Earth Curvature Correction

As a survey line extends over long distances, the Earth’s surface curves away from a straight horizontal line of sight, so points that are “level” relative to the Earth’s surface appear lower than expected. This formula gives the amount of vertical drop, in metres, between a tangent line at the observer and the curved Earth surface, using the standard approximation for Earth’s radius. It is a geometric correction used so height and level measurements over long sight distances are not biased by the planet’s curvature.

Use this when correcting long-distance levelling, trigonometric height measurements, or line-of-sight observations in surveying and geomatics. It becomes important for kilometres-scale sights where curvature can no longer be ignored compared with instrument precision.

• Using metres for K instead of kilometres
• Forgetting to square the distance before multiplying by 0.0675
• Treating the correction as a slope or angle instead of a vertical drop in metres