This Saturday night, the capstone of America’s 250th birthday celebration on the National Mall will close with what its organizers bill as the largest fireworks display in history: 850,000 shells launched from ten sites — the Lincoln Memorial Reflecting Pool, eight barges anchored in the Potomac, and West Potomac Park — in a show running approximately 40 minutes. Meanwhile, The Washington Post reported this week that the National Park Service’s own internal modeling expects the show to produce hazardous air pollution around the Mall and “very unhealthy” conditions across downtown D.C., Arlington, and Capitol Hill.
I will get to the smoke. But I am a mathematician and data scientist, and when a press release hands me a number like 850,000, professional habit takes over. I divide.
Eight hundred fifty thousand fireworks in 40 minutes is 21,250 fireworks per minute. It is 354 fireworks per second. It is one firework, on average, every 2.8 milliseconds, sustained for two-thirds of an hour. At the average rate, ten seconds of this show contains roughly 3,500 fireworks — a respectable grand finale for a midsized American city, repeated 240 times in a row.
Rates like this are hard to grasp until you put them next to the human body, so let me try. Harvard’s BioNumbers database puts a typical blink at 0.1 to 0.4 seconds. Every time you blink on Saturday night, you will miss between 35 and 142 fireworks. Film the show on your phone at a standard 24 frames per second, and each frame will capture about 15 fireworks you have not yet seen; at 60 frames per second, six. And if the launches were spaced perfectly evenly, the firing rate would no longer be in the realm of countable rhythm; it would be in the realm of pitch. The F above middle C vibrates at about 349 cycles per second. The show averages 354 events per second. Nobody on the Mall will experience this as fireworks going off one after another in any ordinary human sense.
The physics of sound arrives at the same place. The National Weather Service teaches the rule of thumb that thunder takes about five seconds to travel a mile. In the 2.8 milliseconds between this show’s average launches, sound travels roughly three feet. With ten launch sites strung along a couple of miles of Mall and river, each throwing its own overlapping impulses, the arrivals will not land as distinguishable booms. They will smear into a continuous roar with no silence inside it.
Perhaps you are thinking that Mall fireworks are always excessive, and this is a matter of degree. The data say otherwise. A typical Fourth of July show on the Mall, per the Post’s reporting, lasts 17 to 25 minutes and uses about 20,000 fireworks, which works out to 13 to 20 fireworks per second. Saturday’s show would run at 18 to 27 times that pace. This is not a longer show. It is a different category of event wearing a fireworks show’s clothing.
The comparisons keep failing upward. Guinness lists the largest fireworks display on record at 810,904 fireworks over a little more than an hour, an average of about 220 per second; Saturday would beat the record count while firing about 60 percent faster. NBCUniversal says the 2026 Macy’s show — the 50th anniversary edition of the marquee fireworks broadcast in America — will use more than 85,000 shells across 27 minutes. Saturday’s plan is ten entire Macy’s shows. Five minutes at the average rate — 106,250 fireworks — would exceed Macy’s full count on its own. And spreading the launches evenly across the ten sites does not tame anything: each individual site would still average 35 fireworks per second, roughly double the pace of an entire ordinary Mall show. Ten of those, at once, for 40 minutes.
I want to be careful with the noise question, because it invites bad math. Decibels are logarithmic; you cannot multiply one firework’s loudness by 354 and report the product. Here is what can be said responsibly. The National Institute on Deafness and Other Communication Disorders places fireworks shows at 140 to 160 dBA — above sirens, in the range associated with impulse-noise hearing risk — and NIOSH’s exposure guidance halves allowable exposure time for every 3-decibel increase. An ordinary show delivers dangerous impulses with recovery gaps between them. This one proposes to fill the gaps with more impulses, from ten directions, for 40 minutes. The organizers appear to understand this better than their superlatives suggest. Their own event page advises that “all attendees should wear hearing protection during the event – especially young children,” concedes that the show may be difficult for veterans and people sensitive to loud noise — this for a program whose fireworks begin between 10:30 and 11 at night — and then offers a reassurance I have now read a dozen times: “Fireworks will proceed as scheduled.”
Then there is what all that combustion leaves in the air. According to the Post’s reporting on the internal documents, the Park Service’s expected scenario puts fine particulate matter — PM2.5, the pollutant that penetrates deep into the lungs and bloodstream — at 600 to 1,200 micrograms per cubic meter around the Mall, with a worst case above 2,000 and elevated levels persisting three to six hours after the show. For scale: the EPA’s 24-hour health standard for PM2.5 is 35 micrograms per cubic meter, and the Air Quality Index’s “hazardous” category begins at 225.5. The expected plume runs 17 to 34 times the daily standard and roughly three to five times the hazardous threshold. One caveat: those benchmarks are 24-hour averages, and the plume is a spike lasting a few hours, so this is a comparison of scale rather than a formal violation. Still, a spike running many times the daily standard is the part worth worrying about. The government’s own draft analysis tells people near the Mall to avoid prolonged exposure, and a companion document advises wearing an N95 outdoors and remaining indoors as much as possible during and after the show. That is the official guidance for attending a birthday party.
We already know what fireworks smoke does, because people have measured it. A study of 315 U.S. monitoring sites found that an ordinary July Fourth raises national 24-hour PM2.5 by 42 percent on average, and a monitor adjacent to one display caught an hourly spike near 500 micrograms per cubic meter. After the 2023 Macy’s show, NYU Langone researchers measured pollution near the display exceeding what the city had experienced during that summer’s Canadian wildfire smoke. Those are the fingerprints of shows a tenth this size or smaller. The low end of Saturday’s expected scenario tops the worst hourly reading in the 315-site study. The worst case quadruples it.
One more detail from the Post’s reporting is worth sitting with. An internal Park Service document advises staff not to “treat race, ethnicity, income, disability, age, or language as risks by themselves.” The Post notes that the launch sites are not far from areas such as Southeast Washington, which it describes as predominantly Black and lower-income — populations in which, as George Thurston, a professor of medicine and population health at New York University, noted in the same reporting, asthma and cardiovascular disease are more prevalent. Whatever that memo intends, the plume will go where the wind takes it, and the wind has not read the memo.
To be fair, “850,000 fireworks” is a slippery unit. Shells, effects, and pyrotechnic events get counted differently across shows and sources, and the comparisons above are order-of-magnitude benchmarks, not audited rankings. It is possible the organizers are counting generously. But notice what happens if, conservatively, you cut their number in half. A show at 177 fireworks per second still runs nine to thirteen times the usual Mall tempo, still packs five entire Macy’s shows into 40 minutes, and does nothing at all to the air-quality projections, because those come from the National Park Service’s scientists, not from my division.
A fireworks show is supposed to be choreography: a launch, a bloom, a breath before the next one. At 354 per second there is no breath. There is a 40-minute wall of light and roar that no blink and no camera frame can resolve into individual fireworks, which means the only witness in a position to appreciate all 850,000 of them will be the launch computer. The organizers seem to have arrived at the same conclusion by their own route. Their guidance calls for hearing protection for all attendees, an N95 outdoors, windows closed at home, and as much time indoors as possible during and after the show. Helpfully, the event page also offers a livestream. Assemble all the recommendations and the optimal way to experience the largest fireworks display in history turns out to be from a sealed room, watching it on a screen. For once, the organizers and the arithmetic agree.
This is the kind of data-driven justice work I do in my book Unlocking Justice, now available from Princeton University Press.