Phoenix radius map: 5, 10, 25 and 50 mile circles

The inner circle has no GeoNames name anywhere on it, which tells you something about how Phoenix is built. At the other end, Florence is 49 mi out to the south-east, near enough the edge of the 50 mi ring. Everything in between scales from those two.

One caution before you lean on the table. A GeoNames centre is a single point, usually somewhere near the historic core, and a city isn’t a point. Tempe Junction is listed at 7.9 mi because that’s the gap between two reference points. Its nearer edge is closer than that, probably by a good margin.

Place names, coordinates and populations come from GeoNames, which the site uses under CC BY 4.0.

Area climbs with the square of the radius, and it catches people out every time. The 5 mi disc around Phoenix covers 79 mi². The 25 mi one covers 1,963 mi², twenty-five times as much for five times the distance. By 50 mi you’re looking at 7,854 mi² of Arizona and whatever lies past its edges.

Put the two tables together and you get a crude density. Inside the 25 mi circle there are about 4,055,112 listed people spread over 1,963 mi², so roughly 2,066 per mi². Crude is the right word. It counts GeoNames settlements only, so villages and open country vanish, and it treats a harbour or a reservoir as populated ground.

Every circle here is a straight-line radius, measured crow-flies. Florence shows up at 49 mi south-east, and the road out there will be longer. Always is. In a town laid out on a grid, reckon on 20 to 40 per cent more actual travel than the radius says. Put a river, a harbour or a decent hill in the way and that rule of thumb stops meaning much at all.

Plenty of sites draw a plain circle, label it drive time and leave it there. Those are worth ignoring. A proper isochrone needs a road graph, turn restrictions and some idea of traffic, and it changes shape by the hour. What a circle gives you instead is a bound that doesn’t move: nothing outside the 25 mi ring is within 25 miles of Phoenix, whatever the roads do.

On the arithmetic. Distances are great-circle distances on a sphere of radius 6,371.0088 km, worked out with the haversine formula, and each bearing is the initial heading you’d take leaving Phoenix. Areas use the spherical cap rather than πr², which shaves a hair off the flat answer. About one part in seventy thousand at 50 miles. Invisible, and true anyway.

One oddity you’ll notice if you compare pages. Population counts come from GeoNames, which records what the national statistics office last published, so some are a few years old and a couple are more. They’re good for ranking and for rough sizing. The figure carried for Phoenix is 1,650,070, which for some cities means the municipality and for others the whole urban area, so compare it with care.

What people actually use these rings for, roughly in order of how often it comes up: delivery and service areas, finding somewhere to live within a sensible distance of work, sizing a catchment for a shop or a clinic, checking how far an event’s noise and traffic will carry. Straight-line distance is the right first pass for all of them.