Latitude, longitude, and height to ECEF

Converts geodetic latitude, longitude, and ellipsoidal height to Earth-centered, Earth-fixed X, Y, Z.

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

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.

845,580.01m

ECEF X 845,580.01 m, Y -4,786,836.717 m, Z 4,116,002.385 m.

Y
Z

Provenance

Computed by: geodesy.frame.geodetic-to-ecef 1.0.0, core 0.1.0
Model: Geodetic to ECEF, WGS 84
Accuracy: Exact formula in double precision; matches GeographicLib CartConvert to 1 µm
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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Paste a coordinateany notation

Latitude Decimal degrees, north positive, like 40.6413 · plain numbers mean degrees Longitude Decimal degrees, east positive, like -73.7781 · plain numbers mean degrees Ellipsoidal heightoptional Height above the ellipsoid (not sea level), like 300 m; default 0 · 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: X = (N + h) cosφ cosλ, Y = (N + h) cosφ sinλ, Z = (N(1 − e²) + h) sinφ

Accuracy: Exact formula in double precision; matches GeographicLib CartConvert to 1 µm

When to use this: Use this when a calculation wants Cartesian coordinates rather than angles: baselines between stations, vector arithmetic on positions, satellite geometry, or feeding a system that works in X, Y, Z. It takes latitude, longitude, and ellipsoidal height on the ellipsoid you choose. It is also the step before any vector arithmetic between two positions: differences, baselines, and rotations are done in Cartesian space, not on latitudes and longitudes.

Limitations: The height must be ellipsoidal; passing a height above mean sea level puts the point off by the geoid separation, which reaches tens of meters. The result is only as well defined as the frame its input belongs to, and this tool converts coordinates rather than datums, frames, or epochs. The ellipsoid matters: the same latitude, longitude, and height on a different ellipsoid gives different X, Y, Z, so the ellipsoid has to be the one the coordinates belong to.

Worked example: Pittsburgh at 300 m. Source: add-geodesy-suite scenario: X ≈ 845,580.010 m, Y ≈ −4,786,836.717 m, Z ≈ 4,116,002.385 m. It is golden test vector v001, and every build checks the tool still gives its answer within its tolerance.

You enter

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

You get

X: 845,580.01 m
Y: -4,786,836.717 m
Z: 4,116,002.385 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: 25 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