How far is the horizon?

High school trigonometry helps figure out how far you can see in flat country or at the seashore.

If you're 6' tall (1.83m) and standing on the beach 4' (1.22m) above the water, you can see about 6.2 km or 3.4 miles.

If you're 6' tall and standing with your feet at the edge of the shore or flat on the desert, it's about 5 km or 3.1 miles.

The derived formula is indicated on this web page and includes all of the math behind the simple formula below:
Goddard Space Flight Center
"Distance to the Horizon" (Stern, April 1, 2014)

The formula is:
D = 112.88 km * h^1/2


D = 112.88 km * SQRT h

D = distance to the horizon in kilometers
(112.88 is actually the square root of the earth's diameter in km)
h = your height in kilometers

Since 10' is about 3 meters or .003 km, D = 6.18 km.


Here's an alternate formula and way to calculate it on the "How Stuff Works" page. The diagram is excellent, but since it mixes feet and miles; meters and kilometers, it's a little more confusing:
How Stuff Works
" When I stand at the water's edge and look out over the ocean, how far away is the horizon?"


Now some caveats:
* Note that you see a ship that's further offshore because it's taller, rising above the horizon -- a fact known to seafarers even in Columbus' time (debunking the stories that Columbus' men believed in a "flat earth"). However, you'll lose the Plimsoll line first, then possibly the name of the ship company along the hull next -- but still see the superstructure.

* Atmospheric conditions can refract light over the horizon. Temperature inversions will have that effect. It's also known in a phenomenon called "looming". Author Nathan Philbrick references it in his book "Sea of Glory," written about the Wilkes Expedition of 1838-1842.

I've seen it on Lake Michigan and it's apparently quite common in Antarctica, as Philbrick says maps created by the Wilkes Expedition made large errors in judging distance when it made the first maps of the Antarctic coast due to looming. Here's an explanation of looming:
"Distance to the Horizon" (Young, 2020)

Andrew Young in that same article explains the "silhouetting" after sunset will also cause the backlighting of an island, mountain or city after sunset because the area behind the distant object is brighter than the air between you and the island or mountain.

As an example, for those near Benton Harbor, MI looking west across Lake Michigan doesn't reveal Chicago -- until the moments after sunset when the city's skyscrapers are backlit.



Last updated: 1/1/2021

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A collection of material written by Andy Czernek, of Mukilteo, WA.

Other websites maintained the author include:
* Mooney Events, a calendar and other resources for owners of Mooney Aircraft

* Fry Family of Ashland County, Ohio, a family genealogy site

* Sinking of the SS Golden Gate, the story of the fire and sinking of the steamship off Manzanilla, Mexico in 1862


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