If ellipsoidal height h equals 100 meters and geoid height N equals 30 meters, what is the orthometric height H?

• A. 130 meters
• B. 100 meters
• C. 70 meters
• D. 0 meters

Answer: (C)

Orthometric height is the height above the geoid, while the ellipsoidal height is the height above the ellipsoid. The geoid height N is how far the geoid sits above the ellipsoid. So the ellipsoidal height h equals H plus N, written as h = H + N. Therefore, the orthometric height is H = h − N.

Plugging in the numbers: H = 100 m − 30 m = 70 m.

The other values would come from adding N to h (130 m) or ignoring N altogether (100 m), or assuming the point lies on the geoid (0 m).