How far can you see at sea level?

Answer 1

height of your eyes above the ground: h

radius of the Earth: r [= 6371000 m.]

distance of furthest visible point on Earth's surface: d

Your eyes, the furthest point that you can see, and the centre of the Earth together form a right angled triangle. (This is because your most extreme line of view by definition is tangential to the Earth's surface.) This enables us to judge the actual distance of the furthest visible point.

d2 = (r + h)2 - r2

Simplifying:

d2 = h(2r + h)

So

d = sqrt[h(2r + h)]

and since r = 6371 kilometres:

d = sqrt[h(12742000 + h)]

For a typical eye height of 1.6m. this evaluates at just over 4515m. The formula gives the distance, in a straight line through the air, from your eyes to the ground: for small values of h this is little different from making a measurement along the ground.

There is a far simpler equation to arrive at a solution in miles, this it the square root of 1.5 times the height of a human above sea level (in feet), using the sum above:

1.6 meters (is 5'3") * 1.5 = 7'9",

the square root of which is 2.810

so using, sqrt of 1.5 times the height, we get 2.810 miles

4.515Km (as previuos equation above) = 2.805miles. Which is close enough for me without knowing the radius of the earth!

so try it yourself, take your height in feet and inches, times it by 1.5 and then square root that and that's how far you can see out to sea!! I'm short @ 5'1" so i can only see out 2.76 miles!!

## This is almost correct. However, we pinged where we kitesurf to a known point using Google Earth and the distance was 3 miles, however we can see something which is at 27 miles!

So the theory is totally correct but it needs to be x 10.

2.7 miles is actually 27 miles at sea level. Remember the higher you go the further you see. Stand on the wall and you see much further. :o)