Horizon Distance Calculator

From 6 feet above the water, the horizon is about 2.9 nautical miles away, or 3.3 statute miles (5.3 km). The higher your eyes, the farther the horizon, but the distance grows only with the square root of the height: from 10 feet it is 3.7 nautical miles, and from 100 feet 11.7 nautical miles. Add a second height to the calculator to see how far away you can see a lighthouse, a mast or a cliff.

How Far Is the Horizon at Sea?

It depends on how high your eyes are above the water. Standing at the water’s edge with your eyes 5 to 6 feet above the sea, the horizon is 2.6 to 2.9 nautical miles away, or 3.0 to 3.3 statute miles. On a boat, add the height of the deck above the water to your own eye height.

The formula comes from The American Practical Navigator (Bowditch), the navigation manual published by the U.S. National Geospatial-Intelligence Agency (NGA), which gives the distance to the visible horizon as 1.17 × √h nautical miles for a height of eye h in feet. It starts from the Earth’s mean radius, 3,440.1 nautical miles, and allows for standard refraction, the slight bending of light in the air near the sea, which lets you see about 10 percent farther than a straight line would reach.

In meters, the same formula is about 2.12 × √h. Bowditch also prints a meter version, 2.07 × √h, which gives distances about 2 percent shorter; this calculator converts meters to feet, so a height gives the same answer in either unit.

Horizon Distance Table

Distance to the horizon by eye height in feet, laid out like Table 12 of Bowditch:

Eye height (ft)	Nautical miles	Statute miles
1	1.2	1.3
3	2.0	2.3
5	2.6	3.0
6	2.9	3.3
8	3.3	3.8
10	3.7	4.3
12	4.1	4.7
15	4.5	5.2
20	5.2	6.0
25	5.9	6.7
30	6.4	7.4
40	7.4	8.5
50	8.3	9.5
75	10.1	11.7
100	11.7	13.5
150	14.3	16.5
200	16.5	19.0
500	26.2	30.1
1,000	37.0	42.6

By eye height in meters:

Eye height (m)	Kilometers	Nautical miles
1	3.9	2.1
1.5	4.8	2.6
2	5.6	3.0
3	6.8	3.7
5	8.8	4.7
10	12.4	6.7
15	15.2	8.2
20	17.6	9.5
30	21.5	11.6
50	27.8	15.0
100	39.2	21.2
200	55.5	30.0
300	68.0	36.7

How Far Away Can You See a Lighthouse or Another Boat?

You can see an object beyond your own horizon as long as its top still rises above that horizon. To find the greatest distance, add your horizon distance to the horizon distance of the object, worked out from its height. Bowditch calls the result the geographic range: the farthest the curve of the Earth lets you see the object.

A light 150 feet above the water has a horizon of 14.3 nautical miles. From an eye height of 5 feet (2.6 nautical miles), its top can be seen up to 16.9 nautical miles away; from 30 feet, up to 20.7 nautical miles. Another boat works the same way: the top of a mast 40 feet above the water can show above the horizon up to 10.3 nautical miles away from an eye height of 6 feet, while the hull comes into view only as you get closer.

Geographic range in nautical miles for objects of different heights. Each total is added before it is rounded, so it can differ by 0.1 from the sum of the rounded horizons. Bowditch notes that an eye height of 15 feet is often assumed when the geographic ranges of lights are tabulated.

Object height (ft)	Object’s horizon	Seen from 6 ft	Seen from 15 ft
10	3.7	6.6	8.2
20	5.2	8.1	9.8
30	6.4	9.3	10.9
50	8.3	11.1	12.8
75	10.1	13.0	14.7
100	11.7	14.6	16.2
150	14.3	17.2	18.9
200	16.5	19.4	21.1

Horizon Distance Is Not Visibility, Radar Range or Light Range

Visibility. The horizon distance assumes perfectly clear air. Haze, fog, rain or spray often limit what you can see long before the horizon does. In the International Visibility Code that Bowditch reproduces, haze means a visibility of 1 to 2 nautical miles, and clear 5½ to 11 nautical miles.

The range of a light. A lighthouse also has to be bright enough. The range the U.S. Coast Guard Light List gives for a light is usually its nominal range: how far it can be seen when the visibility is 10 nautical miles, regardless of its height or the curve of the Earth. A light is first seen at the shorter of its luminous range, which depends on its brightness and the visibility, and its geographic range, so a weak light can stay out of sight even when it is above your horizon.

Radar. The air bends radar waves too, and Bowditch gives the radar horizon as 1.22 × √h nautical miles for an antenna h feet above the water, about 4 percent farther than the visible horizon. A radar can still detect tall targets beyond its horizon, so this is not its detection range either.

When the Horizon Is Closer or Farther

Refraction changes with the air. Bowditch describes looming: when the water is much colder than the air above it, light bends more than usual, the visible horizon moves farther away and objects that are normally below it come into view. When the air cools with height much faster than normal, light bends less, the horizon comes closer and objects look lower than usual, which is called sinking. The calculator uses standard refraction, so treat its answer as a typical value, not a promise.

Waves matter too. In rough seas a light on the horizon may appear and disappear as your boat rises and falls, and wave tops can hide it for moments at a time.

Related Calculators

To convert the result, use the Nautical Miles to Miles Converter, the Miles to Nautical Miles Converter or the Nautical Miles to Kilometers Converter. To find how long it takes to reach a point on the horizon, enter its distance and your speed in the Speed, Distance and Time Calculator, and to measure a route between ports, use the Sea Distance Calculator.

Frequently Asked Questions