Geoid Height Calculator
Our geology & geophysics calculator computes geoid height accurately. Enter measurements for results with formulas and error analysis.
Formula
H = h - N (Orthometric = Ellipsoidal - Geoid Undulation)
Where H is orthometric height (elevation above mean sea level), h is ellipsoidal height (from GPS), and N is geoid undulation (height of geoid above ellipsoid). N is computed from spherical harmonic coefficients of Earth's gravitational potential.
Worked Examples
Example 1: GPS Height Conversion in New York
Problem: A GPS receiver reads an ellipsoidal height of 50.000 m at latitude 40.7128 N, longitude -74.0060 W. Calculate the orthometric height.
Solution: Location: New York City (40.7128N, 74.006W)\nUsing simplified spherical harmonic model:\nGeoid undulation N is approximately -32.5 m at this location\nOrthometric height H = h - N = 50.000 - (-32.5) = 82.5 m\nNote: The actual EGM2008 value for NYC is about -32.7 m\nNormal gravity at this latitude: ~9.8018 m/s2
Result: Geoid undulation: ~-32.5 m | Orthometric height: ~82.5 m above mean sea level
Example 2: Equatorial Location Calculation
Problem: Calculate geoid parameters at the equator (0N, 0E) with an ellipsoidal height of 100 m on WGS84.
Solution: Location: Gulf of Guinea (0N, 0E)\nLatitude = 0, so sin(lat) = 0, cos(lat) = 1\nP2 = (3(0) - 1)/2 = -0.5\nDominant J2 term: a x J2 x P2 = 6378137 x (-484.17e-6) x (-0.5) = ~1543 m\nWith tesseral corrections for longitude 0\nOrthometric H = 100 - N
Result: Geoid undulation: ~17.2 m | Normal gravity: 9.7803 m/s2
Frequently Asked Questions
What is geoid height and how does it differ from ellipsoidal height?
Geoid height (also called geoid undulation, N) is the vertical distance between the geoid and the reference ellipsoid at a given location. The geoid is an equipotential surface of the Earth's gravity field that closely approximates mean sea level in the absence of winds and currents. The reference ellipsoid (such as WGS84) is a mathematically defined smooth surface that approximates the shape of the Earth. Ellipsoidal height (h) is what GPS receivers directly measure — the height above the reference ellipsoid. Orthometric height (H), which is what people traditionally call elevation or altitude, is the height above the geoid (mean sea level). These three quantities are related by the fundamental equation h = H + N, or equivalently H = h - N.
Why is the geoid important for surveying and GPS measurements?
The geoid is critical because GPS satellites provide ellipsoidal heights, but most practical applications require orthometric heights (elevation above sea level). Without accurate geoid models, GPS heights would be meaningless for applications like flood mapping, construction grading, water flow analysis, and topographic mapping. The geoid can vary by as much as plus or minus 100 meters from the reference ellipsoid globally, with the deepest depression of about negative 106 meters near southern India and the highest point of about positive 85 meters near New Guinea. In the continental United States, geoid undulations range from roughly negative 8 to negative 53 meters. Modern geoid models like EGM2008 provide centimeter-level accuracy globally, enabling precise conversion between GPS and traditional height systems.
What is the EGM2008 geoid model?
The Earth Gravitational Model 2008 (EGM2008) is a spherical harmonic model of Earth's gravitational potential developed by the National Geospatial-Intelligence Agency (NGA). It represents the gravitational field complete to spherical harmonic degree 2159 and order 2159, providing geoid undulations with an accuracy of approximately 10-20 centimeters globally and better than 10 centimeters in well-surveyed regions. EGM2008 was developed using data from the GRACE satellite mission, surface gravity measurements, satellite altimetry over the oceans, and digital elevation models. It replaced the earlier EGM96 model and represents a significant improvement in resolution and accuracy. The model contains over 4.7 million coefficients that describe the spatial variations of Earth's gravity field at high resolution.
How does latitude affect geoid undulation?
Latitude has a profound effect on geoid undulation because the Earth's mass distribution is not uniform and the dominant gravitational harmonics are latitude-dependent. The J2 (oblateness) harmonic is the largest contributor to geoid variations, creating a systematic pattern where the geoid is depressed at the poles and elevated near the equator relative to the ellipsoid. However, this effect is largely absorbed into the definition of the reference ellipsoid. The remaining geoid variations are caused by density anomalies in the mantle and crust. Major features include the Indian Ocean geoid low (roughly negative 106 meters) caused by remnants of ancient subducted slabs, and the North Atlantic geoid high caused by mantle upwelling. Regional and local variations of several meters are caused by mountain ranges, ocean trenches, and crustal density variations.
How accurate are the results from Geoid Height Calculator?
All calculations use established mathematical formulas and are performed with high-precision arithmetic. Results are accurate to the precision shown. For critical decisions in finance, medicine, or engineering, always verify results with a qualified professional.
How do I get the most accurate result?
Enter values as precisely as possible using the correct units for each field. Check that you have selected the right unit (e.g. kilograms vs pounds, meters vs feet) before calculating. Rounding inputs early can reduce output precision.