Distance to Horizon at Sea Calculator
Standing on a boat or shore, the visible horizon is closer than many people expect, and it depends on one thing: how high your eyes are above the water. This calculator uses the standard geometric approximation that sailors and surveyors apply: the distance to the horizon in nautical miles equals 1.17 multiplied by the square root of your eye height in feet. The constant folds in the radius of the Earth and the average bending of light through the atmosphere, called refraction, which lets you see slightly farther than pure geometry alone. Enter your height of eye above sea level in feet, and the tool returns the distance to the geometric horizon in nautical miles. The square-root relationship means height has diminishing returns: doubling your height extends the horizon by only about 41 percent, which is why lookouts are placed as high as practical on a vessel. This figure also underlies the bobbing-a-light technique that mariners use to estimate distance off a lighthouse of known height at night. Every figure is computed deterministically from the formula shown below, with a worked example that reconciles exactly to the calculator defaults so you can follow each step.
Distance to the horizon is 1.17 x square root of eye height in feet. From a 9 foot eye height, the horizon is 3.51 nautical miles away.
Distance to horizon formula
Distance (NM) = 1.17 x sqrt(h)
h = height of eye in feet
result is in nautical miles
(1 nautical mile = 1.15078 statute miles)
The 1.17 constant includes the Earth's radius and standard atmospheric refraction. Because of the square root, doubling your height extends the horizon by only about 41 percent.
Worked example
Suppose your height of eye above the water is 9 feet.
- Square root of height: sqrt(9) = 3
- Distance: 1.17 x 3 = 3.51 nautical miles
- In statute miles: 3.51 x 1.15078 = 4.04 statute miles
The horizon is 3.51 nautical miles away, about 4.04 statute miles. These are the calculator's default inputs, so the result matches the widget exactly.
Distance to Horizon at Sea Calculator: frequently asked questions
Why does horizon distance depend on height?
The higher your eyes, the farther over the curve of the Earth you can see before the surface drops away. The relationship follows from the geometry of a tangent line to a sphere, adjusted for atmospheric refraction. That is why a crow's nest or a tall bridge extends the visible range.
What does the 1.17 constant represent?
It packages the Earth's radius and the average bending of light through the atmosphere into a single factor for nautical miles when height is in feet. Pure geometry would give a slightly smaller constant; refraction lets you see a little farther, so the practical value is 1.17.
Why a square root?
Horizon distance grows with the square root of height, so gains shrink as you go higher. Going from 9 to 36 feet, four times the height, only doubles the distance. This diminishing return is why extreme height adds less than people expect.
What is the difference between nautical and statute miles?
A nautical mile is about 1.15 statute miles and is based on one minute of latitude, which is why it is the standard at sea. This calculator returns nautical miles and also shows the statute-mile equivalent for land reference.
How is this used in navigation?
Mariners use horizon distance to estimate the range at which a light or landmark of known height first becomes visible, and to judge distance off when a light is bobbing on the horizon. NOAA publishes charts and navigation resources that rely on the same geometry.
Official sources
- Navigation, charting and marine resources: US National Oceanic and Atmospheric Administration (NOAA). As at 25 June 2026.
Reviewed by the CalculatorHub team, edited by James Graham, 25 June 2026. See our methodology. This is general information, not financial, tax, legal or investment advice.