Methodology
Exactly how Stairs Calc calculates and which code editions it references — the formulas, the sources, our update cadence and corrections policy.
Editorial standard
Built and maintained by builders, drafters and engineers who plan stairs for a living — every code limit is transcribed from the published standard and cited to its exact section.
- Our team combines hands-on carpentry and stair-building experience with structural-engineering and code-research practice, so the geometry is buildable and the limits are right.
- Every code limit in the tools is transcribed from the published standard, verified against the primary source, and shown with its exact section reference in the Code panel.
- We review the code data on a regular cadence and whenever a referenced standard is amended, and we stamp each page with the date it was last reviewed.
- We do not put a fabricated "reviewed by a licensed engineer" byline on results no named professional has signed off on. When a credentialed reviewer signs off on the record, we name them here.
- Spotted a value that does not match your local adopted code? Tell us the section and edition and we correct verified errors quickly — see the corrections policy below.
How the calculations work
Every Stairs Calc tool runs the same pure, deterministic engine in your browser. All lengths are held internally in millimeters at double precision and converted only when a value is read in or displayed, so rounding to a fraction never feeds back into the math — fractions never drift. The number of risers is the total rise divided by your target riser, rounded to a whole number; the rise is then divided back by that count so every riser is exactly equal, which is what codes require.
Stringer length is the hypotenuse of the rise/run triangle, the angle is the pitch of one step (atan of rise over run), and the comfort score blends the Blondel, rise-plus-run and rise-times-run rules. Nothing is stored on a server; your calculation lives only in the page and in the shareable link you choose to copy.
Formulas and their provenance
These are the exact formulas the engine evaluates, with a worked example you can reconcile. The geometry follows classical stair construction: the staircase is a right triangle whose legs are the total rise and total run, so the stringer length is the hypotenuse (Pythagoras) and the pitch is its angle. The comfort band comes from François Blondel’s 1675 stepping-cadence rule (2 × rise + run), still the basis of the comfort guidance in modern codes. The full live comparison of every code limit lives on our stair code requirements page, and the same formulas are documented on the formulas page.
- Number of risers
N = round(total rise ÷ ideal riser)Round to the nearest whole number, then divide the rise back by N for the exact, equal riser height.
- Riser height
riser = total rise ÷ N- Treads
treads = N − 1The upper floor acts as the top step.
- Total run
total run = (N − 1) × run- Stringer length
stringer = √(total rise² + total run²)The hypotenuse of the staircase triangle (Pythagoras).
- Stair angle
angle = atan(rise ÷ run)The pitch of one step.
- Minimum stairwell opening
opening = ((floor thickness + headroom) × total run) ÷ total rise- Throat
throat = board width − (rise × run) ÷ √(rise² + run²)Keep at least 3½″ of solid wood behind the notch.
- Comfort — Blondel
2 × rise + run = 24″–25″The classic stepping-cadence rule.
- Comfort — Rise + Run
rise + run = 17″–18″- Comfort — Product
rise × run ≈ 70–75 in²
Worked example — a 9′-7″ total rise
Dividing by an ideal 7" riser gives 16 risers, so each riser is 7³⁄₁₆". With a 11" run there are 15 treads, a total run of 13′-8¾″, a stringer length of 16′-9″, and an angle of 33.2° — very comfortable and within IRC limits.
Sources and citations
Limits in the tools are transcribed from these published standards and verified against the primary source. Each row lists the standards body, the edition the limits come from, and the exact section references the engine cites in its Code panel — the same section strings the calculators show beside every check, so what you read here matches what the tool enforces.
- 1.
International Residential Code (IRC) — IRC 2021
International Code Council (ICC)
Riser height, tread run, headroom, width, handrail and guard limits for one- and two-family dwellings (Section R311.7 — Stairways).
