Design a code-compliant staircase: rise, run, stringer length and headroom.
The stringer is the inclined structural member supporting the treads. Its length is the hypotenuse of the right triangle formed by the total rise and total run (Pythagorean theorem). The number of risers is calculated by dividing the total floor-to-floor height by the desired riser height, then rounding to keep all risers equal — unequal risers are a trip hazard. IRC code caps riser height at 7.75 in and requires tread depth ≥ 10 in. Blondel's rule (2R + T = 24–25) is the ergonomic comfort check used by European and many North American authorities.
Actual riser height
Riser = total rise ÷ number of risers
Stringer length
Stringer = √(total rise² + total run²)
Blondel's comfort rule
2 × riser + tread depth should be between 24 and 25 inches.
The informal '7-11 rule' says riser height should be ≤ 7 in and tread depth ≥ 11 in. The IRC code is slightly more lenient (7.75 in riser, 10 in tread), but the 7-11 rule gives a comfortable stair that most people find ergonomically natural.
The first 'step' is the finished floor itself; the last 'step' is the landing. Between two floors with n risers, there are n−1 intermediate treads.
The 17th-century architect François Blondel found that a comfortable step satisfies 2R + T ≈ 24–25 in, matching average human stride. A stair with 7 in risers and 11 in treads scores 2(7) + 11 = 25 — exactly in range.
IRC requires a minimum clear width of 36 inches. Handrails may project into this width by up to 4.5 inches per side.