Local ENU, NED, or AER to point

Finds the latitude, longitude, height, and position of a point given in a local tangent plane at an origin: east-north-up, north-east-down, or azimuth-elevation-range.

Go the other way: Point to local ENU, NED, and AER →

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.

40.5095052756°

The point is at latitude 40.5095052756°, longitude -79.8991260647°, ellipsoidal height 1,179.34 m.

Longitude
Ellipsoidal height
ECEF X
ECEF Y, like -4819000 m
ECEF Z, like 3976000 m

Provenance

Computed by: geodesy.frame.from-local 1.0.0, core 0.1.0
Model: Local east-north-up frame, WGS 84
Accuracy: Round trips within 1e-8 m for points within 1,000 km of the origin
Notes: None
Cites: Karney, C. F. F., GeographicLib, GeographicLib Geocentric and LocalCartesian classes

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Your values

Showing an example. Change anything.

Origin latitude Decimal degrees, north positive, like 40.6413 · plain numbers mean degrees Origin longitude Decimal degrees, east positive, like -73.7781 · plain numbers mean degrees Frameoptional enu (default), ned, or aer Ellipsoidoptional wgs84 (default), grs80, clarke1866, intl1924, airy1830, bessel1841, or krassovsky1940

More options 10

Origin heightoptional Ellipsoidal height of the origin, like 300 m; default 0 · plain numbers mean m Eastoptional Meters, like 1000 · plain numbers mean m Northoptional Meters, like 1000 · plain numbers mean m Upoptional Meters, like 1000 · plain numbers mean m Downoptional Meters, like 1000 · plain numbers mean m Azimuthoptional Degrees clockwise from true north, like 45 · plain numbers mean degrees Elevationoptional Degrees above the horizontal plane, like 30 · plain numbers mean degrees Slant rangeoptional Meters, like 1000 · plain numbers mean m 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

Run many at once from a CSV

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

Model: Local offset rotated from the origin's east-north-up frame to ECEF, then Vermeille's closed-form inverse

Accuracy: Round trips within 1e-8 m for points within 1,000 km of the origin

When to use this: Use this when a point is described relative to a known station: east, north and up from an origin, north, east and down in an aircraft or vehicle frame, or as an azimuth, elevation and range from a total station or a tracker. It returns the point's latitude, longitude, height, and ECEF position.

Limitations: The local frame is tangent at the origin you give, so the further out the point lies the more the Earth's curvature matters; round trips stay within a hundredth of a micrometer out to a thousand kilometers. Heights are ellipsoidal. An azimuth here is true and geometric: it carries no refraction, no magnetic variation, and no instrument correction.

Worked example: 10 km out at 045°, 5° up. Source: GeographicLib LocalCartesian reverse of the AER offset.

You enter

Azimuth: 45 deg
Elevation: 5 deg
Frame: aer
Origin height: 300 m
Origin latitude: 40.446111 deg
Origin longitude: -79.982222 deg
Slant range: 10000 m

You get

Latitude: 40.5095052756°
Longitude: -79.8991260647°
Ellipsoidal height: 1,179.34 m
ECEF X: 851,837.223 m
ECEF Y, like -4819000 m: -4,781,764.412 m
ECEF Z, like 3976000 m: 4,121,928.515 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: 23 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.

Terms

AER: azimuth, elevation, range: Direction and distance from a point: azimuth from north, elevation above the horizontal, and straight-line range. Source: GeographicLib
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
ENU: east, north, up: Local Cartesian coordinates centered on a chosen point, with axes toward east, north, and up. Source: GeographicLib
NED: north, east, down: Local Cartesian axes toward north, east, and down, as aircraft navigation uses them. Source: GeographicLib

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