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How do I figure out the longitude and latitude coordinates necessary to create a circular 1 mile radius around one location? I don't mind how many coordinates that takes.

For instance: Latitude = 28.4789 Longitude = -81.4682

What mathematical theorem or formulas would you use to accomplish a task like this?

(I'm not using google maps, I just need to generate the necessary longitude and latitude to form the radius)

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  • Once you realize that in (lat, lon) coordinates a spherical circle is (to a good approximation) a mathematical ellipse (except close to the poles), all the rest of the information you need can be found by looking at our spherical-geometry threads.
    – whuber
    Feb 26, 2014 at 22:07

1 Answer 1

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You can use the Haversine formula in conjunction with basic trig to iterate a series of vertices describing your circle.

Alternatively, if you have access to a GIS (e.g. ArcGIS, QGIS, PostGIS etc) or a GIS API (e.g. OGR, Shapely, GeoTools) you could simply buffer the point by one mile. E.g. for PostGIS you could use ST_Distance_sphere or ST_Distance_spheroid.

Also, one mile is not a huge distance so the error between spherical geometry and a planar approximation will not be great and may not be significant (depending on your use-case and accuracy requirements). So, you could consider working in a projected coordinate system (choosing a suitable one centered close to your area of interest will minimise error) and dispense with Haversine. Obviously over a greater distance it is more of an issue. Only you can say how critical it will be.

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  • (+1) But Haversine really isn't needed for circles this size until you are practically at one of the poles. It's enough to plot an ellipse of 2 mile major axis north-south and 2/cos(latitude) mile minor axis east-west where a "mile" is converted to degrees as if one were at the Equator.
    – whuber
    Feb 26, 2014 at 22:10
  • Distance type to use for latitude/longitude is referred to as the orthodromic distance (also known as the great circle distance). As Mappa says though, since it's one mile only it probably won't make much difference. Aug 30, 2015 at 20:45

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