How far away can the aided eye see in a level line to the horizon?

I heard 25 miles.

2.9 mi says google

Here is a first order approximation.

Distance to horizon (in miles) = 1.23 x Square root of the height in feet.

Example: If someone is on a tower 100 ft above the water they can see 1.23 x sqrt(100) = 12.3 miles.
If they are on the shore 5 ft above the water they can see 1.23×2.23 =2.7 miles

So if they are 5 ft tall and walking away you need to double it = 5.4 miles for them to be completely below the horizon.

If you are both six feet tall the other person would have to walk about three miles to reach the horizon and another three miles until the top of his head disappeared from view making about six miles in all.

If the gravity is strong enough to bend the light to the right degree, you can see the back of your head.

From sufficiently high up, you can see half of a sphere. We can’t see the dark side of the moon.

Is it cloudy? Much shorter then.

I think you need to refine the question. If you’re at a beach and all you have is flat water, then further.

If you’re at a flat desert, also longer.

If you’re in hilly country or next to a mountain, shorter.

If you are a Super Saiyan, you can fire a beam attack to bore a hole through the sphere, enabling you to see through to the other side.

@LuckyGuy “So if they are 5 ft tall and walking away you need to double it = 5.4 miles for them to be completely below the horizon.”
– No, because sight distance is not a direct factor of height. At 10 feet ASL, I think you end up with about 3.9 miles.

However, the way @Ltryptophan worded the question “How far will [another person walking away from you] get before they are out of sight?”, the answer would be your sight distance PLUS their sight distance before you’d lose sight of their eyes behind the horizon. Your sight distance would give you the distance before their feet started to disappear below the horizon.

@ragingloli “If the gravity is strong enough to bend the light to the right degree, you can see the back of your head.”
– Except not, because that amount of gravity means you’re inside the event horizon of a black hole, and you and your eyes and head have no doubt long ago been destroyed many times over by all sorts of phenomena, you have nothing to see with, nothing to stand on, and you’re falling at ridiculous speed.

“If you are a Super Saiyan, you can fire a beam attack to bore a hole through the sphere, enabling you to see through to the other side.”
– But you’re not Super Saiyan. No one in this universe is. And even if something theoretically had the energy to “bore a hole through” a planet, the results would not be a handy viewing tube. It would be more like a cataclysmic explosion, destruction of the would-be observer, and immediate collapse of whatever hole was created, and other almost incalculable levels of destruction.

If anyone is curious as to where the 1.23 comes from in @LuckyGuy ‘s formula and you are willing to look at a few equations, here is a good derivation. Using equation 5 and converting feet to miles and using 4000 miles for the radius of the Earth gives sqrt(2hr) = sqrt(h/5280*2*4000) = sqrt(h)*sqrt(8000/5280) = 1.23 sqrt(h).

@LostInParadise Yes That is the equation. And remember the result by saying to myself, “It’s as easy as 1, 2, 3”
I’ve used it a lot.
When will the radar unit pick up a plane at 10,000 ft? 1.23 x sqrt(10,000) = 12.3 miles.
When will I first see the top of the 400 ft tall building if I am on a raft? 1.23 x sqrt(400) = 24.6 miles.
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