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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 at 22:07

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up vote 6 down vote accepted

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 at 22:10

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