How far is the horizon?
How far can you see from a beach, a cliff or a mountain — and how far away could a rescuer see you?
The formula
The American Practical Navigator (Bowditch), the US government's navigation manual, gives the distance to the visible horizon as 1.17 √h nautical miles, with h your eye height in feet. It includes the normal bending of light by the atmosphere, which lets you see a little further than pure geometry. To see the top of something tall, add its own horizon distance to yours.
| Eye height | Horizon |
|---|---|
| 1.7 m | 5.1 km (2.8 nmi) |
| 10 m | 12.4 km (6.7 nmi) |
| 30 m | 21.5 km (11.6 nmi) |
| 100 m | 39.2 km (21.2 nmi) |
| 1,000 m | 124.1 km (67 nmi) |
In real life
Haze, rain and the light can cut visibility far below these numbers, and unusual temperatures can bend light more, making distant coasts appear above the horizon (looming) or vanish. For signalling, height matters: climbing a 30 m hill takes your horizon from under 5 km to about 21 km.
More navigation tools
Source: National Geospatial-Intelligence Agency, The American Practical Navigator (Bowditch), Pub. No. 9, distance of the horizon.