Data Source and Methodology
Authoritative source: International Code Council (ICC) — 2021 International Residential Code (IRC), Section R311.7 Stairways (published 2021). Direct reference: https://codes.iccsafe.org/content/IRC2021P1/chapter-3-building-planning#IRC2021P1_Pt03_Ch03_SecR311.7
Tutti i calcoli si basano rigorosamente sulle formule e sui dati forniti da questa fonte.
Where local amendments apply, always verify with your jurisdiction or an inspector. This tool provides engineering-friendly calculations and code-aware checks but is not a substitute for a stamped design.
The Formulas Explained
Let total rise be R, preferred riser be rₚ (optional), tread depth (going) be g, number of risers be n, number of treads be t, total run be L, angle be θ, and stringer length be S.
Riser count (code-aware selection):
$$ n = \begin{cases} \left\lceil \dfrac{R}{r_{\max}} \right\rceil, & \text{if code enforced and no } r_p \\ \max\!\left(2,\ \mathrm{round}\!\left(\dfrac{R}{r_p}\right)\right), & \text{if } r_p \text{ provided} \\ \mathrm{round}\!\left(\dfrac{R}{r_{\text{default}}}\right), & \text{otherwise} \end{cases} $$
Actual riser height:
$$ h = \dfrac{R}{n} $$
Treads (assuming upper floor acts as final tread):
$$ t = n - 1 $$
Total run:
$$ L = t \times g $$
Stair angle:
$$ \theta = \arctan{\left(\dfrac{R}{L}\right)} $$
Stringer length (hypotenuse):
$$ S = \sqrt{R^2 + L^2} $$
Top cut drop and bottom rise add for a cut stringer with tread thickness τ:
$$ \text{Top drop} = \tau \qquad \text{Bottom rise add} = \tau $$
Glossary of Variables
| Symbol/Field | Meaning |
|---|---|
| Total rise (R) | Vertical distance from finished lower floor to finished upper floor. |
| Tread depth / Going (g) | Horizontal distance from nosing to nosing per step. |
| Preferred riser (rₚ) | Target riser height used to pick an integer riser count. |
| Riser count (n) | Total number of risers; must be an integer ≥ 2. |
| Riser height (h) | Computed actual riser height: R/n. |
| Treads (t) | Number of treads, assuming the upper floor is the last tread: t = n − 1. |
| Total run (L) | Horizontal projection of the staircase: t × g. |
| Angle (θ) | Inclination of the staircase: arctangent of R/L. |
| Stringer length (S) | Hypotenuse length along the slope: √(R² + L²). |
| Tread thickness (τ) | Thickness of the tread; used for top/bottom cut adjustments. |
How It Works: A Step-by-Step Example
Inputs: Units: Imperial. Total rise R = 112 in, preferred riser rₚ = 7.5 in, going g = 10 in, tread thickness τ = 1 in, code limits enforced.
1) Riser count: n = round(112/7.5) = 15. Actual riser h = 112/15 = 7.47 in (≤ 7.75 in, compliant).
2) Treads: t = n − 1 = 14. Total run L = 14 × 10 = 140 in.
3) Angle: θ = arctan(112/140) ≈ 38.7°. Stringer: S = √(112² + 140²) ≈ 179.1 in (14.9 ft).
4) Cuts: Top drop = τ = 1 in. Bottom rise add = τ = 1 in.
Frequently Asked Questions (FAQ)
What stair angle is typical?
Residential stairs often fall between 30° and 40°. Around 37°–38° is common with a 7.5 in rise and 10 in going. Always confirm comfort and local codes.
Does the nosing change the going?
No. The IRC defines tread depth as the horizontal distance from nosing to nosing. Nosing affects overhang aesthetics and comfort, not the going dimension used here.
How many treads do I cut?
If the upper floor is the last “step,” you cut t = n − 1 treads on the stringer. The top tread is the finished floor.
Can this calculator handle metric projects?
Yes. Switch to Metric (mm). The tool converts inputs, validations, and results instantly.
What if my preferred riser conflicts with the code?
With code enforcement enabled, the tool adjusts the riser count so the computed riser height does not exceed the permitted maximum. You’ll see a compliance note in the results.
Is headroom or handrail design included?
This version focuses on the core stair geometry. Always verify headroom, landings, and guard/handrail requirements with your building code.