Distance to the horizon

Three types of horizon.

Approximate formulas

The straight line of sight distance d in kilometers to the true horizon on earth is approximately

where h is the height above ground or sea level (in meters) of the eye of the observer. Examples:

• For an observer standing on the ground with h = 1.70 metres (5 ft 7 in) (average eye-level height), the horizon is at a distance of 4.7 kilometres (2.9 mi).
• For an observer standing on a hill or tower of 100 metres (330 ft) in height, the horizon is at a distance of 36 kilometres (22 mi).

For Imperial units, 13 is replaced by 1.5, h is in feet and d is in miles. Thus:

Examples:

• For observers on the ground with eye-level at h = 5 ft 7 in (5.583 ft), the horizon is at a distance of 2.89 miles (4.65 km).
• For observers standing on a hill or tower 100 feet (30 m) in height, the horizon is at a distance of 12.25 miles (19.71 km).

These formulas may be used when h is much smaller than the radius of the Earth (6371 km), including all views from any mountaintops, airplanes, or high-altitude balloons. With the constants as given, both the metric and imperial formulas are precise to within 1 pc (see next section for how to derive formulas of greater precision).