On 926 of the 928 days, in the record from 1 May 2015 to 20 October 2026, on which Delhi's AQI was Very Poor or Severe by the hour-by-hour calculation that CPCB's published figures track, CPCB's own documented formula gave a higher figure. The other two were 25 December 2016, on 8 stations, and 30 December 2016, on 4 stations. From 2018 it is every one of 662 such days.

On Delhi's Very Poor and Severe days, the hour-by-hour calculation that CPCB's published figures track gives lower numbers, so the AQI the public sees looks better than CPCB's own formula would make it. On 630 of the 640 days since 2018 that CPCB's bulletin printed Delhi as Very Poor or Severe, CPCB's own formula gave the higher figure. At 13 DPCC stations from 2018 to 2024, CPCB published 8,376 station-days as Very Poor or Severe, and CPCB's own formula gave the higher figure on 8,043 of them.

On cleaner days, mostly Moderate ones, and at single stations where PM10 sets a figure below 350, the documented formula can give the lower figure, as at CRRI Mathura Road on 20 October 2026, 184 against 197, and the evidence shows what CPCB publishes, not why.

CPCB's note "How is AQI calculated?" says each pollutant's sub-index is "calculated using its 24-hourly average concentration value (8-hourly in case of CO and O3)": the readings are averaged first and converted once. No CPCB document opened describes another order. Yet CPCB's published station figures came within 4.1 to 7.9 points of the hour-by-hour calculation in every year from 2018 to 2024, against 15.7 to 25.0 for the documented formula. On the station-days CPCB published as Severe, CPCB's figure sat on average 10.3 points below the hour-by-hour calculation and 41.5 below the documented formula; on Very Poor station-days, 7.3 and 25.9.

In 2025 Delhi was Severe on 22 days on CPCB's documented formula, on 11 hour by hour and on 8 in CPCB's bulletin. The difference between 22 and 11 is the formula alone, on identical readings and stations. The difference between 11 and 8 is everything else: the stations each uses, late or missing data, CPCB's rounding, and any part of CPCB's own arithmetic that the reconstruction does not reproduce. It is not the order of the arithmetic.

Each quotation below is copied from the CPCB document named beside it, and each link opens CPCB's own copy. All of them were opened by this office on 20 October 2026, and every one describes averaging the concentration first.

The table separates the dates a document prints from the dates stored in its file. A printed date is the document's own statement. A file date shows only when CPCB's online copy was made or last saved, and it may be later than the text itself.

CPCB converts a concentration into an AQI figure along a chain of straight pieces, one piece for each category, and the pieces are not equally steep. When a day's hourly readings fall on pieces of different steepness, converting the day's average once and averaging each hour's conversion give different answers.

For PM2.5, each microgram between 60 and 120 µg/m³ adds 3.30 points, and each microgram between 120 and 250 adds only 0.76. On a polluted day whose hours straddle 120, the cleaner hours lose points fast on the steep pieces and the dirtier hours gain them slowly on the flat one, so the average of the hourly figures falls below the figure of the average reading. The PM10 scale does the opposite between 100 and 430 µg/m³, where its pieces run at 0.66, 0.99, 1.24 points per microgram, so a PM10 day spread across those pieces usually gains on the reconstruction.

CPCB's documents give the Severe band no top concentration, only "250+" for PM2.5 and "430 +" for PM10 (CUPS/82/2014-15, Table 3.11). CPCB's AQI Calculator reaches 500 at 380 µg/m³ of PM2.5 and 510 of PM10, and its formula carries on past 500 above them. This office holds both computed figures at 500 there, because CPCB's scale runs from 0 to 500. So in the reconstruction every hour above 380 µg/m³ of PM2.5 counts as 500, however high the hour, while the documented formula keeps those hours in the day's average until the average itself passes 380.

The table and chart use every station-day of the test on 13 DPCC stations, 2018 to 2024, on which the same pollutant set both figures. They show the documented formula's figure minus the reconstruction's, by the level of the documented figure, and the share of days on which the documented formula was the lower of the two.

