When I stand at the water's edge and look out over the ocean, how far away is the horizon?

★ wanayoo — archive 1999 http://www.howstuffworks.com/question198.htm

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Question

I was standing on the beach yesterday looking at the ships on the horizon, and I started wondering how far away the horizon was. Is there an equation to work out how far away the horizon is based on how high your eyes are above sea level?

Answer

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 actually is not flat at all - it follows the curvature of the earth.

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

So the distance of 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 one mile away (1.6 km). A rough formula for calculating the distance to the horizon is:

SquareRoot(HeightAboveSurface / 0.5736) = DistanceToHorizon Where HeightAboveSurface is in feet and DistanceToHorizon 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(HeightAboveSurface / 6.752) = DistanceToHorizon where HeightAboveSurface is in centimeters and DistanceToHorizon is in kilometers.

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