how far can a character see?

[Cakeking]

are there rules covering how far a character on flat terrain, in the middle of the day can see?

[MC Templar]

the rules for it will get ridiculous quickly if applied as RAW (+1/10ft) to perception.

If you are trying to locate things that are actively trying to hide, use the rules, if you are trying to determine if the PCs notice something important at a distance, apply an arbitrary DC to it.

if you are asking how far the human eye can see...

spoiler:

in good light, with nothing to block vision, presuming the same size planet as earth, eyes that are 5.5 ft off the ground will lose line of sight because of curvature of the ground apprx 2.87 miles away.

realistically, there is ALWAYS something in the way on land, and light scattering off clouds and vapor in the air makes any detail over a mile get lost in a haze.

for GMs, handwave this into "how hard do I think this should be" and "how high a DC makes it hard but not impossible"?

the math
Distance Formula
s = sqrt(2rh+h^2)

s = line of sight distance
r = radius of sphere (Earth = ~3959mi)
h = height viewed from (altitude)(ft)

[Cakeking]

sounds good, thanks

[Neo2151]

There are rules, but you should ignore them. Otherwise, you won't be able to see the mountains on the horizon. xD

[MC Templar]

and a person, standing in the open (DC=0) on the other end of a football field (100 yds, 300 ft) is a DC 30 perception check, so functionally invisible to anyone with less than an +10 perception.

:-(

[Vorkar]

Actually, MC Templar's math formula has an error in units. "s" will be in miles and "h" also has to be in miles for the formula to work. It is a common mistake not to keep units consistent in formulae.

Also, it is fairly common to ignore the term "h squared" as it is quite small compared to "2rh".

[MC Templar]

all units converted to feet (radius=20,903,520 ft)

not hard to find on google

[Lincoln Hills]

Look for 'plains terrain' in the CRB index. The terrian descriptions in the wilderness-travel section lists a 'starting range' for encounters on plains. That range is not super-long, but then, even grasslands aren't assumed to be as flat as a pool table. And it does provide a somewhat more plausible distance than that which range imposes on Perception.

[Bizbag]

All these answers, and nobody says "Oh gods! They can see forever!"?

Shame on you!

But yes, the answers above are all good. Lincoln mentioned the best place to find RAW, such as it is, for it.

[Isil-zha]

The rules for maximum encounter distance by terrain are a good way to determine at what distance you can make out a non-hiding creature. Landmarks may be visible even if much further away, depending on size.