One Hundred AQI Points Cover 35.4 Micrograms. The Next Hundred Cover 90.0.

An air quality reading of 150 looks like half again as much particulate as a reading of 100. It is not. The federal Air Quality Index is not a measurement. It is a rescaling of one, and the rescaling changes its stride at every category line. Under the breakpoint table in 40 CFR part 58, appendix G, the first hundred index points cover 35.4 micrograms per cubic meter of fine particulate. The second hundred cover 90.0 micrograms. The third cover 100.0.

That is not an artifact of rounding. It is what the table says, and the rulemaking that set the current numbers said it was abandoning the older method that had set the upper breakpoints by a linear relationship. What follows is the chain that turns an instrument reading into a word on a screen, the arithmetic that fixes how much air one index point is worth at each level, and the two places where the published number is not what a reader assumes.

The Chain

Seven steps stand between a monitor and a color category. Only the first is a measurement. The rest is definition and arithmetic, rewritten as recently as 2024.

  1. A monitor produces hourly concentrations, but the index is defined on a day. The wildfire smoke guidance for public health officials published on EPA's AirNow site puts it in one sentence: “The AQI for PM2.5 and PM10 is a daily (midnight to midnight) 24-hour average, so hourly reporting requires a methodology called the NowCast to estimate the 24-hour AQI for each hour.”
  2. Reporting is triggered by population, not by air. Section 2.1 of the appendix: “The AQI must be reported daily for a metropolitan statistical area (MSA) with a population over 350,000.”
  3. The concentration is cut before any arithmetic runs. Section 3.4 instructs, for fine particulate, “PM2.5—truncate to 1 decimal place”. Truncation is not rounding. A reading of 35.49 does not become 35.5.
  4. The truncated value is located in a row. Table 2 gives six rows for PM2.5 on a 24-hour basis: 0.0 to 9.0 against index 0 to 50, Good; 9.1 to 35.4 against 51 to 100, Moderate; 35.5 to 55.4 against 101 to 150, Unhealthy for Sensitive Groups; 55.5 to 125.4 against 151 to 200, Unhealthy; 125.5 to 225.4 against 201 to 300, Very Unhealthy. The top row is printed open-ended, as 225.5+ against 301+, Hazardous.
  5. The index is interpolated inside that row and nowhere else. Equation 1 takes the truncated concentration, subtracts the lower end of its row, multiplies by the row's index width divided by the row's concentration width, and adds the row's lower index value. Every term in it belongs to a single row.
  6. The result is rounded. Section 3.4 closes the calculation with a seven-word instruction: “Round the index to the nearest integer.”
  7. The largest sub-index becomes the AQI. Section 3.1: “The reported AQI corresponds to the pollutant with the highest calculated AQI.”
From one monitor reading to one index number Only step one is a measurement. Steps two through seven are definition and arithmetic. 1 Monitor Hourly PM2.5 from a continuous instrument 2 Averaging window Midnight to midnight, a 24-hour average 3 Truncation Cut to one decimal place before the math 4 Breakpoint row Five closed rows and one open-ended top 5 Equation 1 Straight line inside the row, not across 6 Rounding To the nearest whole number 7 Highest wins The largest pollutant sub-index is the AQI Before midnight A NowCast estimate stands in for step 2 The day’s own index cannot exist until the 24-hour window closes, so the number shown during the day is a weighted estimate of it, not the same quantity. Source: 40 CFR part 58, appendix G, sections 2.1, 3.1 and 3.4; EPA AirNow wildfire smoke guidance, chapter IV.

Where the Scale Bends

Equation 1 draws a straight line, but only within one row. Each row carries its own pair of ends, and the ratio between those ends is that row's exchange rate between air and index points. Divide a row's width in micrograms by its width in index points and the rate falls out.

  • Good, 0.0 to 9.0 against 0 to 50: 9.0 micrograms spread over 50 points, so one point is 0.18 micrograms.
  • Moderate, 9.1 to 35.4 against 51 to 100: 26.3 micrograms over 49 points, so one point is 0.54.
  • Unhealthy for Sensitive Groups, 35.5 to 55.4 against 101 to 150: 19.9 over 49, so one point is 0.41.
  • Unhealthy, 55.5 to 125.4 against 151 to 200: 69.9 over 49, so one point is 1.43.
  • Very Unhealthy, 125.5 to 225.4 against 201 to 300: 99.9 over 99, so one point is 1.01.

