Your Doorstep, Your Radius: Drawing the Real 20-Minute Neighbourhood

The 20-minute neighbourhood is one of those planning phrases that sounds like a promise. In practice, it is a constraint. And constraints are where algebra earns its keep. As of November 2026, the idea is still doing the rounds in UK local plans, but the only version that matters is the one you can draw around your own front door.

Start with one multiplication

A 20-minute neighbourhood begins with a distance, and a distance begins with a speed:

distance = speed × time

Twenty minutes is one third of an hour. Walk at 3 mph — about 4.8 km/h — and you cover 1.6 km. Walk at 4 km/h and it is 1.33 km. At 5 km/h it is 1.67 km. Already the slogan is wobbling. A parent with a buggy, a wheelchair user, someone carrying shopping, or anyone on a steep hill is not working with the same number.

Pick a speed you can honestly sustain. That is your parameter, not a council leaflet's.

Turn the distance into an inequality

Put your front door at the origin, (0, 0). If your reachable distance is r kilometres, then a point at (x, y) is inside your ideal 20-minute patch when:

x² + y² ≤ r²

That is the circle inequality. The boundary is the 20-minute contour; everything inside is reachable in the flat, barrier-free city of the imagination. Real streets are not like that. A railway line, a ring road, a river, a missing crossing or a steep hill can turn a 400-metre straight line into a 900-metre walk. So use route distance where you can, and treat the circle as a first draft.

You can also add waits. If a crossing costs three minutes, your walking time is not 20 minutes but 17. At 4 km/h, the radius shrinks from 1.33 km to about 1.13 km. The algebra is just:

d ≤ v × (20 − w)

where v is walking speed in km per minute and w is waiting time. Small constraints have large geometric consequences.

Draw yours in five steps

1. Choose a realistic speed. If you are unsure, use 4 km/h and then test a slower one.
2. Calculate r = speed × 20 minutes. At 4 km/h, r ≈ 1.33 km.
3. Draw a circle of radius r around your home on a map. Then redraw it using walking routes, not crow-flight lines.
4. Mark the places you actually use: GP, pharmacy, supermarket, school, park, bus stop, library, café, post office.
5. For each one, estimate route distance and waiting time. Test it against your inequality. If it fails, it is outside — however close it looks on the map.

A simple table is enough. Place, route distance, wait, total time, inside or outside. The result is your neighbourhood, not the one in the brochure.

Two streets, two different circles

Imagine two neighbourhoods with the same 20-minute label. In the first, the shop is 400 m away, the GP is 800 m, the park is 300 m and the bus stop is 200 m. At 4 km/h, all sit comfortably inside a 1.33 km radius. In the second, the shop is 1.1 km away, the GP is 2.4 km, the park is 1.5 km and the nearest bus stop is 900 m but across a dual carriageway with a four-minute wait. Same phrase, very different inequality.

Count the amenities inside each circle and you get a crude score. But the algebra also shows why the score is crude: it treats a pleasant, lit, continuous pavement and a muddy shortcut with no crossing as if they were the same. They are not. You can add a barrier penalty — effectively increasing the distance — but the choice of penalty is a judgement, not a mathematical fact.

One-way or round trip?

Here is the question that changes everything: is the 20 minutes one-way or for the whole trip? Many planning definitions are loose about this. If 20 minutes is the round-trip budget, then your one-way time is 10 minutes and the radius halves. At 4 km/h, r drops from 1.33 km to about 0.67 km. That is the difference between a corner shop being around the corner and being a proper walk.

Algebra will not settle the policy argument. It will, however, stop you from comparing two different definitions as if they were the same.

The gap between slogan and street

Draw the council's circle around a town centre or a high street, then draw yours around your door. The places inside the first but outside the second are the gap. Sometimes it is a small gap — a few hundred metres, a missing crossing, a footpath that floods. Sometimes it is the whole point.

The 20-minute neighbourhood is not a yes-or-no badge. It is an inequality with parameters: speed, time, waits, barriers and whether you are counting one way or two. Change the parameters and the circle changes. Draw yours, date it, and compare it with the leaflet. That is when a planning slogan becomes a street-level fact.