2- or 3- story house cheaper, same sq ft?

For building a house, would it be cheaper to build two or three stories for the same square footage? Basically, if I plan to have the same rooms, just where they’re located is changed.

I’m building up in the sticks, in the Shenandoah mountains, so the land’s pretty rocky and steep. Also would have to clear most of the land myself, although that means I’d have local lumber available. It gets pretty frigid in the winter, so heating’s a major issue, but it almost never gets past ~85 in the summer. It snows fairly heavily, too.

What I’m basically wondering is if the cost savings as far as leveling the land out go would be worth the extra cost of building a firmer foundation and such. I’m also wondering what differences in engineering go into building a three versus a two story. I generally like high ceilings - 10ft+, so would that dramatically affect things?

Does this mean you’re planning to use wood you cut yourself to build the house? Or are you just saying that there’s local lumber mills in the area? Trying to use your own lumber to build a house is worlds of difference from using store-bought lumber. The answers to your questions will likely be different for those two cases.

Although it may not seem to make sense, generally the cost to build a house remains about the same on the basis of square footage of living space. Some exceptions depending on the construction technique would be loft space or below ground space such as a finished basement (which you may not be able to do based on the terrain). You have to bear in mind that aside from walls, floors, and roofs, there is a great deal of cost in the finishing, windows, doors, stairs, and utilities that remains the same based on square footage. OTOH higher ceilings don’t cost much. Your foundation costs would be reduced by building on piers instead of trying to create a slab or full perimeter foundation.

Like TriPolar says, building costs would be largely the same.

So look at occupancy/maintenance costs. Which is more complicated. It’s mostly heating, possibly some AC. Multiple stories have less exposed surface for the same square footage, so reduced heat loss, thus would likely be cheaper.