Earth Curvature Calculator
The Earth curves away from a flat line at roughly 8 inches per mile squared. Over 10 miles, that adds up to about 66 feet of drop. This calculator shows you the curvature drop at any distance, how far you can see to the horizon, and how much of a distant building or landmark is hidden below the curve.
The curvature drop formula:
h = d² / (2R)
Where h is the drop in feet, d is the distance in feet, and R is the Earth's mean radius (about 3,958.8 miles or 20,902,231 feet). This approximation works well for distances under a few hundred miles.
Distance to horizon:
d = √(2Rh)
Where h is your eye height above the surface. Standing at 6 feet tall, your horizon is about 3 miles away. From the top of a 100-foot lighthouse, you can see about 12.2 miles.
Hidden height of distant objects:
When an object is beyond your horizon, part of it disappears bottom-first. The hidden amount depends on how far beyond the horizon the object sits. For example, a 100-foot building at 20 miles is almost entirely hidden for a 6-foot observer since the horizon is only about 3 miles away and the curvature hides roughly 175 feet at that beyond-horizon distance.
Important notes:
- These are geometric calculations. Atmospheric refraction typically bends light downward, letting you see about 8% farther than the geometric horizon.
- Results assume a smooth surface (no terrain features).
- The formula uses Earth's mean radius and treats it as a perfect sphere, which is close enough for practical purposes.