The spread across those five rows is close to eightfold. One index point stands for 0.18 micrograms inside Good and 1.43 micrograms inside Unhealthy, a ratio of 7.93. Ten index points describe 1.8 micrograms at the bottom of the scale and 14.3 micrograms inside the Unhealthy row.

The rate does not simply widen as the air gets worse, either. It narrows once. Read the same rows the other way, in index points gained per microgram added, and Moderate returns 1.86 points per microgram while the row above it returns 2.46. Crossing from Moderate into Unhealthy for Sensitive Groups makes the index 32 percent more responsive to the next microgram, not less.

A uniform scale would look nothing like this. Spread the same 0 to 300 span evenly across the same 0.0 to 225.4 micrograms and every point would be worth 0.75 micrograms.

What one AQI point is worth, row by row Micrograms per cubic meter of PM2.5 covered by a single index point. Computed from the breakpoints. A taller bar means the index moves more slowly through that stretch of air. 0.0 0.4 0.8 1.2 1.6 0.18 Good AQI 0-50 0.54 Moderate AQI 51-100 0.41 Unhealthy for Sensitive Groups AQI 101-150 1.43 Unhealthy AQI 151-200 1.01 Very Unhealthy AQI 201-300 0.75 — one point on a uniform scale over the same range Source: 40 CFR part 58, appendix G, table 2, PM2.5 24-hour column, in force September 2026. Per-point values computed from the row ends.

A Tenth of a Microgram at the Line

Because section 3.4 truncates to one decimal place, 0.1 micrograms per cubic meter is the smallest step the reported concentration can take. The row ends are written to that same resolution, which means each category boundary is exactly one step wide. A day averaging 35.44 micrograms and a day averaging 35.49 micrograms are both reported as 35.4, and both compute to an index of exactly 100, the top of Moderate. A day averaging 35.50 is reported as 35.5 and computes to 101, the bottom of Unhealthy for Sensitive Groups. One hundredth of a microgram at the instrument decides which of two health categories a metropolitan area is told it is in.

Those anchors are not arbitrary. Section 3.1 explains where they come from: “In most cases, the index value of 100 is associated with the numerical level of the short-term standard (i.e., averaging time of 24-hours or less) for each pollutant.” The next sentence covers the lower anchor: “The index value of 50 is associated with the numerical level of the annual standard for a pollutant, if there is one, at one-half the level of the short-term standard for the pollutant or at the level at which it is appropriate to begin to provide guidance on cautionary language.”

Those two standards are stated in 40 CFR 50.20. Paragraph (b): “The primary annual PM2.5 standard is met when the annual arithmetic mean concentration, as determined in accordance with appendix N to this part, is less than or equal to 9.0 µg/m3.” Paragraph (c): “The primary 24-hour PM2.5 standard is met when the 98th percentile 24-hour concentration, as determined in accordance with appendix N to this part, is less than or equal to 35 µg/m3.” The annual figure of 9.0 is the top of the Good row exactly. The 24-hour figure of 35 is not the top of the Moderate row; 35.4 is. A day sitting exactly on the 24-hour standard computes to 99.25 and is reported as 99, one point short of the line.

Where a tenth of a microgram changes the word Concentrations are cut to one decimal place before the index is computed, so 0.1 is the smallest step the reported value can take. Instrument reading, µg/m³ After truncation, µg/m³ Index from equation 1 Category 35.44 35.4 100 Moderate 35.49 35.4 100 Moderate 35.50 35.5 101 Unhealthy for Sensitive Groups The two left columns differ by 0.05 µg/m³ at the instrument and by nothing at all after truncation. The gap between the middle and right columns is 0.01 µg/m³, and it moves the reported label across a category line. Source: 40 CFR part 58, appendix G, section 3.4 and table 2. Index values computed with equation 1.