CPCB's CCR portal publishes a daily AQI for each station. For 13 DPCC stations, 2018 to 2024, this office computed both figures from CPCB's hourly readings over the 24 hours ending 4 PM and set each against CPCB's published figure: the average gap, the share within 5 points, the share in the same category, and the average signed gap.

On the calendar day from midnight to midnight both figures fit CPCB's published station figure worse: the reconstruction's gap rose to 16.7 to 19.8 points and the documented formula's to 22.9 to 31.6. CPCB's published daily station figure fits the 24 hours ending 4 PM, the window of its bulletin.

2017 is reported apart because only 3 stations can be tested, on 418 station-days. The reconstruction came within 16.2 points of CPCB's figure on average against 29.1 for the documented formula, and within 5 points on 57 per cent of days against 19. In that year too, CPCB's published station figure is closer to the hour-by-hour calculation, as in 2018 to 2024, by a smaller margin: the documented formula sat 4.5 points above CPCB's figure on average and the reconstruction 8.9 below it, so in that year neither figure fits well on average. On the 223 station-days on which the two differed by 10 points or more, CPCB's figure was closer to the hour-by-hour calculation on 203 and to the documented formula on 19.

The table takes every station-day of the test, 2018 to 2024, that CPCB published as Very Poor or Severe, and sets both computed figures against CPCB's own figure on that day.

CPCB's own formula gave the higher figure on 8,043 of the 8,376 station-days, was equal on 154 and lower on 179, and put the station in a worse category on 1,309 and a better one on 30. On the station-days CPCB published as Severe, CPCB's figure sat on average 10.3 points below the hour-by-hour calculation and 41.5 below the documented formula. On those it published as Very Poor, it sat 7.3 and 25.9 points below them. On polluted station-days CPCB's published figure is therefore lower, on average, than both computed figures: below the hour-by-hour calculation on 2,294 of the 2,446 Severe station-days and on 5,029 of the 5,930 Very Poor ones.

Where the two orders give nearly the same number, no test can show which one CPCB's figure tracks, so the deciding days are those on which they part. On the 11,656 station-days of 2018 to 2024 on which the two differed by 10 points or more, CPCB's figure was closer to the hour-by-hour calculation on 11,013 and to the documented formula on 597. CPCB's figure equals the hour-by-hour figure exactly on 17.0 per cent of all station-days, so the two are close and not the same.

For carbon monoxide and ozone the two figures also differ in their 8-hour window, and the reconstruction's ozone channel is an open item. The test is therefore repeated on the station-days on which PM2.5 or PM10 set both figures. On those days the two figures differ only in the order of the arithmetic.

The result does not change. On particle-led days the documented formula ran 11.6 to 20.6 points above CPCB's published figure, and the reconstruction came within 4.0 to 7.8 points of it.

Delhi's city figure is the average of its stations' AQIs on each basis, and CPCB's bulletin gives its own for the same 24 hours. The table averages each year over the days on which all three exist.

No day from 1 December 2021 to 31 December 2021 can be computed, because the hourly record holds almost no gas readings for that month and CPCB's rule needs three pollutants. Outside that month, 33 days in the record are absent because one of the three figures is missing for them. In October and November 2021 the record holds no CO, ozone or SO2, and in September 2021 only 804 to 956 station-hours of each, so those months are computed on PM2.5, PM10 and NO2 on both bases. The two category columns compare the documented formula with CPCB's bulletin, so they mix the formula and the station set.

This page asks the station test's question of Delhi's city figure. For each day it measures how far each computed city figure sits from the figure CPCB's 4 PM bulletin printed, and the table gives the yearly average of that gap and the share of days within 5 points.

The reconstruction sits closer to CPCB's published city figure in 12 of the 12 years. From 2018 to 2026 its gap is 2.5 to 8.4 points, against 6.6 to 18.3 for the documented formula. In 2015 to 2017 the computed figures rest on 7.1 stations a day on average or fewer, against CPCB's 5 to 9, and both figures fit far less tightly: the reconstruction's gap is 13.2 to 22.8 points. In those years too the published city figure is closer to the hour-by-hour calculation, by a smaller margin, and the years cannot show when CPCB's published figure came to track that order.

