# Exact conversion of ECEF to geodetic coordinates

I came across the paper "Exact conversion of Earth-centered Earth-fixed coordinates to geodetic coordinates", which describes a series of equations which can be used to calculate a set of geodetic coordinates from a set of ECEF coordinates. However, there seem to be a plethora of methods for doing this type of calculation, and so I'm wondering:

1. Is this method mathematically correct?
2. Does there exist a closed-form solution to the conversion problem which is widely accepted as a standard in the GIS community?

## 1 Answer

1. The equation continues on the following page, so it's hard to tell.
2. Yes, please see EPSG Guidance Note 7.2 in Section 2.2.1 titled "Geographic/Geocentric conversions" (EPSG code 9602) You will want the reverse conversion to get from X/Y/Z to Lat/Long/Height*.

*Note that height here is defined as height above the ellipsoid, which is often confused with elevation. Elevation is (usually) defined as height above the geoid or mean sea level.

• this is exactly what I was looking for. – Nicolas Holthaus Jan 8 '16 at 18:22
• Note that despite the section name stating otherwise ("Geographic/Geocentric conversions") this in fact gives the conversion for geodetic and not geocentric latitude and longitude - geodetic, as it is asked for in the question. – xaedes Apr 12 '17 at 13:32