Bruns’ Formula

Bruns’ formula is a fundamental relation in physical geodesy that links the geoid undulation (geoid height) to the disturbing potential of the Earth’s gravity field. It states that the geoid height equals the disturbing potential divided by normal gravity at the reference ellipsoid.

In geodesy, Bruns’ formula provides the theoretical connection between gravity field modeling and height determination. It allows the computation of geoid undulations from gravity field solutions (e.g., spherical harmonic models derived from satellite gravimetry and terrestrial data). This relationship is essential for transforming GNSS-derived ellipsoidal heights into orthometric heights and for the realization of precise global and regional height systems.