The full count of days in each CPCB category, on each basis, for every year. A city figure is placed in a category after rounding to a whole number, as CPCB's bulletin prints it.

The count continues from 2021 to 2026, and the last three rows add every year from 2015 to 2026.

Severe is CPCB's worst category, an AQI of 401 or more. In 2025, Delhi was Severe on 22 days on CPCB's documented formula, on 11 days on the reconstruction, and on 8 days in CPCB's bulletin. The difference of 11 days between the first two is the formula. The difference of 3 days between the last two is everything else, which includes the station set and the data.

CPCB's own bulletin prints a health statement for each category, and the statement changes when the category changes. CPCB's own formula put Delhi in Very Poor or Severe on 1,117 days, and the hour-by-hour calculation on 928, on the same readings.

For those two categories CPCB's report says: "In case AQI category is severe or very poor, necessary steps need to be taken by further regulating the emissions which are causing maximum impact to ambient air quality." (CUPS/82/2014-15, section 3.4, printed page 36).

The gap between the documented formula and CPCB's bulletin has two parts, measured apart here. The first is the formula: the documented formula minus the reconstruction, on the same readings and stations. The second is everything else: the reconstruction minus CPCB's bulletin, which includes the stations, late or missing data, CPCB's rounding, and any part of CPCB's arithmetic that the reconstruction does not reproduce. Over all days it averages −0.3 points; on the 928 Very Poor and Severe days it averages +4.5 and runs the same way as the formula, so CPCB's bulletin sat 22.8 points below CPCB's documented formula on those days.

On the same months of each year, 1 January to 20 October, the formula's part fell from 11.7 points in 2016 to 4.7 in 2026. About half of that fall comes from a different mix of days, with fewer Poor, Very Poor and Severe days, and about half from smaller additions on the Moderate, Poor and Very Poor days. On Severe days the formula's part was between 18.1 and 28.8 points in every full year, and 26.0 on the 3 Severe days of 2026.

Each dot is one day from 1 May 2015 to 20 October 2026. It is placed along the bottom by Delhi's figure on the reconstruction, and up or down by how far the documented formula sits above or below it. The table counts the days in each category of the reconstruction.

The first two lists take only days with at least 20 computed stations; 993 days, nearly all from 2015 to 2017, have fewer, and the last table keeps them. The largest of those thin days was 12 July 2015, +90.0 points on 3 stations, with CO setting the documented figure, so the 8-hour gas window, and not only the order, made it.

Of the eight days, 21 October 2025 and 13 November 2023, and in the last table 25 October 2022, are the 24 hours after a Diwali night; the festival list on disk starts in 2021. The 928 Very Poor and Severe days count every day, and the median addition on them is 16.4 points. "CPCB's stations" is the count CPCB's bulletin printed, marked where it is under half the computed count.

The table gives Delhi on all three bases for the 24 hours ending 4 PM IST on 20 October 2026, the window of CPCB's 4 PM bulletin. CPCB's bulletin gives a city figure, its category and the number of stations that took part, and no station categories.

At the stations the direction was mixed that day. The documented formula was higher at 18 stations, lower at 24 and equal at 14. The largest rises, documented formula first: Bawana 307 against 270; NSUT Jaffarpur 263 against 238; Jahangirpuri 281 against 259. The other way: CRRI Mathura Road 184 against 197; Wazirpur 190 against 200; Karala 138 against 145. The two bases put 2 stations in a different category, and the reconstruction counts one more station in Poor or worse than the documented formula.

For every city in CPCB's 4 PM bulletin, on the 30 days from 21 September 2026 to 20 October 2026 and the 31 days of December 2025, both city figures were computed from CPCB's hourly readings and set against the bulletin. A city with one station is the cleanest test, because no rule for combining stations enters.

In 246 of 261 cities in December 2025, the AQI that CPCB published is closer to the hour-by-hour calculation than to CPCB's own documented formula. Winter is when the two orders separate most: in cities with one station the median gap from CPCB's figure was 5.1 points for the documented formula and 1.2 for the hour-by-hour calculation. On a polluted day this lowers the published number: on 12 December 2025 CPCB published 291 for Kolkata, Poor, where its own formula gives 308.6, Very Poor. On cleaner days, mostly Moderate ones, and at single stations where PM10 sets a figure below 350, the documented formula can be the lower figure. The evidence shows what CPCB publishes, and not why.

