Lighthouse Visible Range Calculator

Lighthouse visibility distance

How far out a lighthouse first comes into view comes down to two things: how high its light sits above sea level (H) and how high the observer's eye is (h). The classic shortcut in nautical miles is d (nm) ≈ 1.17·√h(ft) + 1.17·√H(ft), which folds in Earth's curvature along with the usual atmospheric refraction. Take the Cabo Frio lighthouse at 78 m above sea level: an observer with an eye height of 5 m picks it up at roughly 20 nautical miles. Push past that and the horizon swallows the light no matter how powerful the lamp is.

Applications

Coastal navigation leans on this constantly, with skippers checking charted lighthouse ranges against what they see to fix a position. It also shows up in the work of the Brazilian Navy SECIRM (Centro de Sinalização Náutica e Reparos), in the Admiralty List of Lights and the Brazilian Lista de Faróis (DHN), in maritime safety audits, and when planning new aids to navigation along the coast.

FAQ

Why does the observer's height matter? Distance to the horizon scales with the square root of eye height. So a bridge officer standing at 15 m will catch the loom of a light well before a sailor sitting in a cockpit at 2 m does.

What is the difference between geographic and luminous range? Geographic range is pure geometry, set by the heights involved and Earth's curvature. Luminous range is about how intense the light is and how clear the air happens to be. Whichever is smaller is what you actually see.

Why 1.17 in the formula? That number is a fitted constant rolling together Earth's radius and a standard refraction coefficient of about 0.13. It returns distance in nautical miles when you feed in heights measured in feet.