Distance to Horizon Calculator

Compute visible horizon distance using geometric optics or standard atmospheric refraction. Includes the empirical 8% rule (maritime/aviation) and the 4/3 Earth radius model (radio/engineering).

? Quick examples:
? Human eye (1.7 m / 5.6 ft)
? Ship mast (10 m / 33 ft)
? Lighthouse (50 m / 164 ft)
? Drone (120 m / 394 ft)
✈️ Airliner (10,000 m / 32,800 ft)
? Extreme height (100 km)
Privacy first: All calculations are performed locally in your browser. No data is transmitted.
Extreme height warning: This height is far beyond typical applications. Atmospheric refraction models may deviate from reality; visualization is adaptively scaled.

The Science of the Visible Horizon: From Geometry to Refraction

The distance to the horizon is the maximum line-of-sight distance from an observer to the apparent boundary where Earth's surface meets the sky. Due to Earth's curvature, this distance is finite and depends on observer height and atmospheric refraction. This fundamental concept is used in navigation, aviation, coastal engineering, and radio propagation.

Geometric horizon distance (ideal sphere, no atmosphere):

d = √(2Rh + h²) ≈ √(2Rh)   (since h ≪ R)

where R = mean Earth radius ≈ 6371 km (3959 mi), h = observer height.

Refraction Models: 8% Rule vs. 4/3 Earth Radius

  • Optical (maritime/aviation) – 8% increase: Under standard atmospheric conditions, air density decreases with altitude, bending light rays slightly toward the Earth. This refraction effectively increases the horizon distance by about 8%. d_optical = d_geo × 1.08.
  • Radio / engineering – 4/3 Earth radius model: For VHF/UHF propagation, refraction is modeled by increasing Earth's radius to R_eff = (4/3)·R ≈ 8495 km. The radio horizon distance becomes d_radio = √(2·R_eff·h) (approximately 15% longer than geometric). This is standard in ITU recommendations and antenna design.
Case Study: Lighthouse Visibility & Marine Navigation

A lighthouse with focal plane at 50 m (164 ft) above sea level. Geometric horizon: ≈25.2 km. Using the 8% optical rule: ≈27.2 km. Using the 4/3 Earth model (for radio beacons): ≈29.1 km. The difference of nearly 4 km can be critical for ship navigation and coastal VHF radio coverage. The table below shows horizon distances for common heights.

Height vs. Horizon Distance (Metric, with refraction)

Observer Height Geometric (km) Optical 8% (km) 4/3 Earth model (km)
1.7 m (human eye) 4.65 5.02 5.37
10 m (small boat) 11.29 12.19 13.04
50 m (lighthouse) 25.24 27.26 29.15
120 m (drone) 39.11 42.24 45.18
10 km (airliner) 357.1 385.7 412.5

 Dip of the Horizon – For Celestial Navigation

In nautical astronomy, the dip of the horizon is the vertical angle between the horizontal plane at the observer and the apparent horizon. It is given by θ (arcminutes) ≈ 0.97 × √h(feet) or θ (arcminutes) ≈ 1.76 × √h(meters). This correction is essential when measuring the altitude of stars or the sun with a sextant. The dip is negative (below the horizontal) and increases with observer height. Example: For h = 10 m, dip ≈ 5.57 arcminutes.

✈️ Practical Applications Across Fields

  • Aviation: Pilots use horizon distance to estimate visual range and plan emergency landing sites.
  • Telecommunications: Antenna height determines line-of-sight distance for microwave links; the 4/3 Earth model is standard for path profiling.
  • Marine Navigation: Lighthouse visibility, radar horizon, and VHF radio range all depend on the horizon formula.
  • Outdoor & survival: Hikers and sailors estimate when distant landmarks will appear.

✅ Trusted geodetic reference – This tool implements formulas from the International Association of Geodesy and NOAA’s National Geodetic Survey. The 4/3 Earth radius model follows ITU-R P.526 recommendation. Reviewed by the GetZenQuery Tech team, last updated April 2026.

Frequently Asked Questions

We use the mean volumetric radius R = 6371 km (3959 mi) as defined by the International Union of Geodesy and Geophysics (IUGG).

Use the 4/3 model for VHF/UHF radio propagation calculations (e.g., antenna coverage, microwave links). It is the standard model recommended by the ITU for normal atmospheric conditions.

It is a good approximation for sea-level conditions with standard temperature/pressure gradient. Extreme temperature inversions or very dry air can alter refraction, but for most practical navigation, the 8% rule is sufficient.

Dip (in arcminutes) ≈ 1.76 × √h(m) or 0.97 × √h(ft). This is used in celestial navigation to correct sextant readings. The dip is always subtracted from the observed altitude.
References: NOAA: Distance to Horizon; Wikipedia: Horizon; Bowditch, N. American Practical Navigator; ITU-R P.526-15 "Propagation by diffraction".