🌍 Flat vs Round Earth Calculator
See the actual geometry behind Earth’s curvature: how much the surface drops below a flat line of sight over a given distance, and how far you can see to the horizon from a given height.
What This Calculator Does
Earth’s surface is a sphere (technically a slightly flattened oblate spheroid), and its curvature has directly measurable, predictable effects over distance — ships disappearing hull-first, distant towers being hidden below the horizon, and how far a raised observer can see. This calculator applies the standard geometry used in surveying, aviation, and navigation to show those effects for real numbers you choose.
The Formula
Using Earth’s mean radius R ≈ 6,371 km, the amount a distant point drops below a flat tangent line over distance d is approximated by drop ≈ d² / (2R), valid for distances small compared to Earth’s radius. The distance to the visible horizon from a height h above the surface is horizon ≈ √(2Rh + h²). These are the same formulas surveyors, sailors, and aviators have used for centuries, and they match real-world observation and satellite measurement.
Note: This is a standard-geometry educational tool using Earth’s well-established, independently measured curvature; results are approximate and don’t account for atmospheric refraction, which can bend light slightly and extend apparent visibility a small amount beyond the pure-geometry horizon distance.