Earth-Centered, Earth-Fixed (ECEF) is a 3-D Cartesian system whose origin is the Earth's centre of mass. The Z axis points to the North Pole, X points to the equator/prime-meridian intersection, and Y completes the right-handed frame.

Which ellipsoid does this use?

It uses the WGS-84 ellipsoid: semi-major axis 6378137 m and flattening 1/298.257223563. GPS positions are reported in WGS-84, so this matches almost every GNSS source.

Is the altitude geodetic or orthometric?

The height entered must be ellipsoidal (geodetic) height — the distance above the WGS-84 ellipsoid, not above mean sea level. If you only have an MSL/orthometric height you must add the geoid undulation first.

How accurate is the conversion?

The closed-form geodetic-to-ECEF transform is exact — there is no iteration or approximation. Output precision is limited only by your input precision and floating-point arithmetic, which is sub-millimetre here.

Can I convert ECEF back to lat/long?

Yes, but the reverse transform needs an iterative or closed-form (Bowring) algorithm because latitude appears inside the radius-of-curvature term. This tool only handles the forward, geodetic-to-ECEF direction.

Lat/Lng to ECEF Converter

WGS-84 geodetic to ECEF

This converter turns a geographic position — latitude, longitude and ellipsoidal height — into Earth-Centered Earth-Fixed (ECEF) Cartesian coordinates. ECEF is the frame used internally by GPS receivers, satellite tracking, and many geodetic computations because it expresses a point as plain X, Y, Z metres relative to the centre of the Earth.

How it works

The transform is closed-form. First compute the prime-vertical radius of curvature N at the given latitude:

N = a / sqrt(1 - e^2 * sin^2(lat))

where a = 6378137 m (WGS-84 semi-major axis) and e^2 = f(2 - f) is the first eccentricity squared from the flattening f = 1/298.257223563. Then:

X = (N + h) * cos(lat) * cos(lon)
Y = (N + h) * cos(lat) * sin(lon)
Z = (N * (1 - e^2) + h) * sin(lat)

with latitude and longitude in radians and h the ellipsoidal height in metres. The (1 - e^2) factor on Z accounts for the Earth being an oblate spheroid rather than a sphere.

Example and notes

The Eiffel Tower at roughly 48.8584° N, 2.2945° E, 330 m gives X ≈ 4 200 952 m, Y ≈ 168 386 m, Z ≈ 4 780 740 m. Remember the height must be above the ellipsoid, not above sea level — in Paris the geoid sits about 44 m above the ellipsoid, so an MSL height needs that undulation added before conversion. The transform is exact in the forward direction; converting back to latitude and longitude requires an iterative or Bowring-style solution.