S3 Series

Distance to the horizon[edit]
Please note: We typically see further along the Earths curved surface than a simple geometric calculation allows for because of the refraction error. Surveyors measuring longer distances than 300 feet subtract 14% from the calculated curvature error and ensure lines of sight are at least 5 feet from the ground to reduce random errors created by refraction.

However, ignoring the effect of atmospheric refraction, distance to the horizon from an observer close to the Earth's surface is about[5]

d \approx 3.57\sqrt{h} \,,
where d is in kilometres and h is height above ground level in metres.

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 the ground with h = 2 metres (6 ft 7 in), the horizon is at a distance of 5 kilometres (3.1 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 an observer standing at the top of the Burj Khalifa (828 metres (2,717 ft) in height), the horizon is at a distance of 103 kilometres (64 mi).
For an observer atop Mount Everest (8,848 metres (29,029 ft) in altitude), the horizon is at a distance of 336 kilometres (209 mi).

With d in miles[6] and h in feet,

d \approx \sqrt{1.5h} \approx 1.22\sqrt{h} \,.
Examples, assuming no refraction:

For an observer on the ground with eye level at h = 5 ft 7 in (1.70 m), the horizon is at a distance of 2.9 miles (4.7 km).
For an observer standing on a hill or tower 100 feet (30 m) in height, the horizon is at a distance of 12.2 miles (19.6 km).
For an observer on the summit of Aconcagua (22,841 feet (6,962 m) in height), the sea-level horizon to the west is at a distance of 184 miles (296 km).
For a U-2 pilot, whilst flying at its service ceiling 70,000 feet (21,000 m), the horizon is at a distance of 324 miles (521 km)