Which formula expresses orthometric height H in terms of ellipsoidal height h and geoid undulation N?

• A. H = h + N
• B. H = h - N
• C. H = N - h
• D. H = N + h

Answer: (B)

Orthometric height is the height above the geoid, while ellipsoidal height is the height above the reference ellipsoid. The geoid undulation N represents how far the geoid sits from the ellipsoid at that location. By definition, the ellipsoidal height is the sum of the orthometric height and the geoid undulation: h = H + N. Rearranging gives H = h − N. So to get height above the geoid from the height above the ellipsoid, you subtract the geoid undulation. For example, if h is 120 m and N is 25 m, then H is 95 m. Adding N or combining signs would misrepresent the relationship between the two reference surfaces.