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Spiral Staircase Geometry Calculator — result sheet
Estimate step count, actual rise, angular tread width, and walking-line arc for a spiral staircase from entered geometry.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Steps = ceil(total rise/max rise); actual rise = total rise/steps; tread angle = turn/steps; walking-line radius = (inner diameter+outer diameter)/4; walking-line arc per step = radius×turn radians/steps.
This is an idealized circular-stair geometry estimate. It makes the chosen rise limit, diameters, and turn explicit and reports the resulting angular and walking-line dimensions without hiding a building-code assumption.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Total vertical rise — m; minimum 1.0E-6; maximum 1000000
- Inner diameter — m; minimum 1.0E-6; maximum 1000000
- Outer diameter — m; minimum 1.0E-6; maximum 1000000
- Total turn — degrees; minimum 1.0E-6; maximum 36000
- Maximum rise per step — m; minimum 1.0E-6; maximum 1000
Worked example
| Input | Value |
|---|---|
| Total vertical rise | 2.7 |
| Inner diameter | 0.6 |
| Outer diameter | 1.8 |
| Total turn | 360 |
| Maximum rise per step | 0.18 |
15 steps at 0.18 m rise; each tread turns 24°; walking-line arc per step ≈ 0.2513 m.
Assumptions and limits
- The stair follows a circular plan with concentric inner and outer diameters and a uniform turn per step.
- The maximum rise per step is a planning input and the result rounds the required step count upward.
- Headroom, clear walking width, handrails, landings, structural support, guard design, and local stair rules are not modeled.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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