Enter the latitude and longitude into the calculator to determine the geoid height (N) at that location. Geoid height is the vertical separation between the WGS84 reference ellipsoid and Earth’s geoid, the correction needed to convert a GPS altitude into a real-world elevation above mean sea level.
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Geoid Height Formula
Geoid height connects the elevation reported by a GPS receiver to elevation above mean sea level. In geodesy, this relationship is written as:
H = h - N
Where:
- H = orthometric height, or elevation above the geoid / mean sea level
- h = ellipsoidal height, or height above the reference ellipsoid used by GPS
- N = geoid height, also called geoid undulation
If you already know any two of these values, the remaining variable can be found by rearranging the equation:
h = H + N
N = h - H
What Is Geoid Height?
Earth is not a perfect sphere, and sea level is not a perfectly smooth mathematical surface. GPS satellites measure position relative to a smooth reference ellipsoid, while practical elevation work usually needs height relative to the geoid, which is an equipotential gravity surface that closely matches global mean sea level. The difference between those two surfaces at a given latitude and longitude is the geoid height.
This is why a raw GPS altitude and a published ground elevation often do not match. The GPS is usually giving ellipsoidal height, while maps, benchmarks, engineering plans, and flood studies usually use orthometric height.
How to Use the Geoid Height Calculator
- Enter the latitude of the point.
- Enter the longitude of the point.
- Select the unit format if needed.
- Calculate the geoid height (N) for that location.
- Use the result with GPS altitude to convert to elevation above mean sea level.
Once the calculator returns N, you can plug it into the height conversion formula:
H = h - N
Variable Definitions
| Symbol | Name | Description |
|---|---|---|
| H | Orthometric Height | Elevation above the geoid, commonly treated as elevation above mean sea level. |
| h | Ellipsoidal Height | Height above the mathematical reference ellipsoid used by GPS/GNSS positioning. |
| N | Geoid Height | Vertical separation between the ellipsoid and the geoid at a specific location. |
Sign Convention for Geoid Height
The sign of N matters:
- If N is positive, the geoid is above the ellipsoid at that location.
- If N is negative, the geoid is below the ellipsoid at that location.
This changes how GPS altitude compares to true elevation:
- Positive N: orthometric height is smaller than ellipsoidal height.
- Negative N: orthometric height is larger than ellipsoidal height.
Example
Suppose a GPS receiver gives an ellipsoidal height of 412 m, and the geoid height at that latitude and longitude is 28 m. The orthometric height is:
H = 412 - 28
H = 384
So the point is 384 m above mean sea level.
If the geoid height were instead -15 m, then:
H = 412 - (-15)
H = 427
In that case, the true elevation would be higher than the GPS ellipsoidal height.
Why Geoid Height Matters
Geoid height is essential whenever satellite positioning needs to be tied to real-world elevation. Common applications include:
- Land surveying: converting GNSS measurements into usable elevations for property and site work
- Civil engineering: matching GPS data to design grades, drainage plans, and benchmark elevations
- Construction: checking cut/fill, slab heights, road profiles, and utility installation depths
- Flood and drainage analysis: working with elevations that reflect gravity-driven water flow
- Mapping and GIS: aligning field GPS measurements with DEMs, contour maps, and elevation datasets
- Aviation, marine, and navigation workflows: translating positional data into consistent vertical references
Why GPS Elevation Often Looks Wrong
Many users assume GPS altitude is the same as elevation above sea level, but that is often not true. A GPS device commonly reports height relative to a reference ellipsoid, not the geoid. Because the geoid can be tens of meters above or below the ellipsoid depending on location, the difference can be large enough to matter in engineering, mapping, and field layout.
Important Notes on Accuracy
- Geoid height varies by location; even nearby points can have slightly different values.
- Different vertical datums and geoid models may produce slightly different results.
- Latitude and longitude should be entered as accurately as possible for best results.
- Unit consistency matters; keep all heights in the same unit system before applying the formula.
- The calculator gives the geoid separation value, but overall elevation accuracy also depends on the quality of the GPS measurement itself.
Common Related Terms
- Geoid: gravity-based surface that approximates mean sea level
- Reference Ellipsoid: smooth mathematical model of Earth used for positioning
- Orthometric Height: practical elevation above the geoid
- Ellipsoidal Height: satellite-derived height above the ellipsoid
- Undulation: another name for geoid height
- Vertical Datum: the framework that defines how elevations are referenced
Frequently Asked Questions
Is geoid height the same as elevation?
No. Geoid height is the separation between the ellipsoid and the geoid. Elevation is typically orthometric height above mean sea level.
Can geoid height be negative?
Yes. A negative value means the geoid lies below the reference ellipsoid at that location.
Why do I need latitude and longitude?
Geoid height is location-dependent, so the calculator uses coordinates to determine the local separation between the ellipsoid and the geoid.
Do all GPS devices show orthometric height?
No. Some devices apply a geoid model internally, while others display ellipsoidal height unless corrected. It is important to know which vertical reference your device is using.
What unit should I use?
You can use meters or feet, but all values in the equation should be in the same unit system before solving.
