Module 2, lesson 4 · 40 minutes
Where the red line is: density thresholds and their sources
Guidance quotes density limits from 2 to 6 p/m², and disasters reach beyond 10. Every one of those numbers was derived for a purpose; knowing which is the skill.
You’ll be able to
- give the main density thresholds with their sources: planning 2, moving critical 2–4, Green Guide standing 4.7, Still’s upper limit 5, Oberhagemann’s critical about 6, Helbing’s flow collapse at 6, observed 8–10 and above;
- explain what each was derived for, and the difference between standing and moving figures;
- explain why any single “safe density” is wrong.
Introduction
In a 2022 television interview, Keith Still explained crowd density like this: “The way I liken that is to a tachometer on a car… There’s a red line… It’s the same as crowd density – you need to keep the crowd below that density in order to keep it moving”
It is a good analogy, and it raises the obvious question: where is the red line? Ask five people who work in crowd safety and you may get five answers: 2, 3–4, 4.7, 5 and 6 people per square metre. Strangely, they can all be right. Each number comes from a different source, was derived for a different purpose, and applies to a different kind of crowd. This lesson lays them side by side so you never quote one out of context.
The thresholds, side by side
Read the table by its last column. A planning figure tells you what to design for. A warning figure tells you when to act. A physical figure tells you what is possible at all.
| Density | Source | What it says | Purpose |
|---|---|---|---|
| 1.75 | Weidmann 1993 | Flow reaches its maximum, about 1.23 p/m/s | Moving: capacity |
| 2 | Oberhagemann 2012 | Germany’s regulatory and evacuation planning basis; a typical UK event safety limit | Planning |
| 2–3 or 2–4 | Still’s web pages | Critical density for flow; his two pages disagree | Moving: warning |
| below 3–4 | Johansson et al. 2008 | Recommended maximum from the Mina analysis | Moving: design and operation |
| 4 | Still | Moving queueing systems (guidance) | Moving: queues |
| 4–5 | Helbing & Mukerji 2012 | “Once the crowd density exceeds between 4 or 5 persons per square meter, congestion can build up quickly” | Moving: warning |
| 4.7 | Green Guide | 47 people per 10 m²: the maximum for standing spectator areas | Standing: design limit |
| 5 | Still | “this should be the UPPER limit for standing/viewing spaces”; labelled “Maximum” on his risk scale | Standing: limit |
| 5–6 | Oberhagemann 2012 | Voluntary peaks observed at events (usually 4 or less); advice to keep sections below 5–6 | Standing: observed and advised |
| about 6 | Oberhagemann 2012 | Critical density: force can no longer be absorbed. “High Risk” on Still’s scale | Physical: danger |
| 6 | Helbing et al. 2007 | Above this local density, local flow falls by a factor of 3 or more | Physical: flow collapse |
| about 7 | Fruin 1993 | “the crowd becomes almost a fluid mass” | Physical: danger |
| 8 and above | Oberhagemann 2012 | Occurs only under external pressure | Physical: crush |
| over 10 | Helbing et al. 2007 | Local densities at Mina in 2006, measured over a 1 m radius | Observed in a disaster |
| 10.74 | Itaewon reconstruction | Simulated density at 22:25 (an AP report gives about 8 at 22:15) | Observed in a disaster |
Oberhagemann’s report also gives the physical ceiling. A clothed body takes about 0.15 m², which caps density at about 6.6 p/m² for people standing normally; up to about 8.2 is theoretically possible; and Weidmann’s minimum body area of 0.085 m² gives a theoretical 11.8
Standing is not moving
A common mistake with these numbers is to use a standing figure for a moving crowd. A standing spectator needs room for their body. A walking person needs room for a stride and for the person in front to move away. That is why the planning and warning figures for moving crowds all sit below the standing ones.
Module 1 showed that flow peaks at about 1.75 p/m²
A colleague reviewing an exit concourse says: “It’s fine, the Green Guide allows 4.7 p/m².” What is wrong with the argument?
4.7 p/m² is a standing figure for spectator areas. An exit concourse carries a moving crowd, whose critical range is about 2–4 p/m² and whose flow peaks near 1.75 p/m². At 4.7 p/m² the concourse would be well past the flow maximum: slow, unstable and liable to stop-and-go waves. The right figures are the moving ones, and the Green Guide itself sizes exits with rates of passage (82 and 66 p/m/min), not with the standing density.
Why a single number is wrong
Even within one kind of crowd, “the safe density” does not exist as a single number. Five reasons:
- Purpose. A planning basis has a margin built in; a warning threshold is where you act; a physical limit is what kills. 2, 4 and 6 p/m² can all be “the” number for the same crowd, used for different decisions.
- Local versus average. At Mina “the maximum local densities are twice as high as the average densities”
. An area averaging 3 p/m² can contain patches at 6, where force stops being absorbed. Oberhagemann likewise reports event-wide averages below 2 alongside local peaks of 5–6 . - Who is in the crowd. Still notes that the Green Guide’s 4.7 p/m² “fails to highlight that the demographics (individual sizes) need to be factored into the density analysis”
. Bigger bodies, winter coats or rucksacks fill space sooner. - How it is measured. “Crowds rarely pack in regular formation”, and “Density can appear higher with lower CCTV angles”
. The Mina thresholds depend on the measurement radius . A density is always a density over some area, from some viewpoint. - Time and dynamics. A crowd standing at 5 p/m² for a few minutes of a goal celebration is a different risk from one held there for an hour with more people arriving. Lesson 1’s force figures pair force with duration for the same reason.
Two pages on Keith Still’s own website give different critical densities for crowd flow: “2–3 people per square metre” on one, “2–4 people per square metre” on the other
Worked example: one square, three numbers
A city square has 400 m² of usable standing space for a concert.
- At a planning density of 2 p/m², the basis used in Germany and a typical UK event limit
, the square holds 400 × 2 = 800 people. - Suppose 1,200 people arrive. The average is 1,200 ÷ 400 = 3 p/m², comfortably below Still’s standing limit of 5
. - But crowds do not spread evenly, least of all in front of a stage. If, as at Mina, local peaks reach twice the average
, the front could be at about 6 p/m², the density at which Oberhagemann says force can no longer be absorbed .
The average says “fine”. The physics at the front may say otherwise. This is why Module 7 spends a lesson on monitoring density where it matters, not just counting heads.
A CCTV operator reports that a square “averages 3 p/m², well under the limit”. Give two questions you would ask before agreeing.
Where is the densest part, and what is the density there? An average can hide local peaks of twice its value. And: which limit, for what kind of crowd? A moving or queueing crowd at 3 p/m² is already at or past the critical range for flow. Good further questions: how was it measured (camera angle, area), how long has it been like this, and is it rising?
- “There is one safe density.” There are planning, warning and physical figures, for standing and for moving crowds. Each answers a different question.
- “4.7 p/m² is safe for a moving crowd.” It is a standing figure for terraces
. Moving crowds reach their critical range at 2–4 p/m². - “The average density tells you the risk.” Local densities can be twice the average
; the danger is in the peaks. - “Experts agree on the number.” Even one expert’s pages disagree (2–3 vs 2–4)
. Always cite the source.