Distance to Horizon Calculator
The distance to the horizon depends on the height of the observer's eye above sea level. The standard marine navigation formula accounts for the curvature of the Earth and typical atmospheric refraction: Distance (nautical miles) = 1.17 times the square root of the eye height in feet. Atmospheric refraction bends light rays slightly downward, making the visible horizon about 8% farther than pure geometry predicts. Enter your eye height in feet or meters and the calculator returns the horizon distance in nautical miles. This distance is used to predict when a lighthouse or other object will be first seen, and to calculate the range at which two vessels become mutually visible.
Horizon distance formula
Distance (nm) = 1.17 * sqrt(height in feet)
Distance (nm) = 2.08 * sqrt(height in meters)
Geographic range = observer horizon + object horizon
= 1.17 * (sqrt(eye height) + sqrt(object height))
The factor 1.17 incorporates standard atmospheric refraction. The geometric factor (no refraction) would be 1.06.
Practical applications
- Light lists (published by USCG) give the nominal and geographic range of lights for planning purposes.
- A lighthouse with a focal plane of 100 ft is visible at 1.17*sqrt(100) = 11.70 nm from sea level.
- Add your eye height distance to the lighthouse distance for the total geographic range.
- Always compare geographic range to the charted luminous range; use the lesser value for planning.
Distance to horizon: frequently asked questions
What is the formula for distance to the horizon?
The standard marine approximation is: Distance (nm) = 1.17 * sqrt(height in feet). For height in meters, the formula is 2.08 * sqrt(height in meters). This accounts for standard atmospheric refraction which slightly increases the geometric horizon distance.
Why does the formula include a correction for refraction?
Light bends slightly as it passes through the atmosphere, which causes the apparent horizon to be farther away than pure geometry would predict. The factor 1.17 (versus the geometric 1.06) incorporates the standard refraction assumption of 7/6 times the geometric distance.
How does this affect the range at which I can see another vessel?
The total range at which two observers can see each other is the sum of their individual horizon distances. A vessel with a masthead light at 40 ft and an observer at 9 ft eye height can see each other at approximately 1.17*(sqrt(40)+sqrt(9)) = 1.17*(6.32+3) = 10.90 nm.
What is the difference between geographic and luminous range?
Geographic range is the maximum distance at which an object can be seen given the curvature of the Earth, based on observer and object height. Luminous range is how far a light source is visible based on its intensity and atmospheric visibility. A light's charted range is the lesser of the two.
Does height of eye affect navigation safety?
Yes. A lower eye height reduces how far you can see traffic and hazards, and how far your vessel's lights and mast are visible to others. Keeping a bow watch with the highest practical eye height improves lookout range and safety.
Official sources
- National Geospatial-Intelligence Agency: Bowditch American Practical Navigator (Pub. 9).
- US Coast Guard Light List: USCG Light Lists.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.