Coordinates · bounding box
Bounding box from a point and radius.
Enter a centre point and a radius. Get the south, north, west and east limits of the box that contains the whole circle, ready for a map or database filter.
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Enter your coordinates.
Bounding box around a radius
A bounding box is a cheap first filter: select the places inside a rectangle of latitude and longitude, then test the few that remain against the exact distance. With angular radius r = distance / R, the latitude limits are φ ± r and the longitude limits are λ ± asin(sin r / cos φ). The longitude half-width grows with latitude because meridians converge, derived from spherical trigonometry; the great-circle relations they rest on are in the Aviation Formulary.
Worked example. A 50 km radius around Toronto (43.6532, -79.3832) gives latitudes 43.2035 to 44.1029 and longitudes -80.0047 to -78.7617. The box is wider in degrees of longitude (1.243°) than of latitude (0.899°) at this latitude. The corners lie outside the circle, so confirm candidates with the distance calculator.
If the circle reaches a pole, the box spans every longitude. If it crosses the 180° meridian, the western limit comes out greater than the eastern one, and you need two boxes. The radius is limited to a quarter of the earth's circumference.
Frequently asked questions
Which earth radius does this use?
The mean radius of the WGS 84 ellipsoid, 6371.0088 km. Treating the earth as a sphere can differ from an ellipsoidal calculation by up to about 0.3%, so it is right for planning and general use but not for surveying.
Can I type degrees, minutes and seconds?
Yes. Each box accepts decimal degrees (43.6532), degrees and decimal minutes (43 39.19 N) or degrees, minutes and seconds (43°39′11″ N). Use a minus sign or the letters S and W for south and west.
Is every point in the box inside the radius?
No. The box contains the whole circle, so its corners are further from the centre than the radius. Use it as a first filter and then check true distance.
What happens near the poles or the 180° meridian?
If the circle contains a pole the box covers all longitudes. If it crosses the 180° meridian the west limit is larger than the east limit, so split the search into two boxes.
Sources
Checked
- Ed Williams, Aviation Formulary v1.47
- EPSG Geodetic Parameter Dataset: WGS 84 ellipsoid (EPSG:7030)
- NIST SP 811 (2008), Guide for the Use of the International System of Units: mile and nautical mile
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Scope
Spherical-earth geometry using the WGS 84 mean radius. A search filter, not a legal or surveyed boundary.