They don’t build the second floor perpendicular to the first floor walls, they independently make sure each floor is level and each wall is plumb.

To add onto this: there are tools that project perfectly vertical or horizontal lines with lasers, which you can then use to build your wall/floor/...

A shocking amount of construction is not level, square, or plumb. Close enough to where it can be unnoticed is the threshold typically used.

But there’s always a lot of levels, squares, plumb lines, and measurements happening. Also, lots of math.

Architect/developer here:

A building is usually not very precise compared to manufacturing tolerances. Look at your counters and where they meet walls. The whole notion of trim and caulking is to hide these imperfections. Even with skyscrapers, you have to account for minor settling and expansion of materials.

Secondly, in terms of construction technique, you either have a plumb or a laser level to make sure you're building plumb and straight. In today's construction, you'll essentially pour your slab and the framers will draw in all the walls on the floors with a tolerance of about a 1/2". They then build straight, and level walls; even if the floor is wonky.

When the building is framed, other trades come in and work with whats on site as it is built. So, for example, you'd come in with window shop drawings afterwards and measure the openings. Then you'd shim and fit in your windows to roughly the opening, and the waterproofing/cladding will work with what is there, and cut things on-site to make sure it more-or-less fits, rather than whats on the plans.

That's why ever subcontractor hates each other. The guy before you installing things can really mess up your contract.

TL:DR; its accurate enough to be hidden with trim/joints/finishes, but also lasers.

And if nothing is square....blame the drywall-ers!

Nothing a little mud can't fix.

8 coats of mud later.

People that make buildings do not work to a high level of precision. A room can be out of square by an inch and you probably wouldn't notice until you tried to put in flooring that comes in accurately cut rectangular sheets. The last pieces you add get cut to fit, not cut to whatever the dimension is supposed to be.

You can use a tape measure to measure opposite corners and compare to the other pair of corners to check squareness. You use a level to check level.

I briefly worked at a place that made things like pre-built ceiling trusses. The tolerance for each board we cut to be assembled into the truss was 1/4inch. So if each board was 1/4in short, you'd be looking at a 1/2in gap at that particular joint.

So yeah, It's not necessarily going to be square when you have tolerances like that.

Not to be contradictory here but there are building systems that need precision.

I'm currently managing a site with a complex structural steel frame and the anchor bolts/ embed plates have to he bang on as cast into concrete. Tolerances within our spec are 1/8" in any direction.

This is generally accomplished through professional surveying. In theory, competent execution will give good results. I am frustrated to report that surveyor on this job made a mess out their work, it is demonstrably incorrect, and as a result expensive change orders have had to go to our steel fabricator to adjust connections at base.

TLDR, accuracy is possible; but it my opinion that when all is said and done, construction boils down to cavemen banging sticks and rocks together and you get what you pay for.

[deleted]

[removed]

I've learned, in my almost 20 years of construction experience across multiple trades, that plumb and square are often just relative terms. Are these window frames plumb? I have no idea. They measure the same offset all the way around from the brick face, or the framing, or whatever place the architect wants. If I make them plumb instead, it only makes me look bad. Nobody sees that the framer, or bricklayer, or whoever is the one that's off. They see the crooked window. So you have to live in whatever world the framer gives you plumb or not. With floor tile or ceiling grid, if you go to the main entrance to whatever room you are in, meaning the most common place people will first see that room, and you make either a joint or a full tile be right down the center everybody will love it. It's what your eye wants to see. A nice straight line. It doesn't matter at all if it's in the middle of the room or not.

So much this. There is not a single right angle anywhere in my house, except where the contractors added a new wall to separate a room into two distinct rooms. ...and it looks wrong because it doesn't match the rest of the angles.