What are ECEF coordinates?

Earth-Centered, Earth-Fixed coordinates describe a point with three Cartesian values X, Y and Z, measured in metres from Earth's center of mass. The axes rotate with the planet, so a fixed point on the ground has constant ECEF values.

Which ellipsoid does this use?

It uses the WGS-84 ellipsoid, the global reference for GPS, with a semi-major axis of 6378137 metres and a flattening of 1/298.257223563. The same model underlies most consumer positioning.

What is ellipsoidal altitude?

Ellipsoidal altitude is the height above the WGS-84 ellipsoid, not above mean sea level. To get height above sea level you must apply a geoid model, which differs from the ellipsoid by tens of metres in places.

Why use Bowring's method?

Bowring's closed-form formula converts ECEF to geodetic latitude in a single non-iterative step with sub-millimetre accuracy at typical altitudes, avoiding the slow iteration that a naive approach would need.

What if all three values are zero?

X = Y = Z = 0 is Earth's center, where latitude and longitude are undefined. The tool rejects that input rather than returning a meaningless answer.

What is the ECEF to Lat/Lng Converter?

Convert ECEF Cartesian coordinates (X, Y, Z in metres) to WGS-84 geodetic latitude, longitude and ellipsoidal altitude. Uses Bowring's closed-form method with the exact WGS-84 ellipsoid constants. It runs free in your browser on Gera Tools, with nothing uploaded.

ECEF to Lat/Lng Converter

Name: ECEF to Lat/Lng Converter
Creator: Gera Tools
License: https://creativecommons.org/licenses/by/4.0/

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ECEF and geodetic coordinates

GPS hardware and orbital software often work in Earth-Centered, Earth-Fixed (ECEF) Cartesian coordinates: a point is just an X, Y and Z distance in metres from the planet’s center. Humans and maps prefer geodetic latitude, longitude and altitude. This tool converts the former into the latter on the WGS-84 ellipsoid.

The need for ECEF-to-geodetic conversion comes up frequently in satellite navigation, precision agriculture, robotics with GPS sensors, GIS pipelines, and drone-path processing. When you download raw GNSS data or receive telemetry from a surveying receiver, the native output is often a three-component Cartesian vector, and mapping software expects latitude and longitude. This is the conversion step between those two worlds.

How it works

Longitude is straightforward: it is the angle in the equatorial plane, computed as atan2(Y, X). Latitude is harder because the Earth is an ellipsoid, not a sphere. The converter uses Bowring’s closed-form method, which estimates an auxiliary angle called the reduced latitude and then solves for the geodetic latitude in one step using the first and second eccentricities of the WGS-84 ellipsoid (semi-major axis 6,378,137 m, flattening 1/298.257223563). Unlike iterative approaches the method reaches sub-millimetre accuracy in a single pass, making it fast and suitable for batch coordinate conversion.

Once latitude is known, the radius of curvature in the prime vertical N(φ) gives the ellipsoidal altitude:

h = sqrt(X² + Y²) / cos(φ) − N(φ)

Worked example

The Eiffel Tower in central Paris has approximate ECEF coordinates:

X =  4,201,152.8 m
Y =    168,331.8 m
Z =  4,780,461.6 m

Applying Bowring’s method yields:

Latitude  ≈  48.8584° N
Longitude ≈   2.2945° E
Altitude  ≈  330 m above WGS-84 ellipsoid

Because the geoid (mean sea level surface) differs from the WGS-84 ellipsoid by roughly +48 m at this location, the true orthometric height above sea level would be about 282 m — close to the Eiffel Tower’s base elevation, as expected.

Practical guidance

Input scale: a typical ground point has X, Y, Z values in the millions of metres. Inputs close to zero indicate a point near Earth’s centre — the tool will reject X=Y=Z=0 where latitude and longitude are undefined.
Altitude vs. elevation: the tool returns ellipsoidal height, not metres above sea level. To convert, subtract the local geoid undulation (the N offset), available from NOAA’s GEOID18 model for North America or EGM2008 globally.
Negative Z: points in the southern hemisphere have negative Z values. That is expected; latitude will be reported as a negative (south) value.
Follow-on conversions: paste the resulting latitude and longitude into the Lat/Lng to Plus Code or Maidenhead tools to express the same location in other coordinate systems useful for amateur radio or logistics apps.