When you look out on the ocean, how far can you actually see until something goes over the horizon ?

Pearlsaw has the right formula, but completely wrong numbers, because he has confused kilometers with meters.

How to figure this out:

- Draw a tangent from a point a distance h above the surface of the ocean (so radius = R + h) to the circle of radius R. The distance from the point at radius = R + h to the point at radius R is d, so by Pythagoras' theorem:

(R + h)^2 = R^2 + d^2

R^2 + 2Rh + h^2 = R^2 + d^2

d = sqrt(2Rh + h^2) ~ sqrt(2Rh)

where R = about 6350 km = 6.35e7 (m)

So d = sqrt(2*6.35e7*h)

= sqrt(1.27*e8*h)

= e4 * sqrt(1.27*h) (m)

If h = 1.5 (m),

d = e4 * sqrt(1.27*1.5) = 1.38e4 (m) = 13.8 (km)

(not 437 (m), as Pearlsaw calculated).

In general, if the height of the observation point is

height = h, the distance is:

d = e4*sqrt(1.27) * sqrt(h)

= 1.127*e4 *sqrt(h/(m))

= 11.27 (km) * sqrt(h/(m))

It depends on how high you are above the waterline and what the visibility is. As a general rule, if visibility is good and you are at the waterline, you can see the mast of a ship come over the horizon at 12 miles and the whole ship at about 9 miles. If your vantage point is higher you can see farther.

Distance to the horizon = SQR(12740*height)

height in km (12470 is the diameter of the earth)

The distance is found using this formula

S = √ [2a h] where a is the radius of earth h is the height from sea level.

Near a beach supposing that one's eye level is a at a height of

1.5 m the distance that he can see is

√ [2*6378* 1.5] = 138.325 m

If h = 15 m

Distance is 437.42m

11 miles out. that's why international waters begin at 11 miles

you can see as far as your vision permits you. Depends on the tides. On calmer days range would be greater

Like you can see the stars at night which are millions of kilometers away from us.

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