Science · Geography / Physics

Earth Curvature Calculator

See how far the horizon is from your eye height, how much the surface drops over a distance, and how much of a distant object stays hidden below the curve.

Observer height

Horizontal distance

Target height (optional)

Leave empty to skip the “visible above the horizon” calculation.

Results · using Earth radius 6371 km

Horizon distance

—

straight-line ground distance

Curvature drop

—

surface falls this much over the distance

Hidden height

—

bottom of target below your line of sight

Visible height

—

top of target above the horizon

Curvature geometry

D = √(2Rh + h²) x = R(1 − cos(d/R))

R = 6371 km is the mean radius of the Earth. The horizon distance D uses only your eye height h. The curvature drop x at horizontal distance d is the vertical distance the surface falls away from a tangent plane. The drop is tiny up close — about 8 cm per kilometre at the start — then grows with the square of the distance.

📍 Horizon distance

Works from any eye height — 1.7 m gives about 4.7 km, 10 m gives about 11.3 km.

🛳 Drop calculation

Exact cosine formula, not the quadratic shortcut, so large distances stay accurate.

👁 Hidden height

Accounts for your own height so it matches what a camera or person really sees.

📚 km / miles

Switch between metric and imperial for distance and heights instantly.

More geometry & physics

Forces and fields use the same kind of inverse-square thinking.

Coulomb’s Law Calculator