Half-turn switchback stairs: solve the flight split, half-landing, and the stairwell footprint including the well gap.
A U-shape stair doubles back 180 degrees around a half-landing. Both flights run parallel, so the stairwell width is two stair widths plus the well gap between them. This is the most compact footprint for a given rise, which is why switchbacks are common in tight stairwells.
A U-shaped (half-turn) stair doubles back 180 degrees around a central landing, stacking two parallel flights side by side. It is the most compact way to climb a full storey, which is why it is common in stairwells and multi-storey homes where floor area is tight. The calculator splits your total rise into uniform risers across both flights and sizes the landing that joins them.
The landing is the key dimension: it must be at least as deep, in the direction of travel, as the stair is wide, and never less than 36 inches under the IRC. Because a U-shape turns at the landing rather than with pie-shaped winder treads, it is easier to build and more forgiving to climb than a winder of the same turn — the trade-off is the floor area the landing consumes.