A tale of two denominators

Where density
actually lives

From their full-city population density figures, Madrid and London might seem equally dense. But are they?

The first impression

The headline numbers are almost a draw.

Divide every resident by every square kilometre inside the administrative boundary and both cities land near 5,700 people per km². That calculation is correct. It is also answering a narrower question than it appears to.

Madrid—people / km²

≈

Greater London—people / km²

Change the viewpoint

Ask where the typical resident lives.

Instead of weighting every square metre equally, weight each small area by its population. The median resident in Madrid lives in a census section at roughly — the density of the median London resident’s LSOA.

City-wide density → median resident’s small-area density

The resident-weighted median is the density of the small area containing the middle resident. It is not a measure of dwelling crowding or personal experience.

The density spectrum

Madrid’s low average is mostly land where almost nobody lives.

66.4% of Madrid’s territory lies in sections below 1,000 residents per km², but those sections contain only 1.6% of its population. London distributes both land and residents more gradually across the middle of the scale.

Share of territory and population by small-area density

Area shares refer to the full administrative territory inside census sections or LSOAs—not independently classified built-up land.

Land and population deciles

Half of Madrid’s least-dense territory holds just — of its residents.

In London, the least-dense half still holds —. Sorting small areas from sparse to dense exposes how sharply Madrid’s population is concentrated into a small part of its municipal footprint.

Cumulative population across territory, least dense → most dense

Vertical guides mark territorial deciles. A lower curve means more residents are concentrated toward the densest end of the city.

Population deciles

Madrid’s density gap persists across the population—not just at the median.

Each dot represents one-tenth of residents, ordered by the density of their small area. The value is the population-weighted average density within that group.

Average small-area density by population decile, least dense → most dense

Boundary units are split proportionally when a population-decile cut falls inside them, so every decile represents exactly 10% of city residents.

Beyond London’s 99th percentile

Only 1% of Londoners live above — people per km².

Apply that same threshold to Madrid and — of residents live in denser census sections. A shared threshold describes the upper tail more meaningfully than comparing two exceptional polygons.

Share of residents living above London’s population-weighted P99 density

The threshold is the London LSOA density at the 99th population percentile: only the top 1% of London residents live in LSOAs above it.

The useful conclusion

The two cities are not “equally dense.” Their administrative averages merely happen to match.

TerritoryMadrid contains far more very-low-density land.

ResidentsThe typical Madrid resident lives at much higher local density.

Upper tailLondon’s P99 density is exceeded by a much larger share of Madrid residents.

Method & limits

Comparable, not identical.

Geographies. Madrid municipality uses 2,450 census sections; Greater London uses 4,994 LSOAs across its 33 local authorities. LSOAs were selected because their usual population range of 1,000–3,000 is much closer to Spanish census sections than OAs.

Dates. Madrid population is from the INE Annual Population Census at 1 January 2024. London population is the ONS mid-year estimate at 30 June 2024 on 2021 LSOA boundaries. Both count usual residents, but the systems and reference dates are not identical.

Area. Density is population divided by full polygon area. No parks, water, roads or industrial zones were removed. A section or LSOA is treated as uniformly dense for distribution calculations.

Interpretation. This is residential population density—not built-up density, floor-space density, household crowding, building height or daytime population. Results depend on administrative boundaries and small-area design.