Distance to Horizon Calculator
How far you can see from a given eye height, and at what distance a lighthouse or headland comes into view — with the refraction correction.
Why both heights matter
Your own horizon is 1.17 times the square root of your eye height in feet, in nautical miles. From a small boat cockpit at nine feet that is about three and a half miles — much closer than most people expect.
But a tall object is visible far beyond that, because its horizon and yours add. The lighthouse appears the moment the two overlap, which is why a 150-foot light is raised at around seventeen miles from a small boat even though your own horizon is only three and a half.
Note the square root. Four times the height buys only twice the distance — which is why climbing the mast helps less than it feels like it should, and why a few extra feet at deck level matters more than a lot of extra feet up high.
Horizon from common heights
| Height | Horizon |
|---|---|
| Standing on a beach (6 ft) | 2.9 nm |
| Small boat cockpit (9 ft) | 3.5 nm |
| Flybridge (15 ft) | 4.5 nm |
| Ship’s bridge wing (50 ft) | 8.3 nm |
| Coastal lighthouse (150 ft) | 14.3 nm |
| Cliff top (300 ft) | 20.3 nm |
Geographic range is not luminous range
This calculates the geographic range — where the curve of the earth stops hiding a light. A chart also gives a nominal or luminous range, which is how far the light is bright enough to see in clear weather. The one you actually get is whichever is smaller, and in haze or rain the luminous range collapses while the geographic one does not move at all.
How to use
- Enter your eye height above the water.
- Read the distance to the horizon.
- Add the object's height to get its rising distance.
- Treat the figure as geometric, not a visibility forecast.
Frequently asked questions
How is the distance calculated?
From the geometry of a sphere: roughly 1.17 times the square root of eye height in feet gives nautical miles, or about 3.57 times the square root of height in metres for kilometres. Both include a standard allowance for atmospheric refraction, which bends light slightly and extends the horizon by around 8 per cent.
Why does my own height matter so much?
Because the relationship is a square root, so gains diminish quickly. Standing at 6 feet gives about 2.9 nautical miles; climbing to 24 feet — four times the height — only doubles it to 5.7. This is why crow's nests were high and why the gain from a slightly taller vantage point is modest.
How far away can I see a lighthouse?
Further than your own horizon, because the light is elevated too. Add the distance to your horizon and the distance to the light's own horizon, which is why charted ranges assume a standard observer height. A light listed as visible at a given range is quoting geometry, not brightness.
Does this tell me whether I will actually see something?
No — it is a geometric limit, not a visibility prediction. Haze, rain, glare and the object's size and contrast all determine whether you can actually make it out. The horizon calculation tells you when something stops being hidden by the curve of the earth, which is a different question.
Why do distant objects seem to rise out of the sea?
Because the top becomes visible before the bottom as it clears the horizon — a ship appears mast-first and a headland appears as a summit before its shore. It is one of the oldest and most direct everyday observations of the earth's curvature.
Does refraction always help?
Usually, and unpredictably. Temperature layers can bend light considerably more than the standard allowance, producing superior mirages where objects well beyond the horizon appear, or the opposite in other conditions. Navigation practice treats the standard figure as typical rather than reliable.
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