Average of all readings in one hour | Real-time display |
| Daily | Average of all readings in one calendar day | Comparison to 24-hour standards |
| NowCast | Weighted average of last 12 hours | Real-time AQI forecasting |
NowCast Formula
NowCast gives more weight to recent hours, making it responsive without being noisy:
\[\mathrm{PM_{2.5}}_{\mathrm{nowcast}} = \frac{\sum_{i=1}^{12} w^{i-1} c_i}{\sum_{i=1}^{12} w^{i-1}}\]Where:
- $c_i$ = hourly concentration ($i = 1$ is most recent)
- $w = \max(c_{\min}/c_{\max},\ 0.5)$, where $c_{\min}$ and $c_{\max}$ are the minimum and maximum concentrations in the 12-hour window
The weighting factor $w$ ensures recent hours dominate when air quality is changing rapidly. At least 2 of the 3 most recent hours must be valid for NowCast to be reported.
NowCast is not a forecast. It is a lag-correction applied to already-measured data — a weighted summary of the past 12 hours, not a prediction of future conditions. It is specifically designed to make the AQI display more responsive to rapid deterioration. Using NowCast output as a forecasting target is valid (it is what AirNow displays), but any study doing this must state clearly that the model is predicting a weighted moving average, not an instantaneous or 24-hour concentration. See the PM$_{2.5}$ Forecasting Literature Review for how this distinction affects operational use.
Calculation Methods
Method 1: Breakpoint Interpolation (US EPA)
\[AQI_p = \frac{I_{Hi} - I_{Lo}}{BP_{Hi} - BP_{Lo}} (C_p - BP_{Lo}) + I_{Lo}\]Where:
- $C_p$ = pollutant concentration
- $BP_{Hi}, BP_{Lo}$ = concentration breakpoints bounding $C_p$
- $I_{Hi}, I_{Lo}$ = AQI index values corresponding to those breakpoints
US EPA breakpoints for PM$_{2.5}$ (24-hour and annual).
Example: PM$_{2.5}$ = 30 $\mu g/m^3$ (24-hour mean)
Look up: falls in the 12.1-35.4 bracket (AQI 51-100)
\[AQI = \frac{100 - 51}{35.4 - 12.1} (30 - 12.1) + 51 \approx 88\]Method 2: Linear Ratio (Australia, Vietnam pre-2019)
\[AQI_p = \frac{C_p}{C_{\mathrm{standard}}} \times 100\]Where $C_{\mathrm{standard}}$ is the permissible concentration for that pollutant.
This is simpler: AQI 50 means the concentration is half the standard. But it produces a purely linear scale with no breakpoints.
Example: PM$_{2.5}$ = 25 $\mu g/m^3$ in Vietnam (C_standard = 50)
\[AQI = \frac{25}{50} \times 100 = 50\]Same concentration in Australia ($C_{\mathrm{standard}} = 25$):
\[AQI = \frac{25}{25} \times 100 = 100\]Vietnam’s 2019 Update
In November 2019 (Decision 1459/QD-TCMT), Vietnam switched from Method 2 to Method 1 — adopting breakpoint interpolation similar to the US EPA approach. This makes the calculation identical in structure, though the breakpoints differ due to different permissible concentrations.
China AQI (HJ 633-2012)
China uses its own AQI system defined in standard HJ 633-2012. The structure is also breakpoint interpolation (same as US EPA), but the PM$_{2.5}$ thresholds are much higher, reflecting China’s current 24-hour standard of 75 µg/m$^3$:
| AQI | Category | PM$_{2.5}$ 24h ($\mu$g/m$^3$) | Health guidance |
|---|---|---|---|
| 0–50 | Excellent | 0–35 | No restriction |
| 51–100 | Good | 35–75 | General population: no restriction |
| 101–150 | Lightly Polluted | 75–115 | Sensitive groups: reduce outdoor activity |
| 151–200 | Moderately Polluted | 115–150 | Sensitive groups: avoid outdoor activity |
| 201–300 | Heavily Polluted | 150–250 | General population: reduce outdoor activity |
| >300 | Severely Polluted | >250 | All outdoor activity suspended |
The top category (Severely Polluted, AQI >300) corresponds to PM$_{2.5}$ levels that would be mapped to a US AQI of approximately 400–500 (Hazardous range). This means a Chinese “Good” reading (AQI 51–100, PM$_{2.5}$ up to 75 µg/m$^3$) would be classified US “Unhealthy for Sensitive Groups” or higher. The two indices are not directly comparable and should never be reported on the same axis without labelling.
