Earth's Curvature Drop Calculator

Earth's Curvature Drop Calculator

How much does Earth's curvature "hide" an object at a given distance, before accounting for observer height or atmospheric effects? This calculator gives the basic geometric answer.

Curvature Drop (km) = Distance² / (2 × Earth Radius)

Example

At 10 km distance:

Drop = 10┬▓ / (2 x 6,371) ≈ 7.85 meters

Why This Grows Quadratically

Because distance is squared in this formula, curvature drop accelerates rapidly at longer distances - this is why distant ships, coastlines, or city skylines appear to gradually sink below the horizon rather than simply shrinking uniformly with distance the way a flat surface would produce. Standing at sea level, the theoretical horizon distance (where curvature drop equals your own eye height above the water) works out to roughly 4.7 km for an average person.

What This Simple Formula Ignores

This calculation doesn't account for observer height above the surface (a taller vantage point extends your visible horizon considerably further), the target object's own height (a tall ship or building remains visible longer than a low one), or atmospheric refraction, which bends light slightly around Earth's curvature and typically extends the visible horizon a bit further than pure geometry alone would predict.