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Geodesy & Distance CalcyZone Calculator

Horizon Distance Calculator

Calculate the line-of-sight distance to the visible horizon based on observer elevation and Earth radius.

📍 Select World Location Presets or Custom Coordinates

WGS-84 Ellipsoid
Point 1 Coordinates (Origin)
Observer & Target Parameters
Calculated Geodetic Solution
Horizon: 4.654 km | Drop: 7.85 m
Geometric Horizon Distance4.654 km
Curvature Drop over Target7.85 meters
Hidden Height Beyond Horizon2.24 meters
🗺️ Interactive Geographic Map & Geodesic Trajectory

Click anywhere on the map or drag pins to update coordinates live.

Map Data: © OpenStreetMap ContributorsWGS-84 Precision Geodesic Curve

Step-by-Step Mathematical Derivation

1. Given Input Coordinates:
  • Eye Level Height: 1.7 m
  • Target Distance: 10 km
2. Model & Ellipsoid Reference:WGS-84 / Earth Sphere R = 6,371 km
3. Governing Geodesic Formula:d_horizon = sqrt(2R*h + h²), Drop = R * (1 - cos(d/R))
4. Variable Substitution:R = 6,371,000m, h = 1.7m
5. Interpretation & Practical Application:

For an observer at 1.7m height, the horizon is 4.654 km away. At 10 km, curvature causes a 7.85m drop.

Mathematical Formula

d = sqrt(2 * R * h + h²), Curvature Drop = R * (1 - cos(d/R))

Overview & Explanation

Determines how far an observer can see before Earth curvature blocks line of sight.

How It Works

  • Uses Pythagorean relationship between observer height and Earth radius R.

Practical Applications

  • Lookout tower range.
  • Maritime vision horizon.
  • Radar range estimation.

Worked Example: Human Standing at Sea Level (1.7m)

Find horizon distance.

1

Compute Horizon

sqrt(2 * 6371000 * 1.7)

= 4.65 km (2.89 miles)

Frequently Asked Questions

Does atmospheric refraction affect horizon distance?
Yes, standard atmospheric refraction extends visible horizon by about 8% (d ≈ 3.57 * sqrt(h in meters) km).

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