How far is the horizon?

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potski205 | 10:39 Thu 19th Jan 2006 | Science
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How far away is the horizon (as in the furthest line you can see) if you were standing on the sea shore (e.g. at sea level)? I have heard various answers ranging from 3 mile to 12 miles to 30 miles. Is there an equation to work this out? Does it matter how tall you are? Does it matter if it is high or low tide?


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<PRE>The equation is: 1.17 times the square root of your height of eye = Distance to the horizon in nautical miles </PRE>

If you're standing at the water's edge, the horizon is about 3 miles away. If you click here that will link you to a web-page which has a handy computer version that helps you work it out. All you do is put the height of your eye relative to the water's edge into the slot and click on 'Compute'. So, if you're eyes are 5 ft 6 inches above the ground - ie 5.5 ft - put that into the slot. If you are standing on a 100 ft cliff, put 105.5 in.

Or, using matt_london�s formula, 1.23 times square root of the height of your eye above sea level to give the answer in statute (ordinary) miles.

This can be determined in a number of ways but perhaps the easiest is by using Pythagoras theorem of right-angled triangles. Using this, the distance to the horizon is:

SQRT (h+2rh)

Where h is the eye height above sea level and r is the radius of the earth (roundly, 4,000 miles).

Using feet throughout (for a six foot eye height) the calculation becomes:

SQRT (6+(2*21120000*6) = 15920 feet.

Divide this by 5,280 (feet in a mile) and you get 3.01 miles

matt_london�s formula is a boiled down version of this one.

A couple of things to beware of:

The principle assumes that the earth is a perfect sphere (which it is not). The calculation is the distance in a straight line from the observer's eye to the horizon and not the distance via the (curved) surface (which would be longer). Although in practice for a sphere the size of the earth this makes no measureable difference.

Roughly 12 miles at sea level

Sorry, xrayspecs, but your answer is wrong. (Perhaps your specs are enabling you to see further than us mere mortals!).

Using the formula I suggested and that provided by mattlondon (which gave the answer in nautical miles) the answer coincides quite nicely with that provided by quizmonster (and backed up by the info contained in the link kindly provided). That is, about 3 miles for a six-foot eye-level.

You have to be almost 100 feet above sea-level before you can see 12 miles.

its amazing how you can see the curvature of the earth from sea level considering its 28,000 miles circumference.makes you wonder why early peeps thought they would fall off the aint so big after all

Standing on the prom at Backpool on a nice day (possibly 25ft over sea level) you can see the Isle of Man to the north west and Angelsea to the south west. The bits you see are obviously above sea level but are a lot more than 3 miles away. You can see these places because (a) your eye level is higher than sea level, and (b) the stuff you see is also above sea level, but not far enough away to be totally obscured by the curved sea in between.

If you were at sea level and saw a ship coming towards you, as it approached your horizon you would see the mast and funnels first, then the superstrucure, followed by the bow-wave when it got to about three miles from you. If you were in the crow's nest on lookout duty you would see the ship at a much greater distance than your sea level colleagues on deck, so be able to give early warning of the approaching vessel (or iceberg or landfall &ct.)

titanicle,why do people use so many words lol ps have you seen the rust on the tower?its gonna go any day now lmao
titanical who cares lol
Approximately 8 miles. Old sailor measure
standing on the prom at blackpool, you can clearly see buildings at Barrow in furness and walney island which is approximately15 miles away

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