Earth Curvature Calculator
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About This Calculator
This Earth Curvature Calculator provides precise geodetic measurements, moving beyond simple approximations. It employs the Haversine formula for calculating the great-circle distance's curvature drop, ensuring accuracy over any distance. The tool is indispensable for surveyors, long-range photographers, sailors, and anyone curious about the tangible effects of our planet's shape.
A key feature is its handling of atmospheric refraction. Light rays bend as they pass through different densities of air, making distant objects appear higher than they are. This calculator uses a standard refraction coefficient (k=1/7) to simulate this effect, which effectively increases Earth's radius for optical calculations, providing a more realistic estimate of visibility.
Horizon (d_h): d_h = sqrt(2 * R_eff * H_obs)
Whether you're planning a shot of a distant city skyline or verifying line-of-sight for a radio link, this tool gives you the data you need. You can adjust parameters like Earth's radius and the refraction coefficient in the advanced options for specialized scenarios.
How to Use the Calculator
1. Enter Distances & Heights: Input the distance to your target, your viewing height (eye level), and the height of the target object. You can instantly switch between metric (km, m) and imperial (miles, ft) units.
2. View Results: The calculator instantly provides six key metrics, including how much the Earth has curved over that distance ("Curvature Drop") and how much of the target is hidden by the curve ("Total Hidden Height").
3. Advanced Control: For more specific needs, open the "Advanced Options" to toggle atmospheric refraction or fine-tune the Earth's radius and the refraction coefficient (k-factor).
4. Visualize: The diagram at the bottom of the results provides a simple visual representation of the observer, the target, and the effect of Earth's curvature on the line of sight.
For Photographers
Planning a shot of a distant subject? Use this to calculate exactly how much of it will be visible over the horizon.
For Surveyors
Incorporate geodetic correction into your long-distance leveling and measurements for improved accuracy.
For Marine Navigation
Determine the distance at which another vessel or a lighthouse will become visible, based on your height above the water.
Understanding the Results
Curvature Drop: This is the geometric "bulge" of the Earth. It's the height difference between a straight, tangential line and the curved surface of the Earth at a given distance.
Total Hidden Height: This is the crucial value. It tells you how much of the target object's base is obscured by the curve of the Earth, from your specific viewing height. A positive value means part of the object is hidden.
Geometric Horizon: This is the distance from your eyes to the horizon, where the sky appears to meet the surface. It increases with your height.
Max Visible Distance: This is the maximum distance at which the top of the target can be seen from your viewing height. If the "Distance to Target" is greater than this, the object is completely hidden.
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