Geoid Height (Undulation) Calculator
Enter any two known values to calculate the third. Units are meters (m).
N = h - H
where h = ellipsoidal height, H = orthometric height, and N = geoid undulation.
What Is a Geoid?
The geoid is an equipotential surface that approximates global mean sea level and extends under the continents. In practical terms, it is the “level” surface that water would follow if oceans could flow freely through channels cut across land. Unlike a perfect ellipsoid, the geoid is irregular because Earth’s gravity field is not uniform.
Surveyors, GIS professionals, and engineers care about the geoid because GPS/GNSS receivers naturally provide ellipsoidal heights. Construction and mapping projects, however, usually need orthometric heights (heights above mean sea level). The geoid is what bridges those two height systems.
Height Types You Need to Know
Ellipsoidal Height (h)
Measured along the normal to a reference ellipsoid (such as WGS84). GNSS systems directly provide this value.
Orthometric Height (H)
Height above the geoid, often interpreted as “elevation above mean sea level.” This is usually what civil plans and topographic maps use.
Geoid Undulation (N)
The separation between the reference ellipsoid and the geoid at a given location. It can be positive or negative depending on region.
The Core Formula Behind This Calculator
The relationship is simple:
- N = h - H
- H = h - N
- h = H + N
This calculator lets you leave one field blank, then computes that missing value from the other two. It is useful for quick checks, field calculations, and quality-control workflows.
Example Calculations
Example 1: Find Geoid Undulation
Suppose GNSS gives h = 152.438 m, and your benchmark elevation is H = 118.902 m. Then:
N = 152.438 - 118.902 = 33.536 m
Example 2: Find Orthometric Height
If h = 240.000 m and N = 29.750 m, then:
H = 240.000 - 29.750 = 210.250 m
Example 3: Find Ellipsoidal Height
If H = 95.330 m and N = -1.220 m, then:
h = 95.330 + (-1.220) = 94.110 m
Common Mistakes and How to Avoid Them
- Mixing sign conventions: Negative geoid undulation values are valid in many regions.
- Mixing units: Keep all inputs in meters (or convert consistently before using).
- Wrong vertical datum: Orthometric heights depend on the vertical datum in use (e.g., NAVD88, local datums).
- Assuming one geoid value everywhere: Geoid undulation changes with location.
When a Simple Calculator Is Enough (and When It Is Not)
A formula-based geoid calculator is perfect when two of the three values are already known and trusted. It is also great for learning, sanity checks, and report preparation.
If you need to derive N from latitude/longitude alone, you need a geoid model (for example, EGM or regional geoid grids). In that case, you must use model interpolation software or APIs and then apply the same height relationship shown here.
Practical Workflow for Survey and GIS Teams
- Collect GNSS ellipsoidal heights.
- Apply a validated geoid model to get local geoid undulation values.
- Convert to orthometric heights for engineering and mapping deliverables.
- Run spot checks with this calculator for QA/QC.
Final Notes
The geoid calculator on this page is intentionally straightforward and transparent. It helps you move confidently between GNSS heights and practical elevation values with minimal friction. For high-precision projects, always document your geoid model, epoch, and vertical datum alongside final results.