Blondel's Formula for Stair Comfort

Most guides claim François Blondel studied human gait and found that climbing takes twice the vertical effort of walking, a principle now known as the Blondel formula stairs. No source for that exists. What Blondel actually published in Cours d’architecture (1675-1683) was a geometric observation: a step that matches a natural stride feels better. He stated it in French pouces (≈27.07 mm each) as 2 × hauteur + 1 × giron = 24 pouces. That converts to about 25.58 modern inches, not the 24-25 inches US references cite. The modern range is an approximation that works for most residential stairs, but it is a convenience, not the original number.

Today the 2r+t formula is written as 2 × rise + tread depth, with a target between 24 and 25 inches. Architectural Graphic Standards (12th edition, 2017) gives this range for general use, but notes it varies by user: public stairs should stay closer to 24 inches; private stairs can drift toward 25 inches. In metric, the target is 2R + T ≈ 610-635 mm, derived from Blondel's original 649.7 mm rounded down for shorter modern strides. Use the lower end for stairs used by children or shorter adults, the upper end for taller populations.

Metric Conversion

Blondel's original 649.7 mm converts to about 25.58 inches. The modern 610-635 mm range is a rounded approximation for shorter strides.

Three rules of thumb work together. The stair comfort formula (2R + T) targets comfort. The safety formula (R + T) requires a sum between 17 and 18 inches, this ensures the pitch is not too steep or shallow. The less common R × T rule targets about 70-75 in² and is mostly a historical footnote. All three are checks, not code. The 2021 IRC R311.7 mandate a maximum riser of 7¾ inches, a minimum tread of 10 inches, and uniformity within ⅜ inch. Blondel's formula helps you pick a combination inside those legal limits that actually feels good.

Worked example: You have a total rise of 105 inches. Divide by a trial riser of 7 inches → 15 risers. Actual rise = 105 ÷ 15 = 7 inches. Treads = 14. Pick a trial tread of 11 inches. Check Blondel: 2 × 7 + 11 = 25 inches, at the upper limit. The stair will feel stretched. Reduce tread to 10.5 inches: 2 × 7 + 10.5 = 24.5 inches, inside the comfort zone. Check R + T: 7 + 10.5 = 17.5 inches, within 17-18. The stair passes both checks and the IRC limits.

Steep attic stairs: A ship ladder or alternating tread stair with risers above 8 inches and treads below 8 inches gives a Blondel value above 27. The formula says it is uncomfortable. It is. These stairs are allowed only for limited access where comfort is not the goal.

Landscape steps: Garden steps with wide treads (14-18 inches) and low risers (4-5 inches) produce a Blondel value as low as 22. The formula says it is choppy. That is correct for indoor stairs, but outdoor steps tolerate a wider range because the gait is different, users take them one step at a time, not in a rhythm.

Winder stairs: The tread depth varies along the step. Apply Blondel at the walkline, 12 inches from the narrow end, where the IRC requires a minimum of 10 inches. The narrow end can be as small as 6 inches, but Blondel's formula is not meaningful there.

Designers pick a riser and tread that land inside the IRC limits but produce a Blondel value of 25.5 or higher, then wonder why the stair feels awkward. The fix is simple: before you cut stringers, run the 2R + T check. If the result is above 25, reduce the tread depth or the riser height until it falls in the 24-25 range. That one step separates a stair that passes inspection from a stair that people actually enjoy climbing.