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1. Home
2. Education
3. Geodesy
4. The Geoid

**The Geoid** Global Positioning Tutorial  Image of the Earth with the pins in it*Because the surface of the Earth is irregular and complex, geodesists use simplified mathematical models of the Earth for many applications. The simplest model of the Earth is a sphere. A much more complex model of the Earth is the geoid, used to approximate mean sea level. Even the geoid is a simplified model, however, when compared to actual topographic relief, as shown in this image of four figures of the Earth (Grand Canyon).*  The Earth's shape is nearly spherical, with a radius of about 3,963  miles (6,378 km), and its surface is very irregular. Mountains and  valleys make actually measuring this surface impossible because an  infinite amount of data would be needed. For example, if you wanted to  find the actual surface area of the Grand Canyon, you would have to  cover every inch of land. It would take you many lifetimes to measure  every crevice, valley, and rise. You could never complete the project  because it would take too long. To measure the Earth  and avoid the problems that places like the Grand Canyon present,  geodesists use a theoretical mathematical surface called the ellipsoid.  Because the ellipsoid exists only in theory and not in real life, it  can be completely smooth and does not take any irregularities — such as  mountains or valleys — into account. The ellipsoid is created by  rotating an ellipse around its shorter axis. This matches the real  Earth's shape, because the earth is slightly flattened at the poles and  bulges at the equator. While the ellipsoid gives a common reference to geodesists, it is still  only a mathematical concept. Geodesists often need to account for the  reality of the Earth's surface. To meet this need, the geoid, a shape  that refers to global mean sea level, was created. If the geoid really  existed, the surface of the Earth would be equal to a level in between  the high-tide and low-tide marks. Although a geoid may seem to be a smooth, regular shape, it isn't. The  Earth's mass is unevenly distributed, meaning that certain areas of the  planet experience more gravitational "pull" than others. Because of  these variations in gravitational force, the "height" of different  parts of the geoid is always changing, moving up and down in response  to gravity. The geoidal surface is an irregular shape with a wavy  appearance; there are rises in some areas and dips in others.
  Geodesy **Lessons** Welcome What is Geodesy? The History of Geodesy The Geoid What is a Datum? The Horizontal Datum The Vertical Datum Gravity The National Spatial Reference System The Global Positioning System CORS and GIS References
  More **Information** Roadmap to Resources Subject Review Is the Earth round? (Ocean Facts)  Geodesy Education Heard of geodesy? These videos from NOAA's National Geodetic Survey offer a deep dive into the science of knowing where you – and everything else is in the world!
  The National Science Teaching Association (NSTA) includes this resource in its database. NSTA provides educators and students access to Web-based, educationally appropriate science content that has been formally evaluated by master teachers.
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  **Last updated:** 11/15/22 **Author:** NOAA How to cite this article Contact Us


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