Cómo funcionan las matemáticas

A staircase is the same right triangle repeated until you reach the top. Get one step right and they all come out right; get the math wrong and every step is a tripping hazard. Everything hangs on one measurement and one famous rule.

Total rise: the one measurement that matters

Total rise is the vertical distance from the finished surface of the lower floor to the finished surface of the upper floor. Measure to the top of the tile, hardwood, or carpet actually going down — not the subfloor. A half-inch of forgotten flooring changes every riser height in the staircase.

The 7-11 rule: comfort in two numbers

Legs like a riser (vertical face) of about 7 inches and a tread (the part you step on) of about 11 inches. Code caps risers at 7¾ inches and demands treads at least 10 inches deep, but code is the legal minimum — 7 and 11 feels effortless. The deeper comfort formula: two risers + one tread = 24 to 25 inches. Seven and eleven gives 25 — right on the money.

The formulas: dividing the rise

Number of risers = Total rise ÷ 7, rounded to a whole number

Actual riser height = Total rise ÷ Number of risers

Number of treads = Risers − 1 (the top "tread" is the upper floor itself)

Total run = Treads × Tread depth

Example: 38-inch total rise. 38 ÷ 7 = 5.43 → 5 risers; actual riser = 38 ÷ 5 = 7.6 inches (under the 7¾ max). Treads = 4 at 11 inches deep → 44-inch total run. Every step identical, because every riser came from the same division.

Stringers: the sawtooth backbone

Stringers are the notched 2×12s running diagonally under the steps — typically three per residential stair (both edges plus center) so treads don't flex. Each notch is one riser tall by one tread deep, laid out with a framing square. Code also demands 6'8" of headroom above every tread nosing — basement stairs fail inspections on headroom more than anything else.

Worked example: 38" rise

• Risers: 38 ÷ 7 = 5.43 → 5 risers at 7.6" each
• Treads: 4 at 11" deep; total run 44"
• Stringers: 3, cut from 2×12 stock
• Waste factor: one miscut stringer ruins a whole 2×12 — buy one extra board.

Cut one stringer, test-fit it, then use it as the template for the rest. Come for answers, leave with confidence — and take the stairs two at a time.