Inputs
Tip: Use the example to see a typical quarter turn with 3 winders. Adjust radii and offset to match your staircase.
Results
Enter inputs and click Calculate to see per-step geometry, cut sizes, and totals.
Example Data
Typical presets for quick testing. Use the Load Example button to fill the form with the first row.
| Turn (deg) | Steps | Inner R (mm) | Outer R (mm) | Walkline offset (mm) | Nosing wrap (mm) | Seam allow (mm) | Roll width | Notes |
|---|---|---|---|---|---|---|---|---|
| 90 | 3 | 100 | 1000 | 300 | 30 | 10 | 12 ft | Quarter turn with three winders |
| 180 | 6 | 120 | 1100 | 300 | 30 | 10 | 15 ft | Half turn with six winders |
| 90 | 2 | 80 | 900 | 250 | 25 | 8 | 12 ft | Quarter turn with two large pie steps |
Formula used
Let θ = (Total turn angle) / (Number of winders) in radians; ri = inner radius, ro = outer radius, rw = ri + walkline offset.
- Arc lengths:
s = r · θat each radius. Sosi = riθ,sw = rwθ,so = roθ. - Chord lengths:
c = 2r·sin(θ/2)⇒ci, cw, co. - Radial depth (cut height):
h = (ro − ri) + nosing wrap. - Piece width for cutting:
w = co + 2×seam allowance. - Area (sector ring):
Asector = ½·θ·(ro2 − ri2). - Bounding rectangle:
Arect = w·h(useful for cut sheet planning). - Roll length approximation: with roll width
W⇒drops = ceil(w/W),L = drops·h.
These are geometric approximations for planning. Field conditions, pattern matching, and installer preferences can change final requirements.
How to use this calculator
- Select your unit system and the roll width you stock.
- Enter the total turn (e.g., 90° for a quarter landing) and the number of winder steps.
- Measure inner and outer radii to the nosing line.
- Set the walkline offset (commonly 300 mm / 12 in from the inner stringer).
- Add allowances for nosing wrap and side seams as needed.
- Click Calculate to see per-step arc and chord values, cut sizes, and totals.
- Use Download CSV or Download PDF to save and share results.
FAQs
The walkline is a reference path offset from the inner stringer representing where people typically step. Standards often use 300 mm / 12 in for consistent tread depth comparisons.
Sheet goods are cut straight. The straight span between riser edges is the chord, not the curved arc. Using chords better approximates the piece width for cutting plans.
It is a planning approximation that assumes chords run across the roll. Real layouts may rotate pieces, add margins for pattern matching, or optimize nesting for waste reduction.
Yes. Add repeat length to the piece height or increase seam/nosing allowances as appropriate. Pattern alignment often increases roll usage beyond geometric minimums.
This tool assumes equal division of the turn. If your winders vary, treat each with its own angle and radius measurements and compute them separately.
It adds to the radial depth (piece height) because the carpet wraps over the nosing. Side seam allowance adds to the piece width.
Choose the roll width you stock or can source. Wider rolls reduce the number of drops when the chord width is large, often saving length but can increase handling complexity.