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Stair Calculator — Blondel's Rule (2R + T = 63–65 cm)

Q: What are the ideal riser height and tread depth for a residential staircase?

The ideal combination for a comfortable home staircase is **R = 17 cm (6.7") and T = 30 cm (11.8")**, giving 2(17)+30 = 64 cm — perfectly centered in Blondel's range. IRC R311.7 sets the hard limits: max riser = 7¾" (19.7 cm), min tread = 10" (25.4 cm). In practice, R between 16–18 cm and T between 27–32 cm covers most comfortable residential designs.

Q: What happens if my Blondel value is below 63 cm?

A 2R + T value below 63 cm means the staircase is **too steep** — the treads are narrow and each step requires a high leg lift, causing fatigue and increasing fall risk. This typically happens when the available horizontal space is very limited. Solutions include an L-shaped layout, a switchback (U-turn) design, a spiral stair, or alternating-tread stairs (requires a permit variance for primary access).

Q: What is the minimum headroom clearance above stairs?

IRC R311.7.2 requires a minimum of **6 ft 8 in (203.2 cm)** of vertical headroom, measured plumb from the stair nosing line to the soffit, ceiling, or other obstruction above. This must be maintained throughout the entire stair flight. Basement stairs are a common violation point — always verify before framing the header above the stair opening.

Q: How does riser height affect injury risk on stairs?

The U.S. CPSC estimates approximately **1 million stair-related ER visits annually**. Research shows that **non-uniform risers** (variation > ⅜" / 0.95 cm between risers in a single flight) significantly increase trip-and-fall risk, because people's legs adapt to the first few steps and lose sync with irregular changes. IRC R311.7.5.1 strictly limits riser variation within one flight to ⅜" maximum.

Calculate stair riser height and tread depth using Blondel's Rule (2R + T = 63–65 cm). Get step count, tread, and riser instantly — with reference table and code compliance check.

🗓️ Updated June 2026 Reviewed by Martín Rodríguez

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Reviewed by: Martín Rodríguez (editorial policy ) · Last reviewed: Jun 20, 2026

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Available Horizontal Run (cm)*

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Blondel's Rule is the foundational ergonomic formula for designing comfortable and safe staircases. It determines the ideal relationship between tread depth (T) and riser height (R) based on average human stride: 2R + T = 63–65 cm (24.8–25.6 in). Enter your total floor-to-floor height and available horizontal run, and this calculator instantly outputs the number of steps, riser height, and tread depth — telling you whether the staircase meets Blondel's comfort zone, building code minimums, or is dangerously steep.

When to use this calculator

Designing a residential staircase from scratch: given a 280 cm floor-to-floor height and 350 cm horizontal run, find the step count and dimensions that satisfy Blondel + IRC code.
Checking an existing staircase for code compliance before a home sale or renovation permit — input measured total rise and run to see if 2R+T falls in the 63–65 cm comfort band.
Planning a deck or outdoor stair addition where the grade change is fixed (e.g., 120 cm drop over 180 cm horizontal) and you need to know if a compliant stair fits the space.
Comparing two staircase layout options (steeper with fewer steps vs. shallower with more steps) to find which configuration meets both Blondel's ergonomic rule and minimum headroom clearance.

Blondel-Compliant Riser + Tread Combinations (2R + T = 63–65 cm)

Riser R (cm)	Riser R (in)	Tread T (cm)	Tread T (in)	2R + T	Comfort Level
15.0	5.9"	34.0	13.4"	64 cm	Very gentle / elderly-friendly
16.0	6.3"	32.0	12.6"	64 cm ✓	Comfortable residential
17.0	6.7"	30.0	11.8"	64 cm ✓	Ideal residential
17.5	6.9"	29.0	11.4"	64 cm ✓	Standard residential
18.0	7.1"	27.0	10.6"	63 cm ✓	Acceptable, slightly steep
18.5	7.3"	26.0	10.2"	63 cm ✓	Minimum comfort zone
19.0	7.5"	25.0	9.8"	63 cm ✓	IRC max riser / min tread
20.0	7.9"	24.0	9.4"	64 cm	⚠ Exceeds IRC R311.7 max riser
22.0	8.7"	21.0	8.3"	65 cm	⚠ Steep — code violation

Fuente: IRC R311.7 (ICC, 2021) & Blondel's Formula (François Blondel, 1675). IRC limits: 15 cm ≤ R ≤ 19 cm; 25 cm ≤ T ≤ 35 cm. Rows outside IRC bounds are flagged ⚠.

