ECEF to latitude, longitude, and height

Converts Earth-centered, Earth-fixed X, Y, Z to geodetic latitude, longitude, and ellipsoidal height, in closed form at any height.

Go the other way: Latitude, longitude, and height to ECEF →

Computing your own values needs JavaScript and WebAssembly. The worked example below was computed when this page was built, and the documentation under "How we got this" applies.

40.446111°

Latitude 40.446111°, longitude -79.982222°, ellipsoidal height 300 m.

Longitude
Ellipsoidal height

Provenance

Computed by: geodesy.frame.ecef-to-geodetic 1.0.0, core 0.1.0
Model: ECEF to geodetic (Vermeille closed form), WGS 84
Accuracy: Round trips close within 5 nm near the Earth's surface (a few units in the last place) and within 1e-15 of the distance at any height; matches GeographicLib CartConvert
Notes: None
Cites: Karney, C. F. F., GeographicLib, GeographicLib Geocentric and LocalCartesian classes; National Geospatial-Intelligence Agency, Department of Defense World Geodetic System 1984, NGA.STND.0036

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X Meters from the Earth's center, like 845580.010 · plain numbers mean m Y Meters from the Earth's center, like 845580.010 · plain numbers mean m Z Meters from the Earth's center, like 845580.010 · plain numbers mean m Ellipsoidoptional wgs84 (default), grs80, clarke1866, intl1924, airy1830, bessel1841, or krassovsky1940

More options 2

Custom semi-major axisoptional With inverse flattening, like 3396190 m (Mars) · plain numbers mean m Custom inverse flatteningoptional Like 169.894; 0 for a sphere

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How we got thisFormula, worked example, sources, and proof

Model: Vermeille (2011) closed form, as in GeographicLib's Geocentric class: no iteration

Accuracy: Round trips close within 5 nm near the Earth's surface (a few units in the last place) and within 1e-15 of the distance at any height; matches GeographicLib CartConvert

When to use this: Use this when a position arrives as Earth-centered X, Y, Z — from a GNSS receiver's raw output, a satellite product, or a coordinate exchange — and you need it as latitude, longitude, and height to plot or compare it. It is the inverse of the geodetic-to-ECEF tool and holds at any height, from below the surface to orbit.

Limitations: The height is above the ellipsoid, not above mean sea level: the geoid tool supplies the separation that turns one into the other. The frame the X, Y, Z came in matters as much as the arithmetic — ITRF, a WGS 84 realization, and a regional frame differ by centimeters to meters — and this conversion does not change frames or epochs.

Worked example: Pittsburgh at 300 m. Source: GeographicLib CartConvert -r: 40.446111, -79.982222, 300 m.

You enter

X: 845580.01037 m
Y: -4786836.716953 m
Z: 4116002.385436 m

You get

Latitude: 40.446111°
Longitude: -79.982222°
Ellipsoidal height: 300 m

Review: Not yet independently reviewed by a geodesist.

Last verified: 2026-09-18, when a maintainer last confirmed this tool's sources at the issuer. See the sources ledger.

Status: version 1.0.0, core 0.1.0. See this tool in the verification report.

Changes

2026-09-19, changed: The four frame conversions are stable: geodetic to ECEF and back, and to and from a local east-north-up frame. They reproduce the IOGP Guidance Note 7-2 worked examples and agree with GeographicLib's CartConvert within 15 nm on 1,000 ECEF points (poles to beyond geostationary orbit) and 500 local targets. Results are unchanged. Changelog

Checked against: 30 golden test vectors (download the test vectors, each with its source and tolerance). See how results are checked and every source.

Sources

GeographicLib Geocentric and LocalCartesian classes, Karney, C. F. F., GeographicLib, GeographicLib 2.x. Geocentric.cpp: Vermeille's closed-form inverse; LocalCartesian.cpp: ENU rotation. Read free.
Department of Defense World Geodetic System 1984, NGA.STND.0036, National Geospatial-Intelligence Agency, NGA.STND.0036_1.0.0_WGS84. Table 3.1 (defining parameters) and Table 3.3 (derived geometric constants).

Terms

ECEF: Earth-centered, Earth-fixed: Cartesian X, Y, Z coordinates in meters from Earth's center, turning with the Earth. X points to 0° longitude on the equator and Z to the North Pole. Source: Department of Defense World Geodetic System 1984