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Distance of the horizon

 Eye-level height


All results have been rounded to significant digits.

With this calculator you can estimate the distance to the horizon or to an object above the horizon that you observe at the sea. The result is not exact. The calculation is performed with an approach that calculates the distance along the tangent between the eye of the observer A and the tangent point at the horizon H, or further on to the lowest point of object B, which is just visible.


The approach does not consider the refraction of light in the atmosphere, caused by the temperature changes of air with height, leading to bended light rays. Therefore the visible horizon is a bit further away than is calculated from geometry. It is difficult to estimate the exact effect of refraction.
The calculation assumes a spherical earth with a uniform radius of 6371 km.

Usage: Type the eye-level height above the sea surface and the height of the lowest visible part of the object in the correct units into the corresponding fields. For calculating the distance to the horizon use a value of "0" for the object height. The calculation is performed after a mouse click on any free space of the window or on the "calculate" button.
You can also type in the distance and one height. The other height will be calculated. The fields with input values get a light green background, output fields are colored pink. The calculation is performed with the two values changed last, or with those, whose radio button (at the top) is activated.
Move the mouse over a unit or click on it to read its full name. Input that is not valid is deleted before the calculation and is not considered.

Example: At the sea you stand about 1 meter above the water surface. Your eye-level is 1.75 m above ground. Above the horizon you recognize the upper edge of the coast of an island, of which you know the height of 120 m. What is the distance to this island?
Type the eye-level above the sea (2.75 m) and the height of the island (120 m) into the corresponding fields. After a mouse click on any free space of the window or the "calculate" button the calculation is performed. As result you get 45 km.

- There is no warranty for the calculation. Cactus2000 is not responsible for damage of any kind caused by wrong results.
- Please send an email if you have suggestions or if you would like to see more conversions to be included.

© Bernd Krüger, 20.01.2010

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Bernd Krüger, 2018