Horizon Dip Calculator

About this calculator

Because the Earth curves away beneath an observer, the true sea horizon appears slightly below the astronomical horizontal — this angle is the horizon dip. For an eye height h in meters, the standard approximation (accounting for normal atmospheric refraction) is dip ≈ 1.76 × √h arcminutes, growing with the square root of height.

The same geometry gives the distance to the horizon, roughly d ≈ 3.57 × √h kilometers (or 1.17 × √h nautical miles for h in feet), the range at which the sea surface itself drops out of sight.

Navigators use dip as a standard correction when taking a sextant altitude of a star, the Sun, or the Moon above the visible horizon — it must be subtracted from the observed altitude, alongside refraction and semi-diameter corrections, before the sight can be reduced to a usable position line in celestial navigation.