Construction

Stairs — Blondel's Rule

Q: What exactly is Blondel's Rule and where does the 63–65 cm range come from?

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 relationship is 2R + T = 63–65 cm. The midpoint target of 64 cm is most commonly used in modern residential design.

Q: What are the US building code limits for riser height and tread depth?

The International Residential Code (IRC) R311.7.5 sets the maximum riser at **7¾ in (19.7 cm)** and minimum tread depth at **10 in (25.4 cm)** for residential occupancies. Commercial stairs under IBC 1011.5 are stricter: max riser 7 in (17.8 cm), min tread 11 in (27.9 cm). All risers in a single flight must be within ⅜ in (0.95 cm) of each other.

Q: Why does the calculator use n−1 treads for the horizontal run, not n?

A staircase with n risers has exactly n−1 tread surfaces in the flight, because the final 'step' lands on the upper floor slab — which is not a stair tread. Using n treads would overestimate the required horizontal run by one full tread depth (typically 28–30 cm), potentially causing the staircase to exceed your available space calculation.

Q: My Blondel result gives 2R+T = 50 (like the example). What does that mean?

A value of 2R+T below 63 cm means the staircase is **too steep and the treads are too narrow** for comfortable, safe walking — it approaches ladder-like geometry. This typically happens when the available horizontal depth is very shallow relative to the height. Solutions include an L-shaped layout, a switchback (U-shaped) design, or alternating-tread stairs (which require a special code variance for primary access).

Q: Does Blondel's Rule apply to outdoor and deck stairs?

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

Q: What minimum headroom must I maintain above a staircase?

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

Q: How much does riser height affect fall risk on stairs?

The CPSC estimates that approximately **1 million stair-related injuries** requiring emergency room visits occur annually in the US. Studies cited in the literature show that non-uniform riser heights (variation > ⅜ in / 0.95 cm between risers in a flight) significantly increase trip-and-fall risk. This is why IRC R311.7.5.1 strictly limits riser variation within a single flight to ⅜ in maximum.

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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.

Last reviewed: May 12, 2026 Verified by Hacé Cuentas Team Source: IRC R311.7 – Stairways (International Residential Code, via ICC Digital Codes), CPSC – Stair and Step Injuries (U.S. Consumer Product Safety Commission), Wikipedia – Blondel's Formula (Stairs) 100% private

When to use this calculator

Designing a residential staircase from scratch: given a 280 cm floor-to-floor height and 300 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.

Calculation Example

270 cm height, 240 cm depth
15 steps
tread=18 cm, riser=16 cm
T+2R = 18+2(16)=50 ✗ (tight)

Result: 15 steps, tread=18, riser=16

How it works

4 min read

How It's Calculated

Blondel's Rule was formulated by French architect François Blondel in 1675. It models the average human stride (≈63–65 cm) as a combination of vertical lift and horizontal travel on a stair:

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

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

Step 1 – Number of risers:
  n = round( TotalHeight / R_target )
  R_target ≈ 17 cm (start here; iterate until Blondel is satisfied)

Step 2 – Actual riser:
  R_actual = TotalHeight / n

Step 3 – Tread from Blondel:
  T = 64 - 2 × R_actual   (targeting midpoint 64 cm)

Step 4 – Check horizontal fit:
  Run_required = (n - 1) × T   ← n-1 because the top step lands on the floor
  If Run_required ≤ AvailableDepth → fits ✓

Step 5 – Verify code bounds:
  15 cm ≤ R ≤ 19 cm
  25 cm ≤ T ≤ 35 cm
  2R + T must be 63–65 cm

> Note: The IRC (International Residential Code) R311.7.5 sets minimum tread at 10 in (25.4 cm) and maximum riser at 7¾ in (19.7 cm) for residential stairs in the US.

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Reference Table

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

Riser R (cm)	Riser R (in)	Tread T (cm)	Tread T (in)	2R+T	Use Case
15.0	5.9	34.0	13.4	64	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 ✓	Common 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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Typical Cases

Case 1 — Standard 9-ft ceiling home (from the calculator example)

Total height: 270 cm | Available depth: 240 cm

Target R ≈ 17 cm → n = round(270/17) = 16 steps

R_actual = 270/16 = 16.9 cm

T = 64 − 2(16.9) = 30.2 cm

Run required = 15 × 30.2 = 453 cm → exceeds 240 cm available ✗

Solution: use R = 18 cm → n = 15, T = 64−36 = 28 cm, run = 14×28 = 392 cm → still exceeds 240 cm

With T = 18 cm, R = 16 cm (as in the example): 2(16)+18 = 50 — fails Blondel (too tight/steep stair design for a very shallow space). An L-shaped or switchback layout is needed.

