Visiting the Outer Banks this week I was standing on the beach wandering just how far away the farthest point of water was that I could see on the horizon. It’s hard to tell – is there a standard answer for this?
Roughly 3 miles if you are of average height and stand at the waters edge.
Cite: How Stuff Works
from wikipedia:
The distance of the horizon on earth, in a plain (standing on the ground or on a tower, or from a plane) or on a hill or mountain surrounded by plains, is approximately kilometers, where h is the height in meters of the eyes.
Examples:
standing on the ground with h = 1.70 m, the horizon is at a distance of 4.7 km
standing on a hill or tower of 100 m height, the horizon is at a distance of 36 km
These figures indicate theoretical visibility (what can be seen depends also on how clear the air is, of course) of objects at ground level. To compute to what distance the tip of a tower, the mast of a ship or a hill is above the horizon, add the horizon distance for that height. For example, standing on the ground with h = 1.70 m, one can see, weather permitting, the tip of a tower of 100 m height at a distance of 41 km.
You might be missing a formula there Soylent Gene 
Hope that helps someone.
Since your question has been answered I don’t mind commiting a hi-jack…
I just got back from the Outter Banks. We stayed at milepost 9, in a condo next to the Ramada Inn in Kitty Hawk.
Where did you stay? We are always looking for new places to stay. Personally I would like to stay further south, inHatteras or one of the towns in between.
From Nasa - Distance To The Horizon
We rented this house farther north in Duck. There’s pleny around just like it if you have a large group like we did.
I notice that the NASA site neglects atmospheric refraction. For general radar work, to estimate the radar horizon it is common to multiply the geometric radius of the earth by 4/3 to account for refraction.
If your eyes are 5 ft. off the ground the geometric distance is 2.74 mi. while that with refraction included is 3.16 mi. For 10000 the comparable figures are 122 mi. vs. 141 mi.
We had 3 families with a total of 8 kids, and we stayed in a similar house last year. It was across the beach road from the beach though. I guess we could add one more family and get your place next time!
…But, did you account for the fact that earth is not a perfect sphere?
That’s an exercise for extra credit.
Out of curiosity, how or when does this formula begin to reach its limits? I mean, if you are tall enough, eventually you will be able to see about 6,000 miles or so, but never any farther, as that would require you to see around to the back of the earth.
Don’t forget the ocean waves. You need to subtract half their height from the observation height. That gets tricky since they change depending on the distance from the shore.
You could see 1/4 of the way around only if the light rays coming from the disc are parallel, i.e. at infinite distance. At any less distance the light converges to the eye and you can’t see quiiiiiite 1/4 of the way around. Possibly refraction would allow you to see that far at some finite distance. One picture is worth 1000 words.
Oh, and by the way, from a satellite 3411 miles above the surface of the earth the horizon would be 6215 miles (equal to 1/4 the circumferance of the earth) away.