Gene asked in Science & MathematicsGeography · 3 months ago

# If when standing 20 feet above the water on a ship in the ocean, how far away is the horizon? I've been told about 7 miles?

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• Bill-M
Lv 7
3 months ago

Height of Eye above the Water is 20 Feet then the Horizon is 5.9 Miles.

There is a Formula:  distance = 1.317 times Square Root of H

Square root of 20 = 4.4721  Times 1.317 = 5.8898 Statue Miles.

if you want Nautical Miles then use 1.144.

This formula comes from U.S. Navy H.O. Publication number 9.

American Practical Navigator.

• derfram
Lv 7
3 months agoReport

I've seen the different constants listed different places.  Anywhere from 1.22 to 1.35.

• 3 months ago

Distance to horizon = 1.22 * √(eye height)

Where Distance in in statute miles

Eye height is in feet.

Assuming the 20 feet is eye height, then:

Distance to horizon = 1.22 * √20 = 5.46 miles.

• derfram
Lv 7
3 months agoReport

Depends on where you look.  I found 1.17√h = nautical miles and converting that to statue yields 1.35√h.  I believe I found the 1.22 in Wiki.

• 3 months ago

Depend on how high your eyes are above the water

. 3.1 miles for some one whose eye height 5 feet 7/9r 8 inches. 7 miles sounds correct for 20 feet..

• Bill-M
Lv 7
3 months agoReport

There is a Formula:  distance = 1.317 times Square Root of H

Square root of 20 = 4.4721  Times 1.317 = 5.8898 Statue Miles.

if you want Nautical Miles then use 1.144.