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Earth Curvature Calculator

Compute the hidden height of distant objects due to Earth's curve. Precise geodesic tool for engineers, photographers, and surveyors.

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About

Long-distance observations inevitably encounter the physical limit of the horizon. As an observer moves away from an object the curvature of the Earth obscures the lower portion of that target. This phenomenon affects telecommunications tower placement and maritime navigation. Engineers and photographers often require precise calculations to determine if a line of sight exists between two distinct points.

This calculator utilizes standard spherical trigonometry to determine the obscured height. It assumes a standard geometric sphere. Note that atmospheric refraction can sometimes allow one to see slightly beyond the geometric horizon. This tool calculates the strict geometric drop and hidden height based on the observer's elevation.

curvature horizon geodesy surveying optics

Formulas

The distance to the horizon d1 is calculated using the observer's eye height h and Earth's radius R.

d1 ≈ √2Rh

The remaining distance d2 is the total distance D minus d1. The hidden height y is derived from this remaining segment.

y ≈ d222R

Reference Data

Observer HeightDistance to Horizon (Geometric)Hidden Height at 100kmHidden Height at 50km
1.7 m (Human Eye)4.7 km712 m161 m
10 m (2nd Floor)11.3 km617 m117 m
50 m (Tower)25.2 km438 m48 m
328 m (Eiffel Tower)64.7 km98 m0 m
828 m (Burj Khalifa)102.7 km0 m0 m
8,848 m (Everest)336.0 km0 m0 m
10,000 m (Plane)357.1 km0 m0 m
408 km (ISS)2,280 km0 m0 m

Frequently Asked Questions

This tool calculates the geometric hidden height. Standard atmospheric refraction typically bends light rays downward which allows observers to see approximately 8% further than the geometric horizon. However refraction varies wildly with temperature and pressure.
The calculation uses the mean volumetric radius of Earth which is approximately 6,371 kilometers or 3,959 miles. This is the standard value used in geodesy and aviation.
"Drop" is the distance from a tangent line at the observer's eye extending infinitely. "Hidden Height" is the part of the object strictly below the horizon curve. Drop includes the height of the observer while Hidden Height subtracts the horizon distance offset.
Yes. This tool provides the mathematically predicted obstruction values based on the WGS84 spherical model. If an object is visible when the math says it should be hidden it usually indicates strong atmospheric refraction (looming) rather than a flat surface.