Ellipsoidal and orthometric height

Converts a GPS ellipsoidal height to height above mean sea level (orthometric) or back, with h = H + N and the EGM96 geoid height N.

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.

71.292m

The converted height is 71.292 m. The geoid is 28.708 m above the ellipsoid here.

EGM96 heights approximate global mean sea level. They are not NAVD 88 (use GEOID18 in the US) and can differ from local vertical datums by a meter or more.

Ellipsoidal height h
Orthometric height H
Geoid height N

Provenance

Computed by: geodesy.height.convert 1.0.1, core 0.1.0
Model: EGM96 geoid, 15′ grid, 12-point cubic interpolation
Accuracy: As good as the geoid: about 0.5-1 m for EGM96. Exact arithmetic otherwise.
Reference data: version 2009-08-29 of a reference dataset
Notes: 1 shown with the answer
Cites: Lemoine, F. G., et al., NASA Goddard Space Flight Center, The Development of the Joint NASA GSFC and NIMA Geopotential Model EGM96, NASA/TP-1998-206861; Karney, C. F. F., GeographicLib, GeographicLib Geoid class and geoid data

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Latitude Decimal degrees, north positive, like 40.6413 · plain numbers mean degrees Longitude Decimal degrees, east positive, like -73.7781 · plain numbers mean degrees Height Like 1655 m · plain numbers mean m Height typeoptional ellipsoidal (HAE, default), orthometric (MSL), or agl above the terrain you give Terrain elevationoptional The ground at this point, above mean sea level, like 250 m · plain numbers mean m

More options 2

Geoid modeloptional egm96 (global, default) Interpolationoptional cubic (default, error under 0.17 m) or bilinear (under 1.2 m)

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

Model: h = H + N with N from the EGM96 15′ grid

Accuracy: As good as the geoid: about 0.5-1 m for EGM96. Exact arithmetic otherwise.

When to use this: Use this whenever a GPS height has to be compared with anything on a map. A receiver gives height above the ellipsoid; a benchmark, a chart, a flood map and an airfield elevation all give height above sea level, and the two differ by tens of metres. Give it either and it returns both, with the geoid height it used.

Limitations: EGM96 is a global model of the geoid, good to about half a metre to a metre against levelled benchmarks and worse in mountains. For survey work the right reference is a national model -- GEOID18 in the United States -- and this is not that. The difference between the two heights is not small anywhere: it runs from about 85 m to -106 m across the world, so a GPS height read as a sea-level height is wrong by that much, not by a rounding. Bilinear interpolation is offered to reproduce an older number, not because it is better.

Worked example: A GPS height of 100 m at Timbuktu. Source: h − N with N = 28.7079 m from GeographicLib GeoidEval (egm96-15, cubic): 71.292 m above sea level. It is golden test vector v004, and every build checks the tool still gives its answer within its tolerance.

You enter

Height: 100 m
Latitude: 16.776 deg
Longitude: -3.009 deg

You get

Converted height: 71.292 m
Ellipsoidal height h: 100 m
Orthometric height H: 71.292 m
Geoid height N: 28.708 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 1.0.1, core 0.1.0. See this tool in the verification report.

Changes

2026-09-23, fixed: Where the geoid is below the ellipsoid, the sentence said the geoid was a negative height above it ("-17.21 m above the ellipsoid"). It now says "17.21 m below the ellipsoid", and a point under the ground given reads as below the ground. The height converter's second example, a drone reporting 120 m above the ellipsoid over 250 m terrain, put the drone underground; it is replaced by a drone at 180 m above the ellipsoid over 40 m terrain, 117.539 m above the ground. Both tools are version 1.0.1; values are unchanged. Changelog

Checked against: 28 golden test vectors (download the test vectors, each with its source and tolerance). See how results are checked and every source.

Sources

The Development of the Joint NASA GSFC and NIMA Geopotential Model EGM96, NASA/TP-1998-206861, Lemoine, F. G., et al., NASA Goddard Space Flight Center, NASA/TP-1998-206861. Geoid undulations relative to WGS 84.
GeographicLib Geoid class and geoid data, Karney, C. F. F., GeographicLib, GeographicLib 2.x (egm96-15 grid, 2009-08-29). Geoid height interpolation: bilinear and 12-point cubic least-squares fit. Read free.

Terms

HAE: height above ellipsoid: Height measured from the reference ellipsoid, as GNSS receivers report it. It differs from height above sea level by the geoid height. Source: EGM96 geopotential model and geoid
MSL: mean sea level: Height above the average level of the sea, in practice the geoid. Airport elevations and altimeter altitudes are given above MSL. Source: Aeronautical Information Manual

Learn the concept: Geoid vs. ellipsoid height explained