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.

ECEF to Lat/Lng Converter

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.

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 and then solves for the geodetic latitude in one step using the first and second eccentricities of the ellipsoid.

X 4201152.8, Y 168331.8, Z 4780461.6  ->  48.8584 N, 2.2945 E, alt 330 m

Once latitude is known, the radius of curvature in the prime vertical gives the ellipsoidal altitude.

Example and tips

The altitude returned is height above the ellipsoid; subtract the local geoid undulation if you need height above sea level. Inputs are in metres, so a typical ground point has values in the millions. Use the result with the Lat/Lng to Plus Code or Maidenhead tools to express the same location in other systems.