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Winder stair calculator

Pie-shaped winder treads done right: narrow-end depth, walking-line depth (measured from the narrow end), and per-tread code checks.

Winder stair calculator
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Plan — winder treads
Steps
Riser
Step angle
Narrow depth
Walk-line depth
Wide depth

Why winders fail inspection

Winder treads are pie-shaped: narrow at the inside of the turn, wide at the outside. Codes set a minimum depth at the narrow end and a minimum depth along the walking line, which is measured a fixed distance from the narrow side. Each winder tread is an arc, so its depth is the radius at that point multiplied by the angle the tread sweeps.

tread depth = radius × step angle (radians)
walk line measured the code-specified offset from the narrow end (varies by code)

A tight inner radius or too many treads in the turn shrinks the narrow end below the minimum — the most common winder failure. Adjust the inner radius, turn angle, or winder count until both checks pass.

Winder thresholds vary significantly by jurisdiction. Pending primary-source verification.