Stairs are a division problem with safety stakes: the total rise must split into perfectly equal steps, each inside the limits human legs expect. This calculator does the division, checks it against IRC reference limits, and sizes the stringer.
The worked example
A 108-inch floor-to-floor rise: targeting ~7⅜″ risers gives 108 ÷ 7.375 ≈ 14.6 → round to 15 risers of 7.2″ each (or 14 at 7.71″ — both legal, the calculator picks the rounder count). With 10.5″ treads, total run is 14 × 10.5 = 147″, and the stringer needs √(108² + 147²) ≈ 182″ — a 16-foot board.
Why equality is non-negotiable
Your feet memorize the rhythm within two steps and then stop looking. A single riser off by more than ⅜″ is where ankles turn — which is why the remainder never goes into one odd step: the whole rise divides evenly, always.
Reference limits and the comfort formula
The IRC residential references: risers ≤ 7¾″, treads ≥ 10″, headroom 6′8″. Comfort has its own arithmetic — 2×riser + tread should land near 24–25″ (the old 7-11 stair scores 25 exactly). The verdict line grades your design on both scales. These are reference values, not a compliance ruling — your local code and inspector govern.
The same triangle everywhere
Stringer length is pure Pythagoras — the same math as the roof pitch calculator one scale up, and the triangle calculator in general form. Deck stairs, basement runs and porch steps all reduce to this one right triangle with rules attached.
Reference guidance only — verify against your local building code.