Designing and building spiral stairs will require a
little more than basic math skills. It will require geometry,
trigonometry, understanding circles, radius, diameters and complicated
math formulas. I have a stair book at home of nothing but math formulas
used to build the stairs.
Designing circular stairs that will be freestanding with nothing underneath them to hold them up will require more math skills and advanced construction skills. Circular stairs are among the hardest parts of house framing. Building a handrail for a set of spiral stairs will be one of the most difficult tasks performed by a finish carpenter.
Spiral stair designing will require more space used in the home due to its massive size. There are different types of spiral stairs, you can have a circular set of stairs for the first two steps to six steps and then the rest of the stairs would be Straight.
This gives the effect of something fancy or rich looking at the bottom eye level. And then the rest of the way Straight which of course is easier to build and cost effective but gives you the elegant look of spiral stairs.