Distance to the Horizon

June 19, 2005


Provided by: Laurent Laveder, Optics of the Atmosphere Gallery
Summary authors & editors: Kevin Patfield; Laurent Laveder; Neil Seymour

The above photo showing a passing ship in the distance, most of which is below the horizon, was taken south of Le Guilvinec, Bretagne, France on April 5, 2005. To determine how far you're able to see in the distance (in miles), use the approximation that the distance to the horizon in miles is 1.23 times the square root of the height of the eye in feet. Thus the horizon is about 2.12 miles away if your eye is 3 feet above the sea. But a simpler (and arithmetically equivalent) calculation is to multiply by 1.5 before taking the square root -- take the height in feet, add 50%, take the square root and this is the answer in miles. This works for a height of up to a few hundred miles or so. However, you should also consider the effects of refraction, which tends to increase the distance one can see. A simple way to allow for this is to change the rule above as follows: take the height in feet, add 75%, take square root, call it miles. So the real answer for the distance to the horizon, for a height of three feet, is approximately 2.29 miles.

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