A Geoid Height Calculator serves as a crucial tool in the fields of geodesy, surveying, and navigation. Its primary function is to determine the geoid height for any specific point on the Earth’s surface. This calculation is essential for converting height measurements between different reference systems, which ensures accuracy in critical applications like mapping, construction, and engineering projects.
Specifically, the calculator bridges the gap between the height measured by GPS systems, known as the ellipsoidal height, and the height we commonly understand as elevation above mean sea level, called the orthometric height. The calculator works by finding the precise separation between two key models of the Earth’s shape: the perfectly smooth, mathematical ellipsoid and the irregular, gravity-defined geoid. This separation value is what we call the geoid height. Modern online calculators perform this task by using complex Earth Gravitational Models, or EGMs, to deliver highly accurate results based on user-provided geographic coordinates.
formula
To properly use a Geoid Height Calculator, it is helpful to understand the basic relationship between the three different types of height measurements.
Primary Formula
This is the fundamental formula that connects ellipsoidal height, orthometric height, and geoid height.
h = H + N
To specifically calculate the Geoid Height (N), the formula is rearranged as follows:
Formula to Calculate Geoid Height:
N = h – H
Reference Table for Key Terms
To help users understand the components of the formula without needing to perform complex research, the table below defines each term in simple language. This will be helpful for using the calculator or performing manual calculations.
| Term | Symbol | Simple Description |
| Geoid Height | N | This value, also called geoid undulation, represents the vertical distance that the geoid surface is above or below the reference ellipsoid. It can be a positive or negative number. |
| Ellipsoidal Height | h | This is the height of a point measured from the surface of the reference ellipsoid. A GPS receiver directly measures this type of height. |
| Orthometric Height | H | This represents the height of a point above the geoid. It is the measurement that most closely corresponds to the elevation above mean sea level. |
Example
Let us consider a practical example to demonstrate how to apply the formula and find the geoid height.
Imagine you are a surveyor and have collected the following data for a specific location:
- The ellipsoidal height (h) provided by your GPS device is 200 meters.
- The orthometric height (H) listed on a local survey marker is 180 meters.
You can now use the formula to calculate the geoid height (N) at that location:
N = h – H
N = 200 m – 180 m
N = 20 m
The result shows that the geoid height is 20 meters. This means that at this specific point, the geoid surface is located 20 meters above the reference ellipsoid.
Most Common FAQs
The ellipsoid is a simplified mathematical model that represents the Earth as a smooth, slightly flattened sphere. It provides a clean, regular surface that is easy to use for global coordinate systems like GPS. On the other hand, the geoid is a much more complex and physically meaningful surface. It represents the level of the Earth’s oceans if they were to extend over the entire globe, shaped by the planet’s uneven gravitational pull. The geoid is irregular and wavy, unlike the smooth ellipsoid.
Calculating the geoid height is a critical step for converting the raw height data from GPS units (ellipsoidal height) into a more practical and widely used elevation (orthometric height). Orthometric height is essential for almost all civil engineering, construction, and environmental projects because it relates directly to how water flows—that is, mean sea level. This conversion ensures that elevation data is accurate and consistent across different maps, plans, and projects.