Geoid Undulation Estimator
Find geoid undulation N from a GPS-measured ellipsoidal height and a leveled orthometric (mean sea level) height at the same point.
🌍 What is Geoid Undulation?
Geoid undulation (often written N) is the vertical distance between the geoid, the Earth's true equipotential (gravity-consistent) surface that approximates mean sea level, and a chosen reference ellipsoid, the smooth mathematical surface used as the basis for GPS and GNSS positioning. The term comes from geodesy, where "undulation" describes how the geoid's irregular, lumpy shape rises and falls relative to the smooth reference ellipsoid it is compared against.
Surveyors and engineers rely on geoid undulation constantly, to convert a GPS receiver's raw ellipsoidal height into a practical elevation above mean sea level for construction and drainage design, to reconcile modern GNSS surveys with older leveling-based elevation networks, to model regional gravity and subsurface mass distribution from geoid shape, and to support satellite altimetry corrections used in oceanography and climate science.
A common misconception is that GPS directly reports elevation above sea level. It does not, GPS naturally reports ellipsoidal height, a purely geometric quantity relative to the reference ellipsoid, which can differ from true sea-level elevation by tens of meters depending on location. The geoid undulation value is exactly the correction needed to bridge that gap.
This calculator applies the standard N = h - H relation used throughout GPS-based heighting and surveying, converting a GPS-measured ellipsoidal height and a leveled orthometric height at the same point directly into the local geoid undulation, along with a plain-language note on whether the geoid sits above or below the reference ellipsoid there.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — GPS Survey Point with a Positive Undulation
h = 125.34 m (GPS), H = 98.87 m (leveled MSL)
Example 2 — Location with a Negative Undulation
h = 310.15 m (GPS), H = 336.80 m (leveled MSL)
Example 3 — Region with a Larger Positive Undulation
h = 512.60 m (GPS), H = 467.35 m (leveled MSL)
❓ Frequently Asked Questions
🔗 Related Calculators
How do you calculate geoid undulation?
Geoid undulation N equals the GPS-derived ellipsoidal height h minus the leveled orthometric (mean sea level) height H at the same point: N = h - H. A positive N means the geoid sits above the reference ellipsoid there; a negative N means it sits below.
What is the difference between ellipsoidal height and orthometric height?
Ellipsoidal height (h) is measured relative to a smooth mathematical reference ellipsoid, typically from GPS or GNSS. Orthometric height (H) is measured relative to the geoid, the Earth's actual gravity-equipotential surface approximating mean sea level, typically from spirit leveling or a benchmark.
What is geoid undulation used for?
Geoid undulation is used to convert a GPS receiver's raw ellipsoidal height reading into a practical, sea-level-referenced elevation. Surveyors, engineers, and mapping agencies apply a geoid model's N value at each location so GPS heights match traditional leveling-based elevations.
What does a positive geoid undulation mean?
A positive N means the geoid, the equipotential surface approximating mean sea level, lies above the reference ellipsoid at that location. This typically occurs where there is a local excess of subsurface mass pulling the equipotential surface outward.
What does a negative geoid undulation mean?
A negative N means the geoid lies below the reference ellipsoid at that location, typically where there is a local mass deficit. The most extreme known example is the Indian Ocean Geoid Low, where the geoid dips roughly 106 meters below the reference ellipsoid.
What is a typical range for geoid undulation values worldwide?
Global geoid undulation values realistically range from about -107 m at the Indian Ocean Geoid Low to about +85 m in parts of the western Pacific near Papua New Guinea, with most populated regions falling well within that range.
Why doesn't this calculator show a chart?
Geoid undulation is a direct subtraction, N = h - H, with no continuous curve or shape to visualize from a single pair of height inputs. A chart would not add information here, so this calculator intentionally omits one and reports the direct numeric result instead.
Where does the orthometric height value come from?
Orthometric height traditionally comes from spirit leveling surveys tied to a known benchmark, or increasingly from applying a gravimetric geoid model to a GPS-measured ellipsoidal height. Either way it represents height above the geoid, the practical mean-sea-level reference surface.
Can geoid undulation be exactly zero?
Yes, N = 0 at any point where the geoid and the reference ellipsoid happen to coincide. Since reference ellipsoids are chosen as a global best fit to the geoid, N stays relatively small (within about 100 meters) everywhere on Earth, crossing zero along certain contour lines.
What reference ellipsoid does this calculator assume?
This calculator does not assume a specific ellipsoid, it simply computes N = h - H from whatever consistent ellipsoidal and orthometric height values you provide. In practice, GPS receivers most commonly reference the WGS84 ellipsoid.
What units does this calculator use?
Both height inputs and the resulting geoid undulation are in meters by default, though the same N = h - H relation works with any consistent unit as long as both inputs use the same one.