How it works

How Blondel's Rule Works

François Blondel (1618–1686) observed that the average adult stride on flat ground is about 63–65 cm. On stairs, each step forces a vertical lift (R) that costs roughly twice the energy of horizontal travel (T), so the ergonomic formula is:

Blondel's Rule:
  63 ≤ 2R + T ≤ 65   (cm)

Where:
  R = Riser height (cm)  — vertical face of each step
  T = Tread depth (cm)   — horizontal surface (nosing to nosing)

Step-by-step calculation:

1. Number of risers: n = ⌈TotalHeight / 18⌉ (using 18 cm as the starting riser target)
2. Actual riser: R = TotalHeight / n
3. Tread depth: T = AvailableRun / n
4. Blondel check: compute 2R + T and verify it falls between 63–65 cm
5. Code bounds: 15 cm ≤ R ≤ 19 cm, 25 cm ≤ T ≤ 35 cm (IRC R311.7)

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Blondel Reference Table

Common Blondel-compliant riser + tread combinations (2R + T = 63–65 cm):

Riser R (cm)	Riser R (in)	Tread T (cm)	Tread T (in)	2R + T	Comfort
15.0	5.9"	34.0	13.4"	64	Very gentle / elderly-friendly
16.0	6.3"	32.0	12.6"	64 ✓	Comfortable residential
17.0	6.7"	30.0	11.8"	64 ✓	Ideal residential
17.5	6.9"	29.0	11.4"	64 ✓	Standard residential
18.0	7.1"	27.0	10.6"	63 ✓	Acceptable, slightly steep
18.5	7.3"	26.0	10.2"	63 ✓	Minimum comfort zone
19.0	7.5"	25.0	9.8"	63 ✓	IRC max riser / min tread
20.0	7.9"	24.0	9.4"	64	⚠ Exceeds IRC max riser
22.0	8.7"	21.0	8.3"	65	⚠ Steep — code violation

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Step Count by Floor Height

Quick reference for typical residential heights using R ≈ 17–18 cm:

Floor-to-Floor Height	Steps (n)	Riser R (cm)	Best Run Depth
240 cm (8 ft)	14	17.1	≥ 392 cm
260 cm (8.5 ft)	15	17.3	≥ 420 cm
270 cm (9 ft)	15	18.0	≥ 405 cm
280 cm (9.2 ft)	16	17.5	≥ 448 cm
300 cm (9.8 ft)	17	17.6	≥ 476 cm
320 cm (10.5 ft)	18	17.8	≥ 486 cm

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Common Errors to Avoid

1. Confusing risers with treads (n vs. n−1): A stair with 15 risers has 14 tread surfaces — the top "step" lands on the upper floor itself. Using n treads overestimates the horizontal run by one full tread depth.

2. Measuring to subfloor instead of finished floor: If tile or hardwood adds 1–2 cm, riser heights become unequal. Design to finished floor height; unequal risers are the #1 trip hazard on stairs (CPSC data).

3. Ignoring nosing: IRC R311.7.5.3 requires a nosing projection of ¾"–1¼" (1.9–3.2 cm) for treads under 11". The structural tread board must be T + nosing depth.

4. Skipping headroom check: IRC R311.7.2 requires minimum 6 ft 8 in (203 cm) measured vertically from the stair nosing line. A Blondel-compliant stair can still fail headroom in a low-ceiling basement.

5. Rounding step count the wrong way: Always round to the nearest whole number, then back-calculate R_actual. Rounding down can produce risers > 19 cm (IRC violation); rounding up can produce wastefully short risers.

Worked Example — 270 cm height, 360 cm run

Total height H = 270 cm, available run = 360 cm

Target riser ≈ 18 cm → steps n = ceil(270 / 18) = 15

Actual riser R = 270 / 15 = 18.0 cm

Tread T = 360 / 15 = 24.0 cm

Blondel check: 2R + T = 2(18) + 24 = 60 cm — below 63 (too steep)

Try deeper run: with 390 cm run → T = 390/15 = 26 cm → 2(18)+26 = 62 cm — borderline

Best: increase run to 420 cm → T = 28 cm → 2(18)+28 = 64 ✓ — ideal

15 steps, R = 18.0 cm, T = 28.0 cm, Blondel = 64 cm ✓

Frequently asked questions

What is Blondel's Rule and what does 2R + T = 63–65 cm mean?

