I'm looking for the formula which converts WGS84 coordinates to EPSG:2163. I know that QGIS can do the calculations. but I need the exact formula?

  • 4
    EPSG 2163 is the Lambert Equal-Area Azimuthal projection, nominally based on the Clarke 1866 spheroid. Because you are converting from WGS84, you likely need the ellipsoidal formulas (rather than the spherical ones) and the change of datum. This site does not have the markup capabilities to present those formulas adequately, because they would take up several pages. You can find the projection formulas in John Snyder's monograph on pp 187-188 with an example on p. 332.
    – whuber
    May 19, 2013 at 15:09

1 Answer 1


EPSG: 2163 is a Lambert azimuthal equal-area projection, and you can easily find a brief idea of the required formulas on the wikipedia page for Lambert azimuthal equal-area projection. Please note that these are valid for a sphere.

Since we work with an ellipsoid, you need more intricate forumlas.

My go to reference for projection related information is Map Projections: A Working Manual, 1987, Snyder, John P.

It contains a lot of information about projections, includes detailed explanations, formulas, and examples. You should refer to it, for the detailed elipsoidal formula.

You can find the projection formulas in the above reference on pp 187-188 with an example on p. 332.

  • +1 But the Wikipedia page does not provide the ellipsoidal formulas, which sensu strictu are required for EPSG 2163.
    – whuber
    May 19, 2013 at 17:26
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    @whuber: I've clarified the answer to indicate that the wikipedia page is only a starting point. May 20, 2013 at 4:01

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