I am trying to calculate the point from a given lat/long, a bearing, and a distance.

This is for plotting weather given a aeronautical way point.

For example:

Given a waypoint with a known lat/long (LAX airport control tower), with a bearing of North by Northwest and a distance of 45 nautical miles, where is the point?

I could treat the world as flat, but I think the resulting calculations would be inaccurate the further north the point is since longitudes get more narrow near the poles.

I am mainly interested in plotting these points in the US. Is there a projection that would help me do this?

This is for a Python application I'm writing, and the libraries I have access to are GDAL and Proj4 for projections. So no fancy tools like ArcGIS are available to me.

Ultimately I want to combine 4 or these calculated points to form a polygon that should roughly be about 100-200 miles in width and height.


  • Hi LeeMobile, what software are you trying to plot in? – Michael Stimson Jun 24 '14 at 0:54
  • This is for a Python application I'm writing. I have access to the GDAL and Proj4 libraries, but that's it. – LeeMobile Jun 24 '14 at 0:56
  • That is interesting, there are mixed units involved, nautical miles can't be measured in DD and bearings don't hold true in UTM. What kind of accuracy are you expecting? I can suggest is project the point, draw a circle, project the circle back and intersect with a bearing line. – Michael Stimson Jun 24 '14 at 1:02
  • Would you be able to edit your Question to include those additional details that seem highly relevant to what you are asking, please? – PolyGeo Jun 24 '14 at 1:06
  • 1
    Off-topic, but I always thought that "north by northwest" was a great film, but isn't a real direction – Stephen Lead Jun 24 '14 at 1:48

Funnily enough I have just answered a similar question a couple of minutes ago.

Calculating a circle in Lat/Lons

This link will take you to a page that has describes algorithms for calculating forward azimuths, which is the type of calculation you have described in your question. I don't know if it will have all of the details you need but it should get you started.

Inverse/Forward Azimuths

  • Thank you! This method seems really accurate and is what I was looking for. – LeeMobile Jun 24 '14 at 16:55

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