Horizon distance calculator
This horizon distance calculator uses the formula of the Bowditch navigation manual: from an eye height of 6 ft the sea horizon is about 2.9 nautical miles (3.3 miles) away, from 100 ft about 11.7 nautical miles. Add an object height to see how far away a lighthouse or ship can be seen.
Example: Calculate: Distance to the horizon · Height of eye above the water 6 · Heights in: feet → Distance: Horizon 3.3 mi away. Source: NGA, Pub. 9 The American Practical Navigator (Bowditch), Vol. 2: Table 12 Distance of the Horizon (D = √(2·r₀·h / (6076,1·β₀)), r₀ = 3440,1 sm, β₀ = 0,8279 Refraktion), Table 13 Geographic Range, Beispiel Leuchtfeuer 150 ft = 14,3 sm (gelesen 10.10.2026). Updated: .
How it is calculated
Distance to the horizon D = √(2 · r₀ · h ÷ (6,076.1 · β₀)) nautical miles, with the height of eye h in feet, the mean earth radius r₀ = 3,440.1 nautical miles and β₀ = 0.8279 for terrestrial refraction. The American Practical Navigator (Bowditch), published by the U.S. National Geospatial-Intelligence Agency, computes its Distance of the Horizon table (Table 12) with this formula. It simplifies to D ≈ 1.17 · √h nautical miles or about 1.345 · √h statute miles.
Horizon distance by height of eye
| Height of eye | Nautical miles | Statute miles |
|---|---|---|
| 5 ft | 2.6 | 3.0 |
| 6 ft | 2.9 | 3.3 |
| 10 ft | 3.7 | 4.3 |
| 15 ft | 4.5 | 5.2 |
| 30 ft | 6.4 | 7.4 |
| 50 ft | 8.3 | 9.5 |
| 100 ft | 11.7 | 13.5 |
| 150 ft | 14.3 | 16.5 |
The distance grows with the square root of the height: four times as high means twice as far. A nautical mile is 1,852 m, a statute mile 1,609.344 m and a foot 0.3048 m (NIST).
When does a lighthouse or ship appear?
An object above the sea has its own horizon, and Bowditch adds the two distances to get the geographic range. Its example: a light 150 ft above the water has a horizon of 14.3 nautical miles. An observer with a height of eye of 5 ft sees it on the horizon from 14.3 + 2.6 = 16.9 nautical miles away, from 30 ft from 20.7 and from 70 ft from 24.1 nautical miles.
- The values are for the visible sea horizon; land in between blocks the view earlier.
- Bowditch notes that the actual distance varies somewhat as refraction changes, and abnormal refraction can change the range.
- Visible only means that the earth’s curve does not hide the object. Fog, haze, dust, smoke or precipitation can obscure a light, and a weak light cannot be seen beyond its luminous range.
Convert feet, meters and miles with the length converter; the angle up to a tall object comes from the angle of elevation calculator and the sun’s height from the sun position calculator.
Frequently asked questions
How far away is the horizon at sea level?
From a height of eye of 6 ft, about 2.9 nautical miles or 3.3 statute miles. From 10 ft it is 3.7 nautical miles.
What is the formula for the distance to the horizon?
Bowditch uses D = √(2 · 3,440.1 · h ÷ (6,076.1 · 0.8279)) nautical miles with h in feet, which simplifies to D ≈ 1.17 · √h.
How far away can you see a lighthouse?
Add the observer’s horizon and the light’s horizon. Bowditch: a light at 150 ft gives 14.3 nautical miles, an eye at 5 ft gives 2.6, together 16.9 – if the light is strong enough and the air is clear.
Why does the formula include refraction?
Bowditch includes terrestrial refraction with β₀ = 0.8279. Without it the formula would give the purely geometric distance; because β₀ is below 1, the calculated horizon is about 10 % farther (1 ÷ √0.8279 ≈ 1.10).
How far can you see from 100 feet?
The horizon is about 11.7 nautical miles or 13.5 statute miles away.
Sources and legal basis
- NGA, Pub. 9 The American Practical Navigator (Bowditch), Vol. 2: Table 12 Distance of the Horizon (D = √(2·r₀·h / (6076,1·β₀)), r₀ = 3440,1 sm, β₀ = 0,8279 Refraktion), Table 13 Geographic Range, Beispiel Leuchtfeuer 150 ft = 14,3 sm (gelesen 10.10.2026)
- NIST Special Publication 811, Appendix B.8: Fuß = 0,3048 m, Seemeile = 1852 m, Meile = 1609,344 m (gelesen 10.10.2026)
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