Line of Sight / Horizon Distance
Calculate how far to the horizon you can see from a given height, and the maximum line-of-sight distance to a target at elevation.
Results
What is it?
The geometric horizon is the maximum distance at which a point on the ground can be seen, limited by Earth's curvature. The formula d = 3.57 * sqrt(h) km gives the horizon distance for an observer at height h metres. Two objects can see each other when the sum of their individual horizon distances exceeds their separation.
How to use
Enter your observer height (e.g. standing on a cliff at 50 m) and the target height (e.g. a lighthouse at 30 m). Toggle atmospheric refraction to add ~7% for more realistic daylight conditions. The result shows your horizon alone and the combined line-of-sight distance.
Example scenario
An observer at 10 m (ship mast) watching a lighthouse at 30 m height: Observer horizon = 11.3 km, lighthouse horizon = 19.6 km. Combined line-of-sight = 30.9 km � the lighthouse is visible from up to ~31 km away in clear conditions.
Pro tip
Atmospheric refraction varies significantly with temperature gradients. On hot days with a cool sea surface (thermal inversion), the effective horizon can extend 20-30% beyond the geometric calculation. For radio/microwave line-of-sight links, use a k-factor of 4/3 to model effective Earth radius under standard atmosphere.