# How far is the horizon **URL:** \ **Category:** Factual Questions\ **Created:** [September 23, 2003, 11:42pm UTC](https://boards.straightdope.com/t/how-far-is-the-horizon/203424 "2003-09-23T23:42:30Z")\ **Posts on this page:** 10\ **Page:** 1
**Author:** ![ltfire](https://avatars.discourse-cdn.com/v4/letter/l/7ea924/32.png) [@ltfire](https://boards.straightdope.com/u/ltfire)\ **Post date:** [September 23, 2003, 11:42pm UTC](https://boards.straightdope.com/t/how-far-is-the-horizon/203424/1 "2003-09-23T23:42:30Z")
Standing on a beach, watching a ship get smaller and smaller, how far are my eyes seeing as the ship disappears from view? ---
**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:** [September 23, 2003, 11:45pm UTC](https://boards.straightdope.com/t/how-far-is-the-horizon/203424/2 "2003-09-23T23:45:27Z")
It depends on your [url-[http://www.boatsafe.com/tools/horizon.htm](http://www.boatsafe.com/tools/horizon.htm)]height above ground. About 2.8 miles for a 6-foot person standing on the ground. ---
**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:** [September 23, 2003, 11:46pm UTC](https://boards.straightdope.com/t/how-far-is-the-horizon/203424/3 "2003-09-23T23:46:34Z")
[Fixed link.](http://www.boatsafe.com/tools/horizon.htm) ---
**Author:** ![Boyo\_Jim](https://avatars.discourse-cdn.com/v4/letter/b/87869e/32.png) [@Boyo\_Jim](https://boards.straightdope.com/u/Boyo_Jim)\ **Post date:** [September 23, 2003, 11:51pm UTC](https://boards.straightdope.com/t/how-far-is-the-horizon/203424/4 "2003-09-23T23:51:39Z")
Also depends on boat’s mast height. ---
**Author:** ![ElJeffe](https://avatars.discourse-cdn.com/v4/letter/e/958977/32.png) [@ElJeffe](https://boards.straightdope.com/u/ElJeffe)\ **Post date:** [September 24, 2003, 12:00am UTC](https://boards.straightdope.com/t/how-far-is-the-horizon/203424/5 "2003-09-24T00:00:00Z")
For the mathematically inclined: Distance to horizon = sqrt(2hr), where h = your height, and r = the Earth’s radius. Distance to boat = sqrt(2hr) + sqrt(2Hr), where h and r are the same, and H = height of the mast. These are fairly close approximations, not exact figures. - Jeff ---
**Author:** ![MonkeyMensch](https://avatars.discourse-cdn.com/v4/letter/m/82dd89/32.png) [@MonkeyMensch](https://boards.straightdope.com/u/MonkeyMensch)\ **Post date:** [September 24, 2003, 12:23am UTC](https://boards.straightdope.com/t/how-far-is-the-horizon/203424/6 "2003-09-24T00:23:14Z")
It ain’t that hard. _Bowditch_ gives a nice easy formula: Distance to horizon in nautical miles = 1.1 x sqrt(h), where h is height in feet of observer. Or, distance to horizon in statute miles = 1.3 x sqrt(h). I tend to round these both off to "square root of height in feet is the distance to the horizon in miles. Tres simple… ---
**Author:** ![Achernar](https://avatars.discourse-cdn.com/v4/letter/a/e274bd/32.png) [@Achernar](https://boards.straightdope.com/u/Achernar)\ **Post date:** [September 24, 2003, 2:04am UTC](https://boards.straightdope.com/t/how-far-is-the-horizon/203424/7 "2003-09-24T02:04:28Z")
Furthermore, [the distance depends on the direction you look](http://www.straightdope.com/classics/a1_167b.html), to a very very small degree. ---
**Author:** ![Bob55](https://avatars.discourse-cdn.com/v4/letter/b/e9c0ed/32.png) [@Bob55](https://boards.straightdope.com/u/Bob55)\ **Post date:** [September 24, 2003, 4:57am UTC](https://boards.straightdope.com/t/how-far-is-the-horizon/203424/8 "2003-09-24T04:57:14Z")
> [@](#): > > \*Originally posted by ltfire \* > \*\*Standing on a beach, watching a ship get smaller and smaller, how far are my eyes seeing as the ship disappears from view? \*\* I disagree with the above calculations with regards to this specific question - when I used to go deep sea fishing we’d lose sight of the tops of buildings over 12 miles out (I think you could still barely see some at 20 miles). A ship that can be seen at the horizon sits pretty high on the water, and I think you can see it a lot further than 3 miles. My citeless answer (but verified by personal experience) is 12 miles. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [September 24, 2003, 5:36am UTC](https://boards.straightdope.com/t/how-far-is-the-horizon/203424/9 "2003-09-24T05:36:55Z")
I’m not sure how that disagrees, **Bob55**. Using the formulae posted by **ElJeffe** and **MonkeyMensch** (actually the same formula, in different units), a building about 150 feet high could be seen out to about 12 miles, and one about 400 feet high could be seen out to about 20 miles. If you’re looking at a big city, these seem like perfectly reasonable heights for buildings. ---
**Author:** ![Bob55](https://avatars.discourse-cdn.com/v4/letter/b/e9c0ed/32.png) [@Bob55](https://boards.straightdope.com/u/Bob55)\ **Post date:** [September 24, 2003, 5:37am UTC](https://boards.straightdope.com/t/how-far-is-the-horizon/203424/10 "2003-09-24T05:37:18Z")
More personal experience - I can easily see the “Pink Palace” hotel (Don Cesar) in St. Pete Beach, FL up the shore at North Redginton Beach, which is ~10 miles away.