Stair Calculator — Rise, Run, Stringer & Headroom

Finished stair geometry

One straight flight has $n$ equal risers and $n-1$ goings, with the upper floor serving as the last tread. The tool keeps $R=H/n$ and $G=L/(n-1)$ unrounded. The pitch is $\theta=\tan^{-1}(R/G)$; using $\tan^{-1}(H/L)$ would describe a different diagonal.

Automatic selection scans integer counts 2–40. It first prefers candidates within the selected rise and going limits, then minimizes $|2R+G-630\,\mathrm{mm}|$. If none meets those limits, the closest Blondel candidate remains visible with a warning. Headroom, the Blondel band and flight/landing limits are checked separately. The 630 mm target is an author-selected value within the published 590–650 mm DIN planning band. IRC does not impose that Blondel band.

Nosing span and stringer estimate

The unit diagonal is $u=\sqrt{R^2+G^2}$. The actual first-to-last nosing-line span is $S_\mathrm{nose}=(n-1)u$. The displayed stringer layout estimate is $S_\mathrm{layout}=nu$, following the riser-count estimating convention in BC Carpenter Level 2 (attached p. 48, printed p. 44). It includes one additional unit diagonal, but is not a guaranteed stock length or a cut schedule.

Headroom

The first nosing is at $(0,R)$ and the upper nosing at $(L,H)$. A finished opening of length $A$ places its lower edge at $x_e=L-A$. The pitch-line height there is $y_e=R+x_eR/G$. Vertical clearance to a flat soffit is $h=H-t-y_e=AR/G-t$. Similar triangles give the minimum finished opening A_\min=(h_\mathrm{req}+t)G/R. BC Carpenter (attached pp. 34–35) uses the same geometry. Its extra 75 mm is a rough-framing allowance and is deliberately excluded from this finished-opening result.

• Finished floor elevations, equal risers and equal goings; nosings lie on one straight pitch line.
• The opening edge is over the flight: $0<A\leq L$. The complete floor/ceiling thickness is uniform, and the space above the opening is otherwise unobstructed.
• The section is an original schematic of finished step edges; tread thickness, nosing projection and the stringer's cross-section are not drawn. Drawing letters match the inputs and results. Diagram dimensions show rounded millimetres and inches together; the unit switch converts physical inputs, result cards and comparison-table columns. Use the precise results for layout, with suitable construction allowances.
• The exact geometric identities and closure checks are derived here. Numerical rule limits and reference examples come from the linked sources. No measurement tolerance is added to a code limit.

Rule basis — checked 25 October 2026

2021 IRC, residential stairs: R311.7.5.1 limits rise to 7¾ in; R311.7.5.2 requires going of at least 10 in. R311.7.2 requires 80 in vertical headroom; R311.7.3 limits a flight to 151 in vertical rise. Exact inch conversions are used instead of the code's rounded parenthetical millimetres. When the going is below 11 in, a reminder calls for the nosing review required by R311.7.5.3.

DIN 18065:2020-08, necessary stairs in general buildings: rise 140–190 mm, going 260–370 mm, Blondel planning band 590–650 mm, vertical headroom at least 2 m, and a landing after at most 18 risers. This profile excludes the separate category for dwellings with up to two apartments and excludes additional/non-necessary stairs. Limits follow the federal stair-geometry guide's cited clauses; no standard table or figure is reproduced.

A riser/going result assesses those two dimensions only. Headroom and flight limits have separate warnings. No overall code approval is issued. Stair width, landings and approaches, guards, handrails, lighting, uniformity on site, nosing geometry, accessibility, structural strength, supports and connections require separate design and inspection. Winders, spiral stairs and split flights are not modeled.

Check against the standard in force, the building authority's adopted edition and local amendments. Installation work belongs to a qualified person. The stringer estimate does not authorize an unsupported span, notch depth, material selection or final cut length.