Across the 7,205 city-days with all three figures in CPCB's December 2025 bulletins, CPCB's own formula put 653 in Very Poor or Severe, against 352 on the hour-by-hour calculation from the same readings and 343 in CPCB's bulletins. On the 6,873 city-days where the computed station count equals CPCB's, the figures are 612, 314 and 307; that matched set holds no Delhi day.

Where the two orders give nearly the same number, no test can show which one CPCB's figure tracks, so the deciding days are those on which they part. The table counts, for one-station cities, the days on which the two figures were 5 points or more apart, and on how many of them CPCB printed exactly one of the two.

On the 1,866 days of December 2025 on which a one-station city's two figures were 5 points or more apart, CPCB published exactly the hour-by-hour figure on 526 and exactly the documented figure on 4.

With the same margin of half a point on both sides, on the gaps as printed in Annexure B, the hour-by-hour calculation is closer in 193 cities, the documented formula in 5, and 91 are within half a point; in December 2025 the counts are 230, 3 and 28.

Among the 259 cities where the hourly order is closer in the autumn, 23 have an hourly gap above 5 points, so neither order fits them well; in December 2025 the figure is 31 of 246. The result rests on days led by particles: on autumn city-days 5 or more points apart, the documented formula was closer on 50 of 771 particle-led days and on 47 of 157 days on which CPCB named a gas.

Of the 20 cities where the documented formula is closer, 15 are within half a point, mostly cities with clean air, where both orders give nearly the same number. In a few others both figures are far off, such as Katihar 30.0, Guwahati 19.0, Kolar 13.6, Durgapur 11.5 points for the documented formula, and neither can match, probably because the readings lack a station or a gas that CPCB used. CPCB names CO or SO2 as prominent on 31.8 per cent of those cities' days, against 10.7 per cent in all cities, and the all-India readings carry CO for a median of 46 stations a day and SO2 for 38, against 514 for PM2.5.

Kolkata's figure on the two orders, set against CPCB's bulletin, in the autumn window and in the winter, on CPCB's own readings for the city's stations.

In the autumn window the air was clean to middling, 6 Good, 11 Satisfactory, 13 Moderate days, and the two orders sat within 2.6 points of each other on every day. On that test the two are level, at 0.9 points each, and the documented formula is within 5 points on more days, 97 per cent against 93.

In December 2025, the example is the city's highest bulletin day, 12 December 2025. CPCB published 291, Poor. CPCB's own formula gives 308.6, Very Poor, and the hourly order gives 291.0, exactly the published figure. Over the month the documented formula sits 8.7 points from CPCB's figure on average and the hourly order 2.7; they are within 5 points on 35 and 84 per cent of days.

The two orders separate when a day's PM2.5 hours sit on both sides of the bend at 120 µg/m³ (page 7), which happens on polluted winter days. In a clean month the two give nearly the same number, so only a polluted month shows which one CPCB's figure tracks, and how far apart the two can be.

CPCB's bulletin of 12 December 2025 printed Kolkata as Poor, for which the same bulletin prints the health statement "Breathing discomfort to most people on prolonged exposure". On CPCB's own formula the same readings are Very Poor, for which the bulletin prints "Respiratory illness on prolonged exposure" (CPCB AQI bulletin of 12 December 2025, pages 7 and 14).

Mumbai's figure on the two orders, set against CPCB's bulletin, in the autumn window and in the winter, on CPCB's own readings for the city's stations.

In the autumn window the air was clean to middling, 3 Good, 19 Satisfactory, 8 Moderate days, and the two orders sat within 2.5 points of each other on every day. The hourly order is the closer, at 1.6 points against 2.1.

