Calculate the Distance to the Horizon

Calculator for the distance to the horizon at clean air and with nothing standing in the way. View height is the height of the eyes above ground. When the eye height is at 1.70 m and the viewer stands on a 20 m high tower, the view height a = 21.70 m. When a high object, e.g. a mountain or a ship, protrudes behind the horizon, then b is its height above ground and c is the distance to this object.
Formulas:
c = f * ( √a + √b )
The unit of f is 1000 * √m
f = √2R
R is the mean Earth radius in 1000 km, 6.371.
With atmospheric refraction, as R is taken the mean apparent Earth radius of 7.68.
You can convert length units here.
The visibility to the horizon for a normal-sized person is about five kilometers if the horizon line is at the same height above sea level as the observer's feet and there is nothing in between that blocks the view of the horizon line. This is the case, for example, if you are standing on the shore of a sea or a very large lake, or on completely flat land. If you are standing on a hill, your view goes further, unless you have an even higher hill in front of you. If, on the other hand, you are in a basin, the horizon is usually closer. However, you can also see more distant parts of the earth from a low position, as long as they are high enough, such as mountains.
The earth's atmosphere bends the path of light rays; this effect is called atmospheric refraction. It makes the visibility change in such a way that it is as if the earth were larger than it actually is. If you do not take this factor into account, the visibility would be simulated on a planet without an atmosphere. Water, for example, bends the path of light rays even more than light; this can be clearly illustrated with the famous experiment of a pencil in a glass of water. For this, see refraction.
Last updated on 06/26/2025. Author: Jürgen Kummer
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