The Hourly Number Is Not the Daily Number

The index in the regulation is a property of a completed day. The number shown while the day is still running cannot be that quantity, and it is not. AirNow's own documentation says so: “Real-time AQI values are based on a NowCast calculation.” And, more precisely, “For AQI values reported in real-time, before a full day's data are available, the AQI is based on a NowCast calculation.” The daily value is the plain average: “For PM2.5, the AQI is simply the 24-hour average.”

EPA's technical assistance document for AQI reporting, issued in May 2026 as EPA-403/B-26-003, is blunt about the general rule: “The AQI is based on daily air quality summaries, specifically daily maximums or daily averages. It is not valid to use shorter-term (e.g., hourly) data to calculate an AQI value.” The NowCast is the exception the document then sets out. The spread of the last twelve hourly readings is divided by the largest of them; the result is subtracted from one to give a weight factor; and “The weight factor must be between 0.5 and 1. The minimum limit approximates a 3-hour average.” If it comes out lower, “If the weight factor is less than 0.5, then set it equal to 0.5.” Each hour is then multiplied by the weight factor “raised to the power of the number of hours ago the value was measured”, and the weighted sum is divided by the sum of the weights. Data completeness is thin by design: “Missing data: 2 of the last 3 hours of data must be valid for a NowCast calculation.”

The consequence of the exponent is worth stating in plain numbers, because the document does not. When air is stable the weight factor sits near 1 and all twelve hours count equally, 8.3 percent each. When air is changing fast the factor is pinned at 0.5, and the most recent hour alone accounts for 50.0 percent of the value, the most recent three hours for 87.5 percent, and the twelfth hour for 0.02 percent. The same label covers a twelve-hour average and something close to a three-hour one, and the switch is driven by the volatility of the readings rather than by anything visible to a reader.

The Scale Moves When a Rule Moves

The unevenness has a date on it. The current breakpoints took effect with EPA's 2024 particulate standards rule: “This final rule is effective May 6, 2024.” That rule lowered the annual standard, in its own words, “by lowering the level from 12.0 µg/m3 to 9.0 µg/m3”, and moved the index anchors with it, “revising the AQI value of 50 to 9.0 µg/m3” while “retaining the AQI values of 100 and 150 at 35.4 µg/m3 and 55.4 µg/m3, respectively.”

The rule says: “First, the EPA is continuing to use the approach used in the revisions to the AQI in 2012 (77 FR 38890, June 29, 2012) of setting the lower breakpoints (50, 100 and 150) based on the levels of the primary annual and 24-hour PM2.5 standards.” And: “the EPA is revising the upper AQI breakpoints (200 and above), and replacing the linear-relationship approach used in 1999 (64 FR 42530, August 4, 1999) to set these breakpoints, with an approach that more fully considers the PM2.5 health effects evidence from controlled human exposure and epidemiologic studies that has become available in the last 20 years.” The upper part of the scale was set by a linear relationship until it was not. Between the 1999 notice and the 2024 effective date lie 9,042 days.

Where This Doesn't Apply

Every figure above is for the PM2.5 sub-index on a 24-hour basis. Ozone, carbon monoxide, sulfur dioxide, nitrogen dioxide and PM10 have their own rows with their own widths, and on any given day the reported AQI is whichever of them computes highest.

The arithmetic stops at 300. The PM2.5 column's top row is printed open-ended, and section 3.4.c handles what lies past it: “If the concentration is larger than the highest breakpoint in table 2 to this appendix then the last two breakpoints in table 2 may be used when equation 1 to this appendix is applied.” No per-point rate is computed here above 300.

None of this says the index is wrong. An index built to track health evidence has no obligation to be proportional to mass. What does not survive is the reflex reading: that ten index points mean the same amount of air wherever they fall. Between the Good and Unhealthy rows they differ by a factor of 7.93.

Finally, the index exists only where an instrument does. The AirNow smoke guidance notes that “Areas without continuous PM monitors may be able to get temporary, portable monitors through their federal, state, tribal, or local air quality agencies or the U.S. Forest Service, especially when associated with a wildfire incident with an assigned Air Resource Advisor.” Where there is no monitor there is no sub-index at all.

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