Case 2 — Split-level addition (120 cm rise, 200 cm run)

n = round(120/17) = 7 steps

R_actual = 120/7 = 17.1 cm

T = 64 − 2(17.1) = 29.8 cm ≈ 30 cm

Run required = 6 × 30 = 180 cm ≤ 200 cm ✓

2R+T = 2(17.1)+30 = 64.2 ✓ — perfect Blondel compliance

Case 3 — Deck stair (90 cm drop, 160 cm run)

n = round(90/17) = 5 steps

R_actual = 90/5 = 18.0 cm

T = 64 − 2(18) = 28 cm

Run required = 4 × 28 = 112 cm ≤ 160 cm ✓

2R+T = 36+28 = 64 ✓ — compliant and fits

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Common Errors

1. Confusing "risers" with "treads" (n vs. n−1): A stair with 10 risers has only 9 tread surfaces — the top landing is the floor itself. Using n treads overestimates the horizontal run by one full tread depth.

2. Measuring total height to the finish floor, not the subfloor: If finish flooring (hardwood, tile) adds 1.5–2 cm, riser heights become unequal. Always design to finished floor height; an unequal first or last riser is a leading trip-hazard cause per CPSC data.

3. Ignoring the nosing: IRC R311.7.5.3 requires a nosing projection of ¾ in to 1¼ in (1.9–3.2 cm) for treads less than 11 in. The tread depth T is measured nosing-to-nosing, so the structural tread board must be T + nosing depth. Forgetting this makes treads feel short.

4. Using Blondel alone without checking headroom: IRC R311.7.2 requires minimum 6 ft 8 in (203 cm) headroom measured vertically from the stair nosing line. A staircase can pass Blondel perfectly and still fail headroom clearance in a low-ceiling basement.

5. Rounding riser count down instead of finding the nearest integer: Always round to the nearest whole number, then back-calculate R_actual. Rounding always down can produce risers > 19 cm (IRC violation); rounding always up can produce risers < 15 cm (excessively gentle and wastes space).

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Related Calculators

Since no related slugs were provided for this calculator, explore other construction tools on Hacé Cuentas for concrete volume, roof pitch, and room area calculations to complement your staircase design project.

Frequently asked questions

What exactly is Blondel's Rule and where does the 63–65 cm range come from?

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 relationship is 2R + T = 63–65 cm. The midpoint target of 64 cm is most commonly used in modern residential design.

What are the US building code limits for riser height and tread depth?

The International Residential Code (IRC) R311.7.5 sets the maximum riser at 7¾ in (19.7 cm) and minimum tread depth at 10 in (25.4 cm) for residential occupancies. Commercial stairs under IBC 1011.5 are stricter: max riser 7 in (17.8 cm), min tread 11 in (27.9 cm). All risers in a single flight must be within ⅜ in (0.95 cm) of each other.

Why does the calculator use n−1 treads for the horizontal run, not n?

A staircase with n risers has exactly n−1 tread surfaces in the flight, because the final 'step' lands on the upper floor slab — which is not a stair tread. Using n treads would overestimate the required horizontal run by one full tread depth (typically 28–30 cm), potentially causing the staircase to exceed your available space calculation.

My Blondel result gives 2R+T = 50 (like the example). What does that mean?

A value of 2R+T below 63 cm means the staircase is too steep and the treads are too narrow for comfortable, safe walking — it approaches ladder-like geometry. This typically happens when the available horizontal depth is very shallow relative to the height. Solutions include an L-shaped layout, a switchback (U-shaped) design, or alternating-tread stairs (which require a special code variance for primary access).

Does Blondel's Rule apply to outdoor and deck stairs?

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

What minimum headroom must I maintain above a staircase?

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

How much does riser height affect fall risk on stairs?

The CPSC estimates that approximately 1 million stair-related injuries requiring emergency room visits occur annually in the US. Studies cited in the literature show that non-uniform riser heights (variation > ⅜ in / 0.95 cm between risers in a flight) significantly increase trip-and-fall risk. This is why IRC R311.7.5.1 strictly limits riser variation within a single flight to ⅜ in maximum.

Can I use a riser height of 20 cm to save horizontal space?

A 20 cm (7.87 in) riser exceeds the IRC residential maximum of 7¾ in (19.7 cm), so it would fail code inspection and could void homeowner's insurance coverage for stair-related injuries. Practically, it also produces a 2R+T ≈ 64 cm only if T = 24 cm — below the 25.4 cm IRC tread minimum. To save space legally, consider a spiral stair (IRC R311.7.10) or alternating-tread device with a building permit variance.