Geoid Height / Undulation Calculator

What Is Geoid Height or Undulation?

Geoid height, also called geoid undulation, is the separation between a reference ellipsoid and the geoid at a specific location. The ellipsoid is a smooth mathematical surface used by GNSS systems such as GPS. The geoid is an irregular gravity-based surface that approximates mean sea level. Because the two surfaces are not the same, a GPS height and a mean sea level elevation can differ by tens of meters.

The standard symbol for geoid height is N. A positive N means the geoid is above the ellipsoid. A negative N means the geoid is below the ellipsoid. That sign matters because the same GPS height can convert to a higher or lower sea-level elevation depending on local gravity and geoid shape.

Ellipsoidal Height vs Orthometric Height

Ellipsoidal height, usually written as h, is the height above the reference ellipsoid. It is the height type produced by GNSS processing before a vertical datum correction is applied. Orthometric height, usually written as H, is height above the geoid, which is the surface used as a practical mean sea level reference in many engineering, mapping, and surveying workflows.

If a drone flight, GNSS rover, or GIS dataset reports ellipsoidal height, it may not match a topographic map elevation or benchmark elevation. The difference is usually not a receiver error. It is a vertical reference surface issue.

How to Convert GPS Height to Mean Sea Level

The conversion is simple once the geoid height is known:

H = h - N

For example, if the GPS ellipsoidal height is 145.230 m and the geoid height is -31.850 m, the orthometric height is 177.080 m because subtracting a negative geoid height increases the result. The calculator shows the formula, substitution, and final result so the sign is visible.

The reverse conversion is h = H + N. If you have both h and H, the geoid height can be solved as N = h - H.

Why the Sign of N Matters

The most common mistake is using the right geoid value with the wrong sign. In areas where N is positive, orthometric height is lower than ellipsoidal height. In areas where N is negative, orthometric height is higher than ellipsoidal height. This calculator keeps the signed value visible in the equation block to reduce that error.

When copying results into CAD, GIS, photogrammetry, or survey notes, include the sign and model source. A value written as 31.850 m is not the same as -31.850 m.

When to Use an Official Geoid Model

The manual geoid height mode is best when you have a project control value or an official model value. Many countries publish local geoid models that are better suited to engineering and survey deliverables than a global approximation. In the United States, NOAA NGS provides geoid model resources. Other national mapping agencies provide local vertical datum tools for their regions.

The estimated mode on this page is intended for planning, education, and quick checks. It does not replace an official geoid grid, benchmark, or national vertical datum transformation. Use official control when setting elevations for construction, flood studies, legal surveys, or deliverables that require traceable vertical accuracy.

Common GIS and Survey Workflows

Surveyors use geoid height when converting GNSS observations into elevations that match local benchmarks. Drone mappers use it when aligning photogrammetry outputs with ground control or DEM products. GIS analysts use it when combining GPS points, LiDAR surfaces, raster DEMs, and vertical CRS metadata. Civil engineers use it when checking whether a GNSS-derived height is compatible with a project datum.

This tool pairs well with the WGS84 to UTM Converter when preparing coordinates, the UTM Zone Finder for zone checks, the EPSG Code Lookup for vertical CRS research, and the GeoTIFF Metadata Reader when inspecting raster elevation datasets.

Frequently Asked Questions

What is geoid height?

Geoid height is the signed vertical separation between the geoid and the reference ellipsoid at a location. It is commonly written as N.

What is the formula for orthometric height?

The standard formula is H = h - N, where H is orthometric height, h is ellipsoidal height, and N is geoid height.

Is GPS height the same as elevation above sea level?

No. GPS height is usually ellipsoidal height. Elevation above mean sea level is usually an orthometric height tied to a vertical datum.

What does a negative geoid height mean?

A negative geoid height means the geoid is below the ellipsoid at that location. In the formula H = h - N, subtracting a negative N increases the orthometric height.

Can I use this calculator for survey deliverables?

Use the manual mode with an official geoid value or control-point value for professional deliverables. The built-in estimate is only for planning and education.

What geoid model should I use?

Use the official geoid model recommended by the national mapping or geodetic authority for your project area and vertical datum.

Where can I learn more?

Authoritative references include NOAA NGS geoid models, NGA earth information resources, and EPSG coordinate reference guidance.