Earth Curvature Calculator
Free Earth curvature calculator: enter a distance to see the curvature drop, your horizon distance and how much of a far-away object is hidden behind the curve, with optional atmospheric refraction.
Diagram (not to scale)
Curvature at common distances
| Distance | Curvature drop | Hidden from your eye height |
|---|
Drop = how far the surface falls below a perfectly straight line that starts level at your feet. Hidden = the part of a distant object below the horizon line as seen from your eye height.
How the Earth curvature calculator works
- Enter the distance in kilometers or miles. The calculator uses the Earth's mean radius of 6,371 km (3,958.8 miles) and shows the curvature drop: how far the surface curves away beneath a straight line. For short distances this is very close to d² ÷ 2R.
- Add your eye height to see the horizon distance and how much of a far-away object is hidden behind the curve. Add the object's own height to see how much of it you can still see.
- Tick atmospheric refraction to model the small bending of light in the air (a standard coefficient of 0.13). It lets you see slightly farther than pure geometry says.
- The 8 inches per mile squared rule of thumb you may have seen is the same parabola: at 1 mile the drop is about 7.98 inches, and it grows with the square of the distance (about 32 inches at 2 miles, 72 inches at 3 miles).
Formulas used
Drop = R × (1 ÷ cos(d ÷ R) − 1) ≈ d² ÷ (2R). Horizon distance = √(2Rh + h²). Hidden height = (d − horizon)² ÷ (2R) once the object is beyond your horizon. With refraction, R is replaced by R ÷ (1 − k).
Is anything sent to a server?
No — everything is computed in your browser. The Earth is modelled as a perfect sphere, so real-world results (terrain, waves, temperature layers) will vary a little.