Earth Curvature Calculator

How much of a distant ship is hidden below the horizon?

Burgart Family Science Project — White Rock Beach, BC

Observer

Eye / Telescope Height Above Sea Level

= 1.83 m

Target (Ship)

Distance to Target

Total Ship Height (waterline to top)

= 65.00 m (typical large cruise ship)

Hull Height (waterline to lowest deck)

= 16.00 m

Earth Model

Flat Earth Mode

Globe model: Earth radius = 6,371 km

Quick Presets

Telescope View — What You Should See

How It Works

On a spherical Earth (radius ≈ 6,371 km), the distance to the horizon from height h is approximately √(2Rh). If a target is farther than your horizon distance, its base is hidden behind the curve.

The hidden height — the amount of the ship below your line of sight — is calculated as (d − d_horizon)² / (2R), where d is the distance to the target and d_horizon is your horizon distance.

The experiment: Observe a cruise ship through a telescope from the beach. Use a ship-tracking website to get the exact distance. Compare what you see (hidden hull) to what the globe math predicts. Then go up a hill and look again — more of the ship should become visible, exactly as the math predicts.

In flat earth mode, no curvature exists, so the entire ship should always be visible regardless of distance. Your own eyes will tell you which model matches reality.

Useful ship trackers: MarineTraffic, VesselFinder, CruiseMapper

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