Distance to Horizon Calculator

Learn the geometry of horizons with our distance to the horizon calculator: on Earth or anywhere else in the Solar System!

Distance to the horizon4.9334 km3.0655 miles, 2.6638 nautical miles

Geometric distance4.6542 kmrefraction extends the horizon by 6%, because the atmosphere bends light downwards around the curve

Observer height1.7 m

Angle below horizontal0.04186°how far down the horizon sits — small, but real, and measurable with a sextant

Drop over the horizon distance1.7 mequal to your own height, by the geometry — the horizon is where the surface has curved away by exactly your eye height

Horizon distance for a 50 m object26.7553 km

Maximum distance you could see it31.6888 kmthe two horizon distances ADD — which is why a ship's mast appears before its hull, and why radio masts are built tall at both ends

How much of it is hidden at 4.9 kmnone — that is your own horizonbeyond your horizon the hidden height grows roughly as the square of the excess distance

At 4× the height9.867 km2× further — the distance goes as the SQUARE ROOT of height, so doubling your altitude gains only 41%

At 100× the height49.335 km10× further — the distance goes as the SQUARE ROOT of height, so doubling your altitude gains only 41%

Height needed to double this horizon6.8 mfour times the height, for twice the distance

The formula

d = √(2Rh + h²); radar horizon multiplies by about 1.23

Square root, so height buys less than you expect

The distance to the horizon goes as the square root of the observer's height. Doubling your altitude extends the horizon by only 41%; quadrupling it doubles the distance. At eye level on a beach the horizon is about 4.7 km away, and from a 100 m cliff still only about 36 km.

A tidy piece of geometry: the surface drops away by exactly your own eye height over the horizon distance. That is what defines the horizon — the point where the curve has fallen by however high you are standing.

Two elevated points see each other much further than either sees the horizon, because the two horizon distances simply add. This is why a ship's masts appear over the horizon before its hull, why radio links raise antennas at both ends, and why lookout positions were placed as high as possible.

The atmosphere bends light downwards, following the curve slightly and extending the visible horizon by about 6% under standard conditions. Radio waves refract more strongly, roughly 23%, which is the origin of the 4/3-Earth-radius approximation used in radio path planning. Both figures vary with temperature gradient, and a strong inversion can produce genuine looming or mirage effects.