How far can you see across the sea, and at what range will a lighthouse first peek over the curve of the Earth? This calculator answers both, separating the purely geometric horizon from the refraction-corrected visible and radar horizons that mariners actually use.
How it works
Each horizon distance is proportional to the square root of the observer’s eye height, with a constant that bundles the Earth’s radius and a refraction coefficient:
geometric horizon (NM) ≈ 1.93 × √(height in m)
visible horizon (NM) ≈ 2.08 × √(height in m)
radar horizon (NM) ≈ 2.23 × √(height in m)
geographic range to target = visible(eye height) + visible(target height)Radio waves used by radar refract more strongly than light, which is why the radar horizon constant is larger. The geographic range to an object is the sum of two horizon distances because the line of sight grazes the same horizon from both ends.
Example and notes
From a bridge 20 m above the water, the visible horizon lies about 9.3 NM away. A lighthouse with a focal plane 40 m high has its own horizon at about 13.2 NM, so the light should first dip above the horizon at roughly 22.5 NM combined, assuming the light is bright enough to be seen that far. Remember that the actual range a charted light is visible is the smaller of this geographic range and the luminous range printed on the chart.