A winder is a wedge-shaped stair tread that turns a corner without a landing. The model stair code asks for a minimum depth at the narrow end (6 in) and 10 in of depth 12 in out from the narrow side. The wall-framing takeoff already solved the smallest inner radius that meets those depths, but it measured depth along the arc: radius times angle.
Nobody builds an arc. The tread has a straight edge, and a tape held across a wedge reads 2 x radius x sin(angle / 2), which is always a little less than radius x angle.
The numbers. Three 30-degree treads need an inner radius of 11.5 in to reach 6 in at the narrow end by arc. By straight edge, 11.5 in gives 5.95 in. At a 13 in radius the arc says 6.81 in and the straight edge 6.73 in, so that one passes both ways.
What changed. layoutWinders now reports, for each tread, its four corners, its area (a shoelace sum, 558 sq in each at 13 in radius and a 36 in stair) and the rectangle of board it is cut from. It also reports the straight-edge depths and says when a stair passes by arc and fails by straight edge. The CLI prints all of it under --stairs.
Limits. This is geometry checked by hand-computed tests. The code edition is yours to confirm, and the tool does not frame under the treads. No real winder stair was built from it.