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The total floor-to-floor vertical rise of the spiral stair.
Measure the total vertical distance the stair climbs, from the bottom finished floor to the top finished floor.
The radius from the center column to the stringer's centerline.
Measure from the central support column axis out to the centerline of the helical stringer, not to the outer tread edge or the inner edge.
The total angle the stair rotates through from bottom to top, in degrees.
360° is one full turn. A stair that turns one and a quarter times would be 450°; one that turns twice would be 720°.
Developed (unrolled) stringer length
16.1 ft
This is a pure geometry calculation (the developed/unrolled stringer length) — it does NOT analyze the stringer's structural adequacy under torsion, bending, or deflection, which is a complex structural mechanics problem requiring a qualified structural engineer's analysis of the specific stringer material, cross-section, and support conditions. Do not use this calculator to size or verify a spiral stair's structural stringer.
- Circumferential arc length
- 12.57 ft
They open the calculator with your figures already in it
Spiral Stair Helix Geometry Calculator: 16.06 ft — shown in imperial, US market. The link sets both, so the result they see is the one on your screen.
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How this was calculated
Formula source(s)
- Developed (unrolled) helix length = √(Total Rise² + (Helix Radius × Total Rotation in Radians)²) — the standard mathematical result for unrolling a helix into a straight line (the circumferential arc length and the vertical rise form the two legs of a right triangle when the helix is developed flat). This is a pure GEOMETRY calculation — it does NOT analyze the stringer's structural adequacy (bending, torsion, or deflection under load), which requires a full structural engineering analysis of the specific stringer's material and cross-section by a qualified engineer.
Inputs used
- Total Vertical Rise
- 10 ft
- Helix Radius (to Stringer Centerline)
- 2 ft
- Total Rotation Angle (°, 360° = One Full Turn)
- 360
Intermediate steps
- Circumferential arc length
- 12.57 ft
Confidence note: This is a pure geometry calculation (the developed/unrolled stringer length) — it does NOT analyze the stringer's structural adequacy under torsion, bending, or deflection, which is a complex structural mechanics problem requiring a qualified structural engineer's analysis of the specific stringer material, cross-section, and support conditions. Do not use this calculator to size or verify a spiral stair's structural stringer.
What this calculation does not cover
- One radius, one length. The outer stringer, the inner rail and the handrail each develop at their own radius, and the gap is not small — over one full turn on a 3 m rise, moving from a 0.6 m to a 0.9 m radius adds about 1.6 m of developed length. Cut a handrail from the stringer figure and it is short by more than any offcut pile will cover.
- The rise and the rotation together fix something this page never reports: the vertical gap from one turn to the turn above. Total rise divided by the number of turns is that gap, and what survives after the tread and its structure come off is the headroom. Take a 3 m (10 ft) rise in two turns and the clear distance is 1.5 m (5 ft) before deductions — geometry that unrolls perfectly and that nobody can climb upright.
- A developed length is a straight line; the flat blank for a helical plate stringer is not. Rolling a strip into a helix stretches the outer edge and compresses the inner one, so the pattern cut from plate is a curved segment of a ring whose two edges differ in length. This figure is the centreline of that strip and the setting for the rolls, not a shape to cut square.
Estimated cost — your price
This site holds no price list for this material — local prices vary too much to publish honestly. Enter your supplier's price and the result is costed with it.
Part of a bigger job
Or plan the space itself: measure it once, doors and windows included, and this figure comes back worked out on that space, with what goes with it.
Computed in your browser — nothing you enter is uploaded. Presented in US customary units and US trade terminology. Where a formula follows a published standard, that standard and its edition are cited beside it on this page; where none governs, the page says so. Local amendments override model codes — verify against the code in force where you build.
Sources checked 2026-09-06 · in the site-wide review of 2026-09-06 · v1.0.1
Regulatory standards & verification citations1
- Developed (unrolled) helix length = √(Total Rise² + (Helix Radius × Total Rotation in Radians)²) — the standard mathematical result for unrolling a helix into a straight line (the circumferential arc length and the vertical rise form the two legs of a right triangle when the helix is developed flat). This is a pure GEOMETRY calculation — it does NOT analyze the stringer's structural adequacy (bending, torsion, or deflection under load), which requires a full structural engineering analysis of the specific stringer's material and cross-section by a qualified engineer.
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