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[ArchimedesWojak]

what the fuck

[A_Curious_Cat]

what the fuck

See here (especially the picture).

[Alastar]

In DF, floors and walls are handled separately. An up/down stair is the combination of a (down) stair through the floor and and an (up) stair where a wall would be.

That's why you can (d)esignate a down stair on a mined-out tile but not an up stair: There's nothing to left to carve it in, you'll need to construct it.

A "normal" functional stair consists on an up stair with a down stair in the floor above. Afaik, a lone up stair doesn't do very much. A lone down stair without a matching up stair lets fluids through, there are situations where you may want that rather than bars/grates.

[ArchimedesWojak]

what the fuck

See here (especially the picture).

oh so like a spiral staircase okok

[A_Curious_Cat]

what the fuck

See here (especially the picture).

oh so like a spiral staircase okok

Not quite.  See Alastar’s post above.

[Schmaven]

If you think of them like escalators it makes the mechanics a little more clear.  You can only go up an up escalator, and only down a down escalator.  If you want to go both up and down from where you are, you need both the up escalator and the down escalator, or the compact 1 tile combo of both of them, the up/down stair. 

[PatrikLundell]

And note that an Up/Down stair is just the connections from the current tile upwards and downwards. To actually make it useful, it has to be connected to a stair with an Down component (i.e. either Down or Up/Down) on the tile above to be able to go up, and a stair with an Up component on the level below to actually be able to go down.

Without the Down component on the level above, trying to go up would have resulted in bumping your head against the ceiling, while trying to go down without an Up component on the level below would (in principle) result in a fall if the level below was open air, or just get blocked by rock trying to go down: you've got a hole prepared in the floor, but the level below is still not dug out.

My mental picture for DF stairs is one of the stairs in an apartment building where you need the both the platform on the level you start on as well as the platform on the level you want to to to for it to work. It's NOT like a ladder you place at a wall and then climb up over the edge (that's basically how ramps and step ladders work, though).

[Quietust]

That's why you can (d)esignate a down stair on a mined-out tile but not an up stair: There's nothing to left to carve it in, you'll need to construct it.

Furthermore, you can also (d)esignate a down stair on an existing up stair in order to turn it into an up/down stair.

[Pyrite]

I find it most helpful to think of them as ladders, actually. Especially because a dwarf falling at the top level can fall all the way down to the bottom.

This is why I typically use a spiral of ramps to go between levels.

[PatrikLundell]

I find it most helpful to think of them as ladders, actually. Especially because a dwarf falling at the top level can fall all the way down to the bottom.
:

You can think of them as (perfectly)vertical ladders mounted at the center of the tile. If there is no down stair at the level above you either bump into a ceiling, or end up in empty space with the distance to the surrounding tiles too large to reach. With the down stair component at the level above you've got a "platform" to step onto, and possibly a bit of ladder to ease the process a little.