If ellipsoid height h and geoid height N are known, how is orthometric height H computed?

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

Answer: (B)

The key idea is how the heights relate to the geoid and the ellipsoid. Ellipsoidal height h is the distance above the reference ellipsoid, while orthometric height H is the distance above the geoid. The geoid height N, also called geoid undulation, represents the separation between the ellipsoid and the geoid, defined as N = h − H. Rearranging gives H = h − N.

So if you know the ellipsoidal height and the geoid height, subtract the geoid height from the ellipsoidal height to get the orthometric height. For example, if h = 100 m and N = 30 m, then H = 70 m. If N is negative, subtracting a negative increases H accordingly.

The other options don’t reflect the standard relationship between these three quantities: adding N, taking N minus h, or multiplying do not correspond to how ellipsoidal height, geoid height, and orthometric height are defined and related.