How far from the shore can you see until the horizon?

Answer

According to Maryln Van DeSavant I seem to recall she said 7 miles.

Answer

From basic geometry, you get that the distance to the horizon is D=sqrt(2Rh)

where D = distance to horizon R = radius of earth h = height of observer, which would be the height of your eyes.

R and h have to be in consistent units, of course. In feet the radius of the earth is about 4000 mi * 5000 ft/mi or 20 million feet. Standing on the shore, your eyes are maybe 5 feet above the surface, so D=sqrt(2*20e6*5)= 14000 feet, or a little under three miles.

There are some other effects that make that number a little different. Refraction bends your line of sight, so you can see a little bit farther. If you're looking at an object on the water, like a ship, you also get the distance on the other side of the horizion that corresponds to the height of the target.

How to calculate the distance yourself

To get an "approximate" distance to the oceanic horizon from a particular observation point, take the square root of the height of the observation point, add 22.5%, and that will give you the distance in statute miles. For example, if your eyes were 6 feet off the ground, and you stood atop a 50' tower, your observation point would be 56'. The square root of 56' is 7.48. Add 22.5% of 7.48 (1.68) to 7.48 and you have 9.16 statute miles from your eyes to the horizon.

First answer by ID2560844939. Last edit by Joepoidog. Contributor trust: 726 [recommend contributor]. Question popularity: 26 [recommend question]