Earth Curvature Calculator
Calculate how much Earth curves over any distance and whether a distant object is visible above the horizon. See the geometry with the cross-section diagram.
Inputs
Famous examples
Cross-section Diagram
Vertical scale is exaggerated for clarity. Distances shown to scale horizontally.
7.85 m
Earth's surface drops 7.85 m below a flat line over 10.0 km
4.7 km
From 1.7 m eye height, your geometric horizon is 4.7 km away
7.8 m visible
2.2 m of the object is hidden below the horizon
6.83 m
Standard atmospheric refraction (~7% correction) reduces the apparent drop to 6.83 m
On a flat Earth, the drop would be 0 m. The object would be fully visible at any distance, limited only by atmospheric haze. The measured drop of 7.85 m over 10.0 km matches the spherical Earth model (R = 6371 km) with less than 0.1% error at these distances.
The Geometry of Earth's Curve
Curvature Drop Formula
For a distance d, the surface drops approximately d squared divided by 2R meters below a flat line, where R is Earth's radius (6371 km). Over 10 km this is about 7.8 meters. Over 100 km, it reaches roughly 785 meters.
Atmospheric Refraction
Air bends light slightly downward, which extends the visible horizon by about 7-8%. Standard refraction correction multiplies the geometric drop by about 0.87 to get the apparent drop. Temperature inversions can increase this effect dramatically.
Horizon Distance
From height h meters, the geometric horizon is approximately sqrt(2Rh) meters away. A person at 1.7 m height sees the horizon at about 4.7 km. From a 100 m lighthouse, it extends to 35.7 km.
Visibility Calculation
An object at distance d is visible if its height exceeds the curvature drop beyond the observer's horizon. The observer's horizon extends sqrt(2Rh) meters. For any remaining distance, the object must stand taller than the additional curvature drop over that gap.
Real-World Examples
Chicago's skyline (440 m tallest building) is partially visible from the Michigan shore (~90 km) because the skyscrapers rise above the curvature. The White Cliffs of Dover (110 m) can sometimes be spotted from the French coast (33 km) on a clear day.
