The Stair Comfort Formula (Blondel’s Formula) Explained Simply

Blondel’s formula says twice the riser height plus one tread depth should land between 24 and 26 in / 610–660 mm (2R + T = 24–26 in) — step outside that range and a stair starts to feel cramped or exhausting to climb, even when it’s fully code-legal. French architect François Blondel worked out the ratio in the 1670s from average human stride length and published it in his 1675 Cours d’Architecture. Modern building codes worldwide still lean on the same relationship — the UK’s 2R+G rule in Approved Document K is a direct descendant of it. Check any riser/tread pair against the ratio with the stair comfort formula calculator before committing to a layout.

How to apply Blondel’s formula

The working version of the formula, solved for tread depth, is T = 25 − 2R (inches) or T = 63 − 2R (cm), where R is riser height. Take a riser of 7.5 in / 190 mm — plug it in: T = 25 − 15 = 10 in / 254 mm. That’s a tight but valid stair, since it lands exactly on the IRC’s tread minimum with no spare room. Try a shallower riser of 7 in / 178 mm instead: T = 25 − 14 = 11 in / 279 mm — and that number isn’t a coincidence, since it matches the IBC’s 11 in commercial tread minimum almost exactly. At standard riser heights, Blondel’s comfort formula and the code minimums converge, which is part of why the formula has held up for 350 years.

Most references give the target as a range rather than one fixed number — some cite 24–26 in / 610–660 mm, others extend it to 24–27 in / 610–686 mm, and a secondary check, R + T ≈ 17–18 in / 432–457 mm, is sometimes used alongside it. Treat the range as a design target, not a single correct answer, and use whichever riser/tread pair from your riser calculation actually falls inside it. Confirm the pair with the riser height calculator and tread depth calculator before checking comfort, since Blondel’s formula only means something once both numbers are real, buildable dimensions.

Why the formula works

Blondel’s insight was that stride length on a level surface stays roughly constant — close to 24–25 in / 610–635 mm for an average adult — and that climbing a riser shortens the horizontal component of that stride by roughly twice the vertical rise. A taller riser means less horizontal distance is needed to cover the same effective stride, so the tread can shrink; a shorter riser needs a deeper tread to keep the total motion comfortable. It’s an empirical heuristic based on observed human gait, not a physical law, which is why different sources give slightly different acceptable ranges rather than one exact number.

The formula also explains why very steep stairs (ladders, alternating-tread devices) and very shallow ones (garden steps, ramps-adjacent stairs) both fall outside its comfortable middle. A ladder-like riser of 10 in with almost no tread produces a 2R+T value far above the comfort range — legal for a specific use case, but never described as comfortable. A shallow garden step with a 4 in riser and 20 in tread falls below the range for the opposite reason: too much horizontal distance for too little vertical gain, which reads as a lazy, inefficient stride rather than a genuine hazard.

Common mistakes

Treating Blondel’s formula as a legal requirement in the US. The IRC and IBC don’t reference 2R+T directly — they set independent riser and tread minimums instead — so a stair can be fully code-compliant while sitting outside Blondel’s comfort range, or vice versa. Use the formula to judge comfort, and the actual code table to judge legality; they’re separate checks.

Solving Blondel’s formula before fixing a whole-number riser count. Plugging in an arbitrary riser height gives a tread depth that looks fine on paper but doesn’t correspond to any riser count that actually divides evenly into the real floor-to-floor rise. Solve the riser height first with the stair rise and run calculator, then check the resulting riser/tread pair against Blondel’s range — not the other way around.

Using stringer-cut depth instead of code-measured tread depth in the formula. A tread with a 1 in nosing overhang measures deeper (nose to nose) than the raw stringer notch, and running the formula on the wrong number can make a genuinely comfortable stair look non-compliant, or the reverse. Always plug in the finished, code-measured tread depth.

Related calculators you might need

Blondel’s formula only works as a check against real riser and tread numbers, so start with the riser height and tread depth calculators linked earlier in this article to lock those in first. The stair rise and run calculator ties both together for a full flight, and the number of steps calculator converts the final numbers into a buildable stringer layout. If you’re designing to UK rules specifically, the UK Building Regs Part K calculator applies the 2R+G formula with the UK’s own 550–700 mm range built in.

Frequently asked questions

What is Blondel’s formula for stairs?

Blondel’s formula, also written as 2R + T, states that twice the riser height plus one tread depth should fall between roughly 24 and 26 in / 610–660 mm for a comfortable stair. French architect François Blondel developed it in the 1670s based on average human stride length and published it in 1675. It’s still the basis for comfort checks used by architects and for the UK’s 2R+G building regulation formula today.

Is Blondel’s formula a legal building code requirement?

In the US, no — the IRC and IBC set independent riser and tread minimums and don’t cite Blondel’s ratio directly, though most code-compliant stairs happen to land close to it anyway. In the UK, a close variant (2R+G between 550–700 mm) is written directly into Approved Document K, making it an enforceable requirement there rather than just a comfort guideline.

How do I use the 2R+T rule to design a stair?

First fix a riser height that divides evenly into your total rise, then solve T = 25 − 2R (inches) to find the tread depth Blondel’s formula suggests for that riser. Check whether the result also clears your local code’s tread minimum — if it doesn’t, adjust the riser count and recalculate. The stair comfort formula calculator runs both checks in one step.

What’s the ideal riser and tread combination for comfort?

A 7–7.5 in / 178–190 mm riser paired with a 10–11 in / 254–279 mm tread is the combination most often cited as ideal, and it satisfies Blondel’s formula, most US code minimums, and typical stride comfort all at once. Outside that band, riser and tread still need to trade off against each other to stay within the 24–26 in comfort range.

Why does the UK use a different comfort formula than the US?

The UK didn’t invent a different formula so much as write Blondel’s original ratio directly into law. Approved Document K requires 2R+G (rise plus going) to fall between 550 and 700 mm, which is metric Blondel with a wider tolerance band than the 24–26 in range commonly cited in the US. The US never codified the ratio at all, leaving it as a design guideline rather than an inspected requirement.