In December 2025, the example is the city's highest bulletin day, 4 December 2025. CPCB published 138, Moderate. CPCB's own formula gives 141.1, Moderate, and the hourly order gives 138.6. Over the month the documented formula sits 3.9 points from CPCB's figure on average and the hourly order 3.0; they are within 5 points on 71 and 77 per cent of days.

The two orders separate when a day's PM2.5 hours sit on both sides of the bend at 120 µg/m³ (page 7), which happens on polluted winter days. In a clean month the two give nearly the same number, so only a polluted month shows which one CPCB's figure tracks, and how far apart the two can be.

The table states only what each authority's own document says, with the document and page. None of the eight documents describes averaging hourly sub-indices into a daily figure. For a daily index, each of the others averages the concentration first and converts once, and the European index converts each hour and reports that hour.

Each column puts the same hourly readings through one method, and each cell is the yearly average of Delhi's daily figure on the days on which every column has one. The US and British methods use the calendar day; the CPCB-based columns use the 24 hours ending 4 PM.

Each method has its own scale, so only the three CPCB-based columns can be read against one another. The US figure is extended above 500 as EPA's Table 6 directs: 504 days exceed 500, the highest at 1,532, and they enter the US average. The British index stops at band 10. Because the days are matched across all the columns, the CPCB columns differ a little from the city pages.

The table counts the days each method puts Delhi in its own two worst categories, on the same matched days. Each method names and draws those categories differently, so the cells are read within a column and across the years.

Each column of the two tables is defined below: its day, how it averages within a station, how it combines stations, and what to keep in mind when reading it. Every method is computed from the same readings, with the same check on each reading, which counts a reading above 0 and below 1,000 µg/m³, or 50,000 for carbon monoxide.

The US, UK and "CPCB formula, US area rule" columns each take one monitor's reading for the whole city, so each describes the worst monitored neighbourhood on that day. CPCB's real-time readings are "fed directly from the analysers without scrutiny" (CPCB, "Limitations", item 1), so a single faulty analyser can set such a column, and on days with few stations it can lift the city figures as well.

The readings for 2015 to 2017 and for the whole of 2022 come from CPCB's own readings in the Kaggle compilation, because CREA's compilation holds nothing for 2015 and 2016, only PM for 2017, and only PM for January to September 2022. In November 2018 the two compilations agree to the last digit on every matched hourly reading of all six pollutants, 112,761 readings at the 29 stations whose names are identical in both files. In 2022 they agree exactly on every PM hour of March, and in November on 99.7 per cent of readings exactly and 99.8 per cent or more within one unit. No compilation overlaps 2015 to 2017, so the agreement there is assumed from the two later years. That reading check cannot catch carbon monoxide at Wazirpur and Sonia Vihar, which both compilations store at about a thousandth of its size; Annexure A says what that changes.

The investigation states what the record shows and where it stops. Each row names a question the data on disk cannot settle, what the record does show, and what would settle it.

On 20 October 2026 this office searched for any document that describes averaging hourly sub-indices, or that revises the AQI calculation after 2015. The search covered PIB's current and archive sites, the sites of both Houses of Parliament for replies on AQI method, CPCB's sites, the CCR portal, the Environment Ministry's and CAQM's sites, and an open web search. Nothing was found that describes the hourly order or a change of method. One CPCB page, clip.cpcb.gov.in's answer to "How is AQI calculated?", could not be opened, so its content is not known.

When Delhi's air is at its worst, the hour-by-hour calculation that CPCB's published AQI tracks gives a lower figure than CPCB's own written formula gives for the same readings: on 926 of 928 Very Poor or Severe days in the record from 1 May 2015. On 630 of the 640 days since 2018 that CPCB's bulletin printed Delhi as Very Poor or Severe, CPCB's own formula gave the higher figure, so on those days the air looks less bad than CPCB's own formula rates it. On cleaner days, mostly Moderate ones, and at single stations where PM10 sets a figure below 350, the documented formula can give the lower figure.

None of these questions changes the station test. CPCB's published station figures sit 4.1 to 7.9 points from the hourly order and 15.7 to 25.0 from the documented formula.

This annexure gives the data, the definitions, the scripts and the checks behind every figure in the investigation.

