In 1675, the French architect François Blondel studied the staircases people actually walked comfortably and published the relationship that still predicts it: twice the riser height plus the tread depth should equal about 25 inches (his original metric: 24–25 French inches). Three and a half centuries of biomechanics have refined the numbers but not the shape of the rule.
Why the relationship holds
Walking is a pendulum: the leg swings a stride length that depends on how high it must lift (riser) and how far it must reach (tread). Climb a step and the "stride" shortens — every inch of riser removes roughly two inches of needed tread. The formula is the pendulum's geometry: 2R + T = constant, with the constant ~25 in tuned to human legs. Short-riser stairs (6 in) want long treads (13 in); tall risers (7¾) want short treads (9.5–10) — and both combinations feel natural, while violating pairs (6-in riser on a 10-in tread) feel wrong on the way down.
The code numbers echo it
| Combination | 2R + T | Feel |
|---|---|---|
| 6.5 in riser, 12 in tread | 25.0 | Palace stairs — shallow, long |
| 7.0 in riser, 11 in tread | 25.0 | The residential sweet spot |
| 7.75 in riser, 10 in tread | 25.5 | Code-max — compact, still honest |
| 8.5 in riser, 9 in tread | 26.0 | The old farmhouse — leggy |
The IRC caps (7¾ riser, 10 tread) sit right on the formula's comfort band — code is comfort, formalized.
Using the formula
- Count risers first (total rise ÷ target riser, rounded) — risers equalize; treads follow.
- Solve the formula for tread at your equalized riser: T = 25 − 2R.
- Check both caps: riser ≤ 7¾, tread ≥ 10. If the formula's tread undercuts 10, reduce the riser until both pass.
- Run it in the layout calculator — it enforces the sequence automatically.
The descent test
The formula's authority shows descending: down-stairs are where mismatched geometry bites, because the leg reaches blind. A stair that "feels fine up" and treacherous down has broken the 25-inch balance — usually with long treads on tall risers. Blondel measured what legs already knew; the formula just made it a layout line.