Earth Curvature Calculator

What is the Earth Curvature Calculator?

An Earth curvature calculator works out how much the Earth's surface drops below a straight line of sight over a given distance, using the planet's mean radius. It works using the geometric chord approximation, drop = distance² ÷ (2 × Earth's radius), which is accurate for terrestrial distances, then applies a typical atmospheric refraction correction (light bends slightly as it passes through the atmosphere, effectively reducing the visible drop by around 13%) to give a more realistic "what you'd actually see" figure. To calculate it manually: square your distance in metres, divide by twice the Earth's radius (2 × 6,371,000m), and optionally multiply by 0.87 to account for typical refraction — actual refraction varies with weather and temperature, so this correction is illustrative rather than exact.

How it works

Over the relatively short distances relevant to everyday viewing (rather than the full scale of the planet), the drop caused by Earth's curvature can be closely approximated using a simple formula: drop equals distance squared divided by twice Earth's radius. This "flat chord" approximation is highly accurate at terrestrial viewing distances, even though it's technically a simplification of the full spherical geometry.

UK context

Atmospheric refraction bends light slightly around the Earth's curve, which means objects at a distance are typically visible slightly further than the pure geometric calculation alone would suggest — this is why a standard correction factor (commonly around a 13% reduction in the apparent drop) is often applied when estimating what's actually visible on the horizon, though the exact refraction amount varies with temperature, pressure and atmospheric conditions.

Tips

• The geometric (unrefracted) figure is the more mathematically precise answer to "how much does the Earth curve," while the refraction-adjusted figure better approximates what an observer would actually perceive.
• This calculation is most accurate at the distances relevant to viewing across water, land or from height — it uses an approximation that's excellent at these scales, not a full orbital-mechanics calculation.

A quick note

Uses the standard flat-chord approximation with Earth's mean radius. Atmospheric refraction varies with weather and temperature, so the refracted figure is illustrative, not exact.