In height conversion, ellipsoidal height h equals orthometric height H plus geoid undulation N.

• A. True
• B. False
• C. Only when N is zero.
• D. Only for ellipsoidal coordinates.

Answer: (A)

The key idea is that heights come in two reference surfaces and a difference between them. Ellipsoidal height is how far the point sits from the reference ellipsoid along the normal, while orthometric height is how high the point is above the geoid (a surface close to mean sea level). The geoid undulation N is the offset between these two surfaces at that location. By definition, N = h − H, so rearranging gives h = H + N. This holds for all locations, regardless of the sign of N or the coordinate system used, which is why the statement is true. For example, if the orthometric height is 60 m and the geoid undulation is 20 m, the ellipsoidal height is 80 m; if N is negative, the ellipsoidal height can be less than the orthometric height. The other options would impose unnecessary constraints (such as needing N to be zero or requiring a specific coordinate framework), which isn’t the case here.