geo-distance Verified Precision Tool
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 EllipsoidPoint 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 = 1.7m5. 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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