# Horizon

**URL:** <https://boards.straightdope.com/t/horizon/167865>\
**Category:** Factual Questions\
**Created:** [April 10, 2003, 7:45pm UTC](https://boards.straightdope.com/t/horizon/167865 "2003-04-10T19:45:23Z")\
**Posts on this page:** 6\
**Page:** 1

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**Author:** ![aubries](https://avatars.discourse-cdn.com/v4/letter/a/53a042/32.png) [@aubries](https://boards.straightdope.com/u/aubries)\
**Post date:** [April 10, 2003, 7:45pm UTC](https://boards.straightdope.com/t/horizon/167865/1 "2003-04-10T19:45:23Z")

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If I’m standing on the deck of a ship in the middle of the Atlantic ocean, how far away is the horizon?

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**Author:** ![Q.E.D](https://avatars.discourse-cdn.com/v4/letter/q/51bf81/32.png) [@Q.E.D](https://boards.straightdope.com/u/Q.E.D)\
**Post date:** [April 10, 2003, 8:00pm UTC](https://boards.straightdope.com/t/horizon/167865/2 "2003-04-10T20:00:54Z")

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> [@](#):
>
> The distance in km of the horizon on earth, in a plain (standing on the ground or on a tower, or from a plane) or on a hill or mountain surrounded by plains is approximately ã(13h), where h is the height in meters of the eyes.
> 
> Examples:
> 
> standing on the ground with h = 1.70 m, the horizon is at a distance of 4.7 km  
> standing on a hill or tower of 100 m height, the horizon is at a distance of 36 km.

From [url=http://www.wikipedia.org/wiki/Horizon[Wikkipedia.

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**Author:** ![ChalkPit](https://avatars.discourse-cdn.com/v4/letter/c/a88e4f/32.png) [@ChalkPit](https://boards.straightdope.com/u/ChalkPit)\
**Post date:** [April 10, 2003, 8:08pm UTC](https://boards.straightdope.com/t/horizon/167865/3 "2003-04-10T20:08:57Z")

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Using a bit of simple Pythag, I get 16km to the horizon, assuming a height above the water of 20m, which seems a good guess for a decent sized ship.

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**Author:** ![Q.E.D](https://avatars.discourse-cdn.com/v4/letter/q/51bf81/32.png) [@Q.E.D](https://boards.straightdope.com/u/Q.E.D)\
**Post date:** [April 10, 2003, 8:10pm UTC](https://boards.straightdope.com/t/horizon/167865/4 "2003-04-10T20:10:04Z")

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That funny symbol in the formula is meant to be a radical. :rolleyes:

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**Author:** ![ChalkPit](https://avatars.discourse-cdn.com/v4/letter/c/a88e4f/32.png) [@ChalkPit](https://boards.straightdope.com/u/ChalkPit)\
**Post date:** [April 10, 2003, 8:35pm UTC](https://boards.straightdope.com/t/horizon/167865/5 "2003-04-10T20:35:22Z")

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The formula I used was:

d=sqrt((6378+h)squared - 40678884)

where d is the distance to horizon and h is the height above the surface. All units being kilometres.

Comes up with 35.7km for 100m height, so that ties in with QED’s distances.

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**Author:** ![John\_Kentzel-Griffin](https://avatars.discourse-cdn.com/v4/letter/j/ccd318/32.png) [@John\_Kentzel-Griffin](https://boards.straightdope.com/u/John_Kentzel-Griffin)\
**Post date:** [April 10, 2003, 9:01pm UTC](https://boards.straightdope.com/t/horizon/167865/6 "2003-04-10T21:01:14Z")

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The Master answers: [Are the north and south horizons not equally distant?](http://www.straightdope.com/classics/a1_167b.html)