Distance to Horizon Calculator

Calculate geometric and atmospheric refraction line-of-sight horizon distance from observer and target elevation.

Observer Eye Height Above Water 1.83 m

Height of observer's eye above sea level in feet

Target / Object Height (Optional) 30.48 m

e.g. Lighthouse focal plane or ship mast height

Atmospheric Refraction Model

Observer Height Presets

Distance to Horizon

2.87 NM

3.30 Statute Miles (5.31 km)

Total Geographic Range to Target

14.57 NM

Visible distance before dipping over horizon

Dipping the Light When approaching a lighthouse from sea, the light first appears as a loom on the horizon when the sum of observer horizon + lighthouse horizon is reached.

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How Horizon Distance and Refraction Are Calculated

Due to the curvature of the Earth (mean radius 6,371 km or 3,440 nautical miles), the visual horizon distance for an observer at height h (in feet) is given by Bowditch's American Practical Navigator:

d (Nautical Miles) = 1.17 × √h
Total Geographic Range = 1.17 × (√h_observer + √h_target)

Terrestrial atmospheric refraction bends light rays slightly downward following the Earth's curve, extending the visual horizon by roughly 8% beyond purely geometrical line-of-sight. For marine radar pulses, the effective refraction factor is even greater (4/3 Earth radius or 1.23 × √h).

Frequently Asked Questions

How far is the horizon for an average person standing on a beach?

For an eye height of 5.5 to 6 feet, the horizon is approximately 2.8 nautical miles (3.2 miles or 5.2 kilometers) away.

Why can radar see further than the human eye?

Electromagnetic radar frequencies in the X-band (9 GHz) and S-band (3 GHz) experience greater atmospheric bending than optical light wavelengths, extending radar horizon by approximately 5% to 8% beyond optical sight.

What is the formula in metric units?

Using height in meters: Distance to horizon (km) = 3.57 × √h_meters, or distance in nautical miles = 1.93 × √h_meters.