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Geodesy & Distance CalcyZone Calculator

Earth Curvature Drop Calculator

Calculate vertical drop and hidden obstacle height over distance due to Earth curvature.

📍 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

Drop = R * (1 - cos(d/R)) approx 8 inches per mile squared

Overview & Explanation

Calculates how many meters an object drops below the geometric horizon at a specified distance.

How It Works

  • Applies circular arc drop formula over Earth radius.

Practical Applications

  • Telecommunications tower height planning.
  • Long-range vision checks.

Worked Example: 20 km distance

Calculate curvature drop.

1

Compute Drop

20km target distance

= Drop: 31.39 meters | Hidden: 18.2 meters

Frequently Asked Questions

What is the rule of thumb for Earth curvature drop?
The approximate rule of thumb is 8 inches per mile squared (0.667 feet * miles²).

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