Sections enforced: IRC R311.7.5.1 · IRC R311.7.5.2 · IRC R311.7.2 · IRC R311.7.1 · IRC R311.7.8 · IRC R312.1 · IRC R311.7.3
Read the standard (opens in a new tab) - 2.
International Building Code (IBC) — IBC 2021
International Code Council (ICC)
Commercial stairway geometry, width by occupant load, headroom, handrails and landings (Section 1011 — Stairways).
Sections enforced: IBC 1011.5.2 · IBC 1011.3 · IBC 1011.2 · IBC 1011.11 · IBC 1015 · IBC 1011.6 / 1011.8
Read the standard (opens in a new tab) - 3.
OSHA Standard Stairs — 29 CFR 1910.25
U.S. Occupational Safety and Health Administration
Workplace fixed-stair angle, riser/tread, width, handrails and guardrails for general industry.
Sections enforced: OSHA 1910.25(c) · OSHA 1910.25(b) · OSHA 1910.28 · OSHA 1910.29 · 29 CFR 1910.25 · 29 CFR 1910.28 · 29 CFR 1910.29
Read the standard (opens in a new tab) - 4.
ADA Standards for Accessible Design — 2010 ADA Standards
U.S. Department of Justice
Accessible stairs (§504), ramp slope and landings (§405), and the closed-riser rule for accessible routes.
Sections enforced: ADA 504.2 · ADA 307 · ADA 504.3 · ADA 505 · ADA 504.6 · ADA 405 · ADA 405.2 · ADA 504
Read the standard (opens in a new tab) - 5.
Approved Document K — Approved Document K (2013)
UK Ministry of Housing, Communities & Local Government
Protection from falling, collision and impact — England & Wales stair pitch, going and rise.
Sections enforced: ADK 1.1 · ADK 1.10 · ADK 1.13 · ADK 1.34 · ADK 3.3 · ADK 1.21
Read the standard (opens in a new tab) - 6.
National Building Code of Canada (NBC) — NBC 2020
National Research Council Canada
Stairs, ramps, handrails and guards for housing and small buildings (Section 9.8).
Sections enforced: NBC 9.8.4 · NBC 9.8.2 · NBC 9.8.7 · NBC 9.8.8 · NBC 9.8.6
Read the standard (opens in a new tab) - 7.
National Construction Code (NCC) — NCC 2022
Australian Building Codes Board
Stair construction, riser/going and balustrade requirements for Australian buildings.
Sections enforced: NCC D3.3
Read the standard (opens in a new tab) - 8.
DIN 18065 — Building Stairs — DIN 18065:2020
Deutsches Institut für Normung (DIN)
German standard for building stairs: terms, measuring rules and principal dimensions.
Sections enforced: DIN 18065 §6 · DIN 18065 §7 · DIN 18065 §5 · DIN 18065 §9 · DIN 18065 §8
Read the standard (opens in a new tab)
Code editions referenced
- IRC 2021/2024
- IBC 2021
- OSHA 1910.25
- ADA 2010
- UK Approved Document K (2013)
- Canada NBC 2020
- Australia NCC 2022
- Germany DIN 18065:2020
Limits are transcribed from these published editions and verified against primary sources. We review them on a regular cadence and whenever a referenced code is updated.
Corrections policy
If you spot a value that doesn’t match your local adopted code, email [email protected] with the section and edition. We correct verified errors quickly and update the “last updated” date on the affected pages. Results are estimates for planning — always confirm against your local adopted code and a licensed professional before you build.
Written by the Stairs Calc editorial team. Methodology and code references: see our methodology.
Built and maintained by builders, drafters and engineers who plan stairs for a living — every code limit is transcribed from the published standard and cited to its exact section.
Last reviewed 2026-06-20 against IRC 2021/2024
Stairs Calc gives accurate geometry and checks it against published building-code limits, but results are estimates for planning. Codes are adopted and amended locally and change over time. Always confirm dimensions against your local adopted code and a licensed professional before you build.