Inputs
Results
Computed step count
—
N = ⌈ H / rtarget ⌉
Actual riser height
—
r = H / N
Angle per step
—
α = rotation / N
Walking line radius
—
Rw = Rinner + p × (Router − Rinner)
Tread arc at walking line
—
tw = Rw × α (radians)
Total walking line length
—
N × tw
Outer/Inner arc per step
—
souter=Routerα, sinner=Rinnerα
Total carpeted sector area
—
A = ½ × rotation(rad) × (Router2 − Rinner2)
Compliance check
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| Metric | Value | Units |
|---|
Formula used
- Step count: N = ⌈ H / rtarget ⌉
- Actual riser: r = H / N
- Angle per step: α = rotation / N (degrees); αrad = α × π / 180
- Walking line radius: Rw = Rinner + p × (Router − Rinner) where p ≈ 2/3
- Tread arc at walking line: tw = Rw × αrad
- Edge arcs: souter = Router × αrad, sinner = Rinner × αrad
- Sector area for one step: Astep = ½ × αrad × (Router2 − Rinner2)
- Total area for all steps: A = ½ × rotationrad × (Router2 − Rinner2)
Adjust inputs to match local code. Many codes measure tread depth along a walking line at a fixed offset; this model parameterizes that offset via p.
How to use this calculator
- Select your unit system and enter floor-to-floor height H.
- Choose a target riser height; the tool rounds step count N and recomputes actual r.
- Enter total rotation in degrees (e.g., 360° for one full turn).
- Enter inner and outer radii to the finished nosings.
- Use walking line factor p (default 0.6667) or set a custom value.
- Provide minimum tread depth and acceptable riser range for compliance feedback.
- Press Calculate. Export the results as CSV or PDF for project records.
Example data
Illustrative scenarios for quick reference.
| H | Rotation | Rinner | Router | N | r | α | tw |
|---|
FAQs
A common convention is p ≈ 2/3 of the clear width from the inner edge. You can change p to match your jurisdiction or design standard.
Use 360° for a complete turn. Landings or entry/exit positions often require 270°, 360°, 450°, etc. Coordinate with floor plans and headroom constraints.
No. It provides adjustable checks for tread depth and riser limits. Always verify local code requirements and manufacturer specifications before construction or ordering materials.
Measure to the finished nosing line: inner radius near the center column and outer radius at the outside edge. Avoid including baluster offsets unless carpeting crosses under them.
Yes. The total sector area uses rotation in radians and the annulus radii. Add waste based on your fabrication process and seaming strategy.
That configuration is invalid. Ensure Router > Rinner. The calculator highlights this and blocks computation until corrected.
They closely approximate the centerline of traffic. Add allowances for nosing wraps, seams, and pattern matching where applicable.