The Earth's shape is best described as an ellipsoid, a slightly flattened sphere created by rotating an ellipse around its minor axis. This flattening results in the polar axis being about 21 kilometers shorter than the equatorial axis. In contrast, the geoid represents the Earth's gravitational shape and aligns with the mean sea level (MSL). The geoid is an irregular equipotential surface where gravity is perpendicular at every point. Variations in Earth's mass distribution cause geoid undulations, leading to global MSL differences of up to 100 meters.

Traditionally, vertical distances were measured using spirit levels, referencing MSL or the geoid. This method was suitable for small-scale surveys but ignored the Earth's ellipsoidal shape and global geodesic effects. Modern surveying uses GPS technology, which measures heights relative to an ellipsoidal model, such as the World Geodetic System 1984 (WGS 84). WGS 84, aligned with the Geodetic Reference System 1980 (GRS 80), incorporates satellite data to refine measurements of Earth's size, shape, and gravitational forces, significantly improving accuracy.

The Earth-Centered, Earth-Fixed (ECEF) coordinate system is widely used for describing positions on the ellipsoid. This Cartesian system has its origin at Earth's center of mass, with the x-axis extending to the equator at the Greenwich meridian, the y-axis lying perpendicular to the x-axis on the equatorial plane, and the z-axis aligned with the polar axis, perpendicular to the xy-plane.

Using GPS, Cartesian coordinates can be calculated and converted into latitude, longitude, and ellipsoidal height. These coordinates are transformed into systems like state plane coordinates, for practical tasks like surveying and mapping. Integrating ellipsoidal and geoidal data ensures precision in geospatial measurements and global positioning applications.