Other Regional AQI Systems
European CAQI. The EU Common Air Quality Index uses a 0–100+ scale. PM$_{2.5}$ background bands: Very Low 0–15, Low 15–30, Medium 30–55, High 55–110, Very High >110 µg/m$^3$. The overall CAQI is the maximum sub-index across pollutants. Adopted by ~20 European countries; displayed on the EEA European Air Quality Index viewer.
UK DAQI. The Daily Air Quality Index uses a 1–10 scale grouped into four named bands. PM$_{2.5}$ 24-hour breakpoints:
| DAQI Level | Band | PM$_{2.5}$ ($\mu$g/m$^3$) |
|---|---|---|
| 1–3 | Low | 0–35 |
| 4–6 | Moderate | 36–53 |
| 7–9 | High | 54–70 |
| 10 | Very High | ≥71 |
Health advice escalates from Level 4 onward for sensitive groups and from Level 10 for the general population. Note that DAQI Level 2 (up to 23 µg/m$^3$) already exceeds the WHO 2021 24-hour guideline of 15 µg/m$^3$.
Japan prefectural advisory. Japan does not use a named AQI scale for PM$_{2.5}$. Instead, prefectural governments issue advisories when a forecast daily average is expected to exceed 70 µg/m$^3$ — the public communication threshold, not an index. Real-time monitoring data are available via the national SORAMAME (そらまめ君) network.
Comparing US and Vietnam AQI
Same AQI category, different PM$_{2.5}$ thresholds: “Good” in Vietnam allows higher PM$_{2.5}$ than “Good” in the US.
Converting PM$_{2.5}$ concentration to AQI by both standards. The US EPA curve is steeper at lower concentrations — stricter for “Good” and “Moderate” categories.
Key differences:
- For Good/Moderate categories, the same AQI number corresponds to lower PM$_{2.5}$ under US EPA (stricter)
- For Unhealthy/Hazardous categories, Vietnam’s standard triggers at lower PM$_{2.5}$ (stricter at the high end)
- After the 2019 update, the structural calculation is identical — only the breakpoint values differ
AQI Health Scale
Standard AQI color bands used by most reporting systems.
Takeaways
- AQI is country-specific — the same air can have different AQI values depending on which standard is applied
- Two calculation methods: breakpoint interpolation (flexible, non-linear) and linear ratio (simple)
- Vietnam adopted the US EPA breakpoint method in November 2019
- For lower AQI categories (Good, Moderate), the US standard is stricter
- When comparing AQI numbers, always check which standard was used
- WHO 2021 guidelines are roughly half the 2005 values; no major national standard has yet matched them
- NowCast is a reporting formula, not a forecast
Further Reading
The companion forecasting literature review covers how AQI systems connect to operational PM$_{2.5}$ forecasting, including how agencies convert continuous model output into AQI categories for public communication:
- PM$_{2.5}$ Forecasting Literature Review — agency systems (US NAQFC, EU CAMS, Japan VENUS/SPRINTARS/MASINGAR, China MEE, Australia BoM), evaluation metrics (IA, CSI, MFB), and the resource-limited single-station forecasting problem
- Hanoi PM$_{2.5}$ Forecasting Experiments
- Statistical Modeling
References
- Decision 1459/QD-TCMT (Nov 12, 2019) — Vietnam AQI calculation guidance
- MONRE Handbook for AQI Calculation (2015)
- US EPA Technical Assistance Document for AQI Reporting (2018)
- WHO Ambient Air Quality Guidelines
- QCVN 05:2013/BTNMT — Vietnam National Technical Regulation on Ambient Air Quality
- Evaluation of the Chinese New Air Quality Index (GB3095-2012), Fanyu Gao
Originally published on b-io.info, updated January 2020.