The documented formula takes, for each station, the 24-hour average of PM2.5, PM10, NO2 and SO2, and the highest 8-hour average of CO and ozone among the 8-hour blocks lying wholly inside the 24 hours, converts each through CPCB's breakpoints, and takes the highest. The reconstruction takes, for each of the four, the average of each hour's converted figure, and for CO and ozone the converted 8-hour average ending at 4 PM, and takes the highest. A sub-index needs 16 valid hours, and a station's AQI needs three pollutants including PM2.5 or PM10, on both.

On every one of the 8,708 station-days of the station test that the reconstruction put in Very Poor or Severe, PM2.5 or PM10 set the documented figure, so the 8-hour block of CO and ozone plays no part on those days. Above 380 µg/m³ of PM2.5 and 510 of PM10, CPCB's calculator carries on past 500; this office holds both computed figures at 500 there, as CPCB's scale of 0 to 500 does. This can only lower the documented figure, and in the station test it held the documented figure at 500 on 1,403 station-days. This investigation uses the 8-hour ozone value throughout; CUPS/82/2014-15, Table 3.11, marks the ozone cells above 208 µg/m³ "*One hourly monitoring (for mathematical calculation only)".

Higher means higher before rounding. After rounding to whole numbers, as CPCB prints its figures, the documented figure is higher on 923 of the 928 days and equal on 3, and from 2018 higher on 660 and equal on 2.

Every figure is on the 24 hours ending 4 PM, the window of CPCB's bulletin. Delhi's city figure is the average of the station AQIs on each basis; each basis keeps its own station set, which was the same on 4,031 of 4,127 days and one station apart on the rest. A city figure is placed in a category after rounding half up to a whole number. The station test covers 28,826 station-days at 13 stations in the 4 PM window, and the same station-days give the direction counts. CPCB's bulletin station count could not be read on 212 of the days, mostly from 2015 to 2019; its Delhi figure was read on every day, and was checked against the bulletin's own page on 13 and 29 May 2015. Selected instead on the category CPCB's bulletin printed, 923 days were Very Poor or Severe; the documented formula was higher than the reconstruction on 920 of them and higher than the bulletin on 859.

The cover's count is the number of Delhi's Very Poor or Severe days on which CPCB's documented formula gives the higher figure. The table repeats it with the days chosen in other ways.

Banded by CPCB's own published category, CPCB's figure sat 7.3 points below the hour-by-hour calculation on Very Poor station-days and 10.3 on Severe ones. Banded instead by the hour-by-hour figure's own category, the gaps are 7.0 and 12.1, so the overshoot does not come from which series chooses the days.

At two stations, Wazirpur and Sonia Vihar, both hourly compilations store carbon monoxide at about a thousandth of its size in every year from 2018, so carbon monoxide can never set either station's figure here. Both computed figures read the same values, the effect falls on days below 200, and it cannot reach a Very Poor or Severe figure. The repair, a check on each station-year's median, waits for the next run of the computation.

The station test and the city computation call the same functions that compute Delhi's daily air record, with nothing retyped. The station test reads CPCB's published station figures from the CCR portal's files and computes both figures for every published station-day. The city computation does the same for every day and every Delhi station, and a summariser joins Delhi's row of CPCB's bulletin by date. The method comparison computes the US and British methods whole, and CPCB's formula with the US area rule, from the same readings, and a second summariser builds the yearly tables on matched days.

Every city of CPCB's 4 PM bulletin from 21 September 2026 to 20 October 2026, with its average gap from CPCB's figure on each order and one example day, 20 October 2026 where the city was in that day's bulletin. Stations are CPCB's count and the computed count; "1 / 1" is a city with one station. "Hourly" is the reconstruction. Delhi's daily record for 20 October 2026, computed on 56 stations, prints 180.1 and 177.6 (page 25); this table's comparison rounds and matches stations its own way, on a median of 45 computed stations against CPCB's 44.

Not compared: Kalaburagi -> no CREA city; Moradabad -> no CREA city. Matched by spelling: Chikkaballapur -> matched by spelling to CREA 'chikkaballarpur'; Mangalore -> matched by spelling to CREA 'manglore'.