Medium creatures take up a 5 by 5 space and Large is 10 by 10, but what about vertical space?  I am asking for the sake of underwater and aerial combat where creatures could be either above or below another.   A cube was my first thought, but that does not make much since as a 6' tall human would be outside it's own space.  I know that going with a standard reach for each size category is the best way to go, but going with the standard base size breaks down really quickly as a giant would not be able to attack anything above it's own waist. 

If a character is flying and fighting a giant at what point does the character leave the giant's threat range when traveling upwards?  I am most likely thinking to much about this, but thought I would see what people thought about it.  

I think you're overthinking it! My understanding is that a creature can strike anything within that distance of their person. So, if a human is standing within 10 feet (the range of a giant's melee attack in the Monster's Manual) of any part of the giant, at any height, that person is able to be hit.Keep in mind, the giant is moving to attack his target, not swinging from a static position. He is likely stooping to swing or reaching up to strike at airborne creatures within his 10 foot melee range. 

So to answer your question, as soon as the player flies more than 10 feet above that giant, he shouldn't be able to reach them (unless he has a ranged weapon).

Hopefully that clears things up a little bit.

Oh, one more thing. The giant is free to jump on his turn whilst attacking. I'm not sure of the exact range, but he can jump to attack players flying slightly higher than his 10 foot range.

I thinking mostly for things like triggering attacks of opportunities and stuff.  But yeah, probably over thinking it.  

Oh! Yes he still gets his attack of opportunity to my knowledge. What sort of other stuff did you have in mind?

This whole thing was a about aerial and underwater combat where not everyone in the combat is at the same elevation but potentially in or out of reach. Being in area of effects was the other that comes to mind.  Honestly, I will most like just wing it.

I always consider reach as the area threatened by a creature outside of its own self.

That means that those 5feet for a medium creature are considered from any point of said creature 's body. Same goes for any other size, so the 10 feet of a giant would start from the top of his head, for example.

Is somewhat unrealistic, but it's the easiest way to crawl with these situations, imho.

When land bound you can think of creatures taking up a square, and up to their height vertically. When floating, flying or hovering it is probably best to assume everyone and everything fills a cube of their size (5x5x5, 10x10x10, and so on). People tend not to be stretched out at full extension when floating underwater, there is more contorting of the body, twisting and such. Seems a sensible simplification.

Quote from LeK >>

I always consider reach as the area threatened by a creature outside of its own self.

That means that those 5feet for a medium creature are considered from any point of said creature 's body. Same goes for any other size, so the 10 feet of a giant would start from the top of his head, for example.

Is somewhat unrealistic, but it's the easiest way to crawl with these situations, imho.

Thanks to everyone for the replies.