If ellipsoidal height is 50 m and geoid undulation is 5 m, what is the orthometric height?

• A. 60
• B. 55
• C. 45
• D. 40

Answer: (C)

The key idea is how the three heights relate: ellipsoidal height h is the height above the reference ellipsoid, orthometric height H is the height above the geoid, and geoid undulation N is the difference between the ellipsoid and geoid along the vertical. The relation h = H + N allows you to solve for the height above the geoid: H = h − N. With h = 50 m and N = 5 m, you get H = 50 − 5 = 45 m. So the orthometric height is 45 m. This reflects that the geoid is about 5 m different from the ellipsoid at that location, reducing the height above the geoid relative to the ellipsoidal height.