Radius Map

How the Radius Map works

What a radius map shows, and what it does not

A radius map answers one question: what lies within a given straight-line distance of a point? That is distance as the crow flies, the same measure used for many real rules and decisions:

• a planning notice sent to every address within 50 metres of a site
• a school admissions policy that ranks applicants by distance from the gate
• the delivery zone of a restaurant that stops at 3 miles
• the 5 km exercise limit Ireland set during its 2020 lockdowns
• the 400 m and 800 m walking catchments that transport planners draw around bus stops and stations, roughly five and ten minutes on foot
• the range of a radio transmitter or a drone. UK rules require a recreational drone to stay within visual line of sight, commonly taken as about 500 m.

What a circle cannot show is travel time. A 10 km circle around a town on a river crossing takes in places that are 40 minutes away by the nearest bridge. A map of time rather than distance is called an isochrone, and it depends on the road or path network. Treat the circle as the upper bound: nothing outside it is closer than the radius by any route.

How the circle is drawn

The circle is drawn at its true ground radius, so it stays correct at every zoom level. On the web map it looks larger the further you are from the equator, because the Web Mercator projection used by nearly every online map stretches distances north and south. A 100 km circle over Oslo covers about four times the screen area of the same circle over Lagos. That is the map being honest about the distortion, not a fault in the circle.

The GeoJSON download traces each circle as a 64-sided polygon. Each vertex is placed with the spherical destination-point formula on a sphere of 6,371,008.8 m, the mean radius of the Earth. For a 5 km circle, the gap between a polygon edge and the true arc is under 7 m.

Reading the result

• Radius is the distance you set, shown in both kilometres and miles to two decimal places. One mile is exactly 1.609344 km, so 5 miles is 8.05 km.
• Diameter is twice the radius, the full width of the circle across the centre.
• Area per circle is π × radius², in km² and mi². A 5 km circle covers 78.54 km² and a 5 mile circle 78.54 mi², which is 203.4 km². Area grows with the square: doubling the radius quadruples the area, so a 10 mile delivery zone has four times the addresses of a 5 mile one, not twice.
• Circumference is 2π × radius, the length of the edge. It is useful for fencing a circular exclusion zone or estimating a loop run around a point.
• Circles counts how many centres you have placed. The coordinates of each appear below, to five decimal places, about 1 m.

The flat π r² formula ignores the Earth's curve, but the error is tiny at useful sizes. At a 100 km radius, the true area on the sphere is less than 0.01% smaller.

Common radius sizes at a glance

Tips for accurate circles

• Paste coordinates for precision. Clicking is good to a few metres at street zoom, but a precise point needs decimal coordinates such as 51.5074, -0.1278. Right-click a spot in most online maps to copy them. The first circle moves there. After that, typed coordinates move the most recent circle.
• Compare sites with several circles. Every circle shares one radius, which suits questions like "which of three warehouse sites covers the most towns within 25 miles?". Undo point removes the last circle.
• Different radii need two exports. Download the GeoJSON at one radius, change it, download again, and merge the files in QGIS or another GIS.
• Frame before saving the PNG. The image is the current view with its tiles, circles and an OpenStreetMap credit, sized to the map on screen, so zoom and pan first.
• Check the unit. A drone permission written in metres and a delivery radius in miles differ by a factor of 1,609. The km to miles converter handles the switch.

Related map tools

To measure the actual distance along a route rather than a radius, use the map distance calculator. Map area measures an irregular shape such as a field or a catchment boundary, and draw on map lets you sketch lines, shapes and labels over the same base map.

Related tools