Earth Curvature Calculator. Enter your observer height, target distance, and target height to find out how much of a distant object is hidden below the Earth's curvature. The Earth Curvature Calculator returns the hidden height, horizon distance, and curvature drop — useful for understanding what you can and cannot see across long distances. Also try the Wavelength Calculator.
The Earth is an oblate spheroid with a mean radius of about 6,371 km (3,959 miles). Because of this curvature, objects far away gradually dip below the horizon. The further an object is, the more of its base is hidden — this is what we call the Earth's curvature effect. See also our calculate Angle of Deviation (δ), Angle of Refraction at First Surface (r₁) & Angle of Refraction at Second Surface (r₂) — Prism.
Your horizon distance depends on your eye height above the ground. For an observer standing at sea level (eye height ~1.7 m), the horizon is roughly 4.7 km (about 2.9 miles) away. Climbing higher dramatically extends how far you can see.
The horizon distance is calculated using the formula: d = √(2 × r × h), where r is Earth's radius (~6371 km) and h is observer height. This gives the straight-line distance to the point where your line of sight is tangent to Earth's surface.
Using the exact geometric formula, the hidden height h₂ = √((r + h_observer_horizon_gap)² − r²) where the gap is the remaining distance after subtracting the observer's horizon from the total target distance. In practice, for moderate distances the approximation h ≈ d²/(2r) is also commonly used for the curvature drop. You might also find our calculate Total Radar Horizon Distance, Sensor Horizon Distance & Target Horizon Distance — Radar Horizon useful.
This calculator uses the exact geometric formula based on a spherical Earth with radius 6,371 km, which gives results accurate to within a fraction of a percent for most practical distances. Note that atmospheric refraction can slightly extend your visible range beyond the geometric horizon, but refraction is not included here.
At sea level with eyes at about 1.7 m (5.6 ft), the geometric horizon is roughly 4.7 km (2.9 miles). With typical atmospheric refraction, this can extend to around 5 km (3.1 miles).
The closest point between England and France (Dover to Cap Gris-Nez) is about 34 km (21 miles). At sea level, the combined horizon of two observers each at eye height would need to cover this distance. Standing on the White Cliffs of Dover (~110 m high), the horizon extends roughly 37 km, making it geometrically possible on a clear day.
Earth drops approximately 8 inches (20 cm) per mile squared, or about 7.85 cm per km squared. For example, at 10 km the drop is roughly 7.85 m, and at 10 miles it is about 66.7 feet. This approximation uses h ≈ d²/(2r). Check out our find Focal Length with Focal Length Calculator as well.