How this calculator works
The total rise is split into the smallest whole number of uniform risers not exceeding your target. Rotation is split across those riser intervals, with the upper floor treated as the landing and one fewer separate tread. Inner and outer edges follow helices. A full overlapping revolution has vertical separation equal to rise times 2pi divided by total rotation; subtracting tread thickness gives an idealised clearance. The floor opening, landings and actual overhead structure still need separate checks.
Formula
Risers = ceil(total rise / maximum riser); actual riser = rise / risers; interval angle = rotation / risers; walking depth = walking radius x interval angle; arc = radius x rotation; helix length = sqrt(arc^2 + rise^2). Angles in these formulas are radians.
Worked example
A 3 m rise over one full revolution with a 200 mm maximum riser gives 15 risers at 200 mm and 24 degrees per interval. An outside diameter of 2 m and inside diameter of 0.2 m leave 0.9 m radial tread width.
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Frequently asked questions
Does the result establish stair compliance?
No. Walking-line location, usable width, headroom, tread shape, landings, guards and permitted use must be checked under the applicable design requirements.
Why are there fewer treads than risers?
This convention treats the upper floor as the final landing surface. If the stair product includes a separate top platform, account for its geometry separately.
Is tread depth an arc or a straight chord?
The reported depth is an arc at the entered walking line. A manufactured tread and the applicable measurement convention may require a different check.