How far can I see on the ocean?

One of the funniest things about the ocean is the fact that its surface is curved. We tend to think about water forming large flat sheets, but the surface of a large body of water is not actually flat at all -- it follows the curvature of the Earth.

Because of the curvature of our planet, the distance between you and the horizon when you look out over the ocean depends on your height above the surface of the water. The following diagram shows you how the distance to the horizon can change depending on the height of the observer:

So the distance to the horizon depends on the height of your eyes above the water. If your eyes are 8 inches (20 cm) above the water, the distance of the horizon is about 1 mile (1.6 km) away. A rough formula for calculating the distance to the horizon is:

SquareRoot(height above surface / 0.5736) = distance to horizon

where "height above surface" is in feet and "distance to horizon" is in miles. If you are 6 feet tall and standing right at the water's edge, then your eyes are about 5.5 feet above the surface. The distance to the horizon is:

SquareRoot(5.5 / 0.5736) = 3 miles

In metric, the equivalent is:

SquareRoot(height above surface / 6.752) = distance to horizon

where "height above surface" is in centimeters and "distance to horizon" is in kilometers.

These links will help you learn more:

• Why does the moon look so much bigger when it is near the horizon?
• How can you measure the height of a tall tower?
• What is a nautical mile, and how does it differ from a normal mile and a kilometer?

Originally Published: Apr 1, 2000

How Far Is The Horizon FAQ

What is the horizon?

The horizon is the mid-way point between the Earth and the sky. It's where these two parts seem to meet.

How far can you see on the horizon?

If you are looking at the horizon from the ground, the horizon is approximately 5 kilometers from you.

How far is the horizon in miles?

The furthest distance to the horizon that the human eye can see varies slightly depending on a person’s height. In miles, the horizon is approximately 3.1 miles away.

How far can you see clouds on the horizon?

If you’re standing on level ground, in clear weather and with ample light, you can see clouds on the horizon from about 66 kilometers away.

How do you calculate the distance to the horizon?

The formula to calculate the distance from you to the horizon is 1.17 times the square root of the height from the ground to your eyes.

How far can you see out to sea? It depends how high above the sea you are. The curvature of the earth means that, on the sea shore at a height of two metres, you can see just 5km or 3 miles.

This calculator works out how far you can see at sea at a variety of locations around the UK coastline, including Plymouth Hoe, the top viewing platforms of Portsmouth’s Spinnaker Tower and Blackpool Tower, the White Cliffs of Dover, Beachy Head, the cliffs near Boulby (the highest sea-cliff on England’s east coast, Great Hangman in north Devon (the highest sea-cliff in England), Conachair on St Kilda (the highest sea-cliff in the UK) and a jet at cruising altitude.

The result tells you the distance of the horizon at sea level. It may also be possible to see the tops of objects that are further away.

When you choose a location, its height above sea level in metres will appear in the lower box. You can also use this box to enter any other height.

Heights are from Ordnance Survey mapping or the websites of the towers in question.

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Pan American clipper pilots have found that most of their passengers have surprisingly hazy notions of how far they can see in the air. One passenger, 20,000 feet above Brazil, insisted that she could see the coast of Africa, 1,822 miles away. To set such passengers straight (and help military pilots) Pan Am's clipper captains have worked up a handy "vision range" table.

At sea level the curvature of the earth limits the range of vision to 2.9 miles. The formula for determining how many miles an individual can see at higher levels is the square root of his altitude times...

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