Blondel's Rule (formulated by French architect François Blondel in 1675) states that the sum of twice the riser height (R) plus the tread depth (T) should equal 63–65 cm: 2R + T = 63–65 cm. This mirrors the average adult stride (~64 cm) — on stairs, each step requires two vertical lifts (R) for every one horizontal step (T). The midpoint of 64 cm is the most widely used design target.

What are the ideal riser height and tread depth for a residential staircase?

The ideal combination for a comfortable home staircase is R = 17 cm (6.7") and T = 30 cm (11.8"), giving 2(17)+30 = 64 cm — perfectly centered in Blondel's range. IRC R311.7 sets the hard limits: max riser = 7¾" (19.7 cm), min tread = 10" (25.4 cm). In practice, R between 16–18 cm and T between 27–32 cm covers most comfortable residential designs.

How do I calculate the number of stairs for a given height?

Divide the total floor-to-floor height by your target riser height (typically 17–18 cm) and round to the nearest whole number. Example: for a 270 cm height, n = round(270 / 17) = 16 steps, giving R_actual = 270/16 = 16.9 cm. Then compute tread T = 64 − 2(16.9) = 30.2 cm. Check that the total run (n−1) × T fits your available space.

What happens if my Blondel value is below 63 cm?

A 2R + T value below 63 cm means the staircase is too steep — the treads are narrow and each step requires a high leg lift, causing fatigue and increasing fall risk. This typically happens when the available horizontal space is very limited. Solutions include an L-shaped layout, a switchback (U-turn) design, a spiral stair, or alternating-tread stairs (requires a permit variance for primary access).

Does Blondel's Rule apply to outdoor deck stairs?

Yes. Blondel's Rule applies to any walking stair, indoors or out. IRC R507.4 (deck stairs) references the same R311.7 riser/tread limits. For outdoor stairs, also ensure a cross-slope of ≤2% on tread surfaces for drainage, and use open-riser or non-slip tread materials to prevent ice and water accumulation.

Why does the calculator show n risers but only n−1 treads in the horizontal run?

A staircase with n risers has exactly n−1 tread surfaces within the flight, because the final "step" lands on the upper floor slab — which is not a separate stair tread. Using n treads would overestimate the required horizontal run by one full tread depth (typically 27–30 cm), making the stair appear to require more space than it actually does.

What is the minimum headroom clearance above stairs?

IRC R311.7.2 requires a minimum of 6 ft 8 in (203.2 cm) of vertical headroom, measured plumb from the stair nosing line to the soffit, ceiling, or other obstruction above. This must be maintained throughout the entire stair flight. Basement stairs are a common violation point — always verify before framing the header above the stair opening.

How does riser height affect injury risk on stairs?

The U.S. CPSC estimates approximately 1 million stair-related ER visits annually. Research shows that non-uniform risers (variation > ⅜" / 0.95 cm between risers in a single flight) significantly increase trip-and-fall risk, because people's legs adapt to the first few steps and lose sync with irregular changes. IRC R311.7.5.1 strictly limits riser variation within one flight to ⅜" maximum.

Can I use a 20 cm riser to save space?

A 20 cm (7.87") riser exceeds the IRC residential maximum of 7¾" (19.7 cm) and would fail a code inspection — potentially voiding homeowner's insurance for stair-related injuries. At R = 20 cm, a Blondel-compliant tread of T = 64 − 40 = 24 cm also falls below the IRC minimum of 25.4 cm. To legally save space, consider a spiral stair (IRC R311.7.10.1) with a permit variance.

Sources & references

Methodology & trust

Editorial

Calculadora de construcción revisada por el equipo editorial de Hacé Cuentas, contrastada con IRC R311.7 – Stairways (International Residential Code, ICC Digital Codes), según nuestra política editorial y metodología.

Updates

Última revisión: June 20, 2026. Los parámetros se verifican periódicamente con las fuentes citadas.

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Limitations

Indicative results. For critical decisions, consult a professional.

📌 How to cite this calculator

Rodríguez, M. (2026). Stair Calculator — Blondel's Rule (2R + T = 63–65 cm). Hacé Cuentas. https://hacecuentas.com/stair-calculator-blondel-rule

Contenido bajo licencia CC-BY 4.0 — reutilizable citando la fuente con enlace a Hacé Cuentas.

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