Floor height, available length, the number of risers, the going, the landings and the balustrades set the basic geometry. Alongside that we look at the sections, the bearing points and the connections.
On projects that require a structural check, the final solution has to follow the study of the qualified engineer.
The geometry is settled before the material. Floor height and available length decide how many steps fit and how high each one is; the rule of thumb for comfort wants twice the riser plus the tread to come to around 60–65 cm, with the limits set by the building regulations for the use in question. After that what counts is free head height at every point of the climb, landings where the stair changes direction, the height and infill spacing of the balustrade — particularly where children move about — and the noise. Where structural verification is required, an engineer signs the design.