Above four people per square meter, a crowd behaves like a fluid. Above six, the fluid starts to behave like a solid that's trying to be a fluid, and people die. Almost everything that matters about crowd safety is in those two sentences, and almost everything the public believes about it is wrong.

Level of service

The engineering framework comes from John Fruin, who in the early seventies turned pedestrian flow into something you could put in a table. He defined levels of service, A through F, by density, the way traffic engineers already did for roads.

• Below about 0.3 people per square meter, everyone walks freely, chooses their own speed, passes at will.

• Around 1 per square meter, you start adjusting to others. Passing needs care.

• At 2, movement is constrained to the crowd's pace. You can't easily reverse.

• At 3 to 4, contact is frequent. You're walking with your arms in.

• At 4 to 5, contact is constant. Movement is a shuffle. You're touching people on all sides.

• Above 5, you no longer control your own motion.

That last line is the whole subject. Below it, a crowd is a collection of individuals who are each choosing where to go. Above it, the individuals are still choosing, but the choices have stopped mattering, because the medium moves them. The unit of analysis is no longer the person.

The fluid

At around 4 per square meter, each person's shoulders touch the neighbors'. Force applied at any point transmits through the bodies. If the crowd is moving, a stop at the front propagates backward as a compression wave, exactly like traffic, except that cars have bumpers and a fixed minimum spacing and people do not. People compress. That's the difference between a traffic jam and a crush.

Dirk Helbing, who has done the most careful physics on this, analyzed video from the Hajj in 2006, where 346 people died on the approach to the Jamarat Bridge. What he found was a transition. First the crowd went from free flow to "stop-and-go," waves of motion and halt moving backward through the mass. Then, above about 7 per square meter, it entered what he called crowd turbulence: sudden, unpredictable displacements of groups of people in random directions, several meters at a time, driven by pressure differences within the crowd. People were lifted off their feet. They couldn't fall because there was no room to fall into. Shoes came off and stayed behind.

Turbulence is the fatal regime. In it, the forces are not coming from any direction you can push back against. They come from everywhere and change by the second.

How people actually die

The word everyone uses is "stampede," and it's almost always wrong. A stampede implies people running over each other. In nearly every mass-casualty crowd event on record, nobody was trampled. They were crushed standing up.

The mechanism is compressive asphyxia. At crowd pressures that have been measured above 4,500 newtons per meter, strong enough to bend steel barriers, the chest can't expand. You can't inhale. It takes only a few minutes. People die upright, held in place by the people around them, and are found still standing when the pressure releases. Those who fall are often at the bottom of a pile that forms not because anyone ran but because a wave pushed the front of the crowd into an obstacle and the people behind kept coming, unaware.

That last part is the key. The people at the back don't know. They feel a slow forward drift and they lean into it, because that's what you do at a concert or a gate. Their lean is force. It transmits forward through a hundred bodies and arrives at the front as a wall. Nobody at the back is panicking. Nobody at the back is doing anything wrong. The physics is doing it.

The panic myth

Which is why the "panic" in the title is a bit of a trap. The crowd-safety researcher Keith Still has spent decades arguing that mass panic, in the sense of a crowd losing its collective mind and turning on itself, essentially doesn't happen. Video and survivor accounts from crush after crush show the opposite: people helping each other, passing children overhead, trying to lift the fallen. Crowds are cooperative right up to the point where cooperation is physically impossible.

What looks like panic from outside is people responding rationally to a force they can't see the source of. If you're being crushed, you push. Pushing is correct. It is also, aggregated across thousands of people, the thing that kills.

The myth matters because it changes who gets blamed. "Panic" says the crowd did it. The evidence says the venue did it: the layout, the capacity, the entry rate, the one point where too many people were allowed to converge on too little space. Hillsborough in 1989 was blamed on fans for over two decades before an inquiry concluded the deaths were caused by a decision to open a gate into already-full pens. The crowd didn't fail. The pen did.

Design

The engineering response is unglamorous.

Flow rates: a crowd can pass through an opening at roughly 80 people per minute per meter of width before density on the upstream side starts to climb. Exits are sized to that. If your inflow exceeds your outflow, density accumulates, and the accumulation is at the exit, which is exactly where you don't want it.

No bottlenecks in series. Two chokepoints in a row create a reservoir between them that fills before anyone notices.

Monitor density, not headcount. A venue at half capacity can have a fatal pocket in front of the stage if everyone moves forward at once. Astroworld in 2021 had ten deaths in a crowd well under the venue's total rating. The number that mattered was local.

And the strange one: put an obstacle in front of the exit. A column placed a couple of meters upstream of a door, slightly off center, breaks the arch of people that forms at a bottleneck and lets them through in a steadier stream. It looks like it should make things worse. In simulation and in practice, it improves flow. The physics of granular materials is not intuitive and that's why it needs engineers.

Feeling it

I've been in a crowd at 4 per square meter, once, in a stadium concourse after a match, and the thing I remember is how calm it was and how completely I was not in charge of my feet. I moved because everyone moved. I did not push. Nobody around me was pushing. And I was moving anyway, at a pace I didn't choose, toward a stairwell I couldn't see, and if that stairwell had been blocked I'd have arrived at it as force, along with everyone behind me, and none of us would have been doing anything wrong.

Four. That's the number. Below it you're a person. Above it you are a fluid, and fluids don't panic. They just flow toward whatever is downhill, and if there is a wall there, they flow into the wall.