Going from a floor-to-floor height to a finished staircase
Everything about a staircase's dimensions starts from one number: total rise, the exact vertical distance from the lower finished floor to the upper one. Pick a comfortable riser height, divide it into the total rise, and round to a whole number of steps — then divide the total rise by that whole number to get the exact riser height that makes every single step identical.
Number of risers = round(Total rise ÷ Target riser height)
Actual riser height = Total rise ÷ Number of risers
A 108-inch total rise with a 7-inch target works out to 108 ÷ 7 ≈ 15.4, rounded to 15 risers. Recalculating gives 108 ÷ 15 = 7.2 inches per riser — close to the target, and just as important, exactly the same for every step in the flight.
Why riser and tread size trade off against each other
A classic rule of thumb called 2R + T keeps stairs feeling natural to climb: twice the riser height plus the tread depth should land in the 24-25 inch range. It's a proxy for stride length — a taller riser means less horizontal room is needed per step, so the tread can be a little shallower without feeling cramped, and a shorter riser wants a deeper tread so the foot doesn't overreach.
2 × Riser + Tread = 24 to 25 inches
7.2 in riser: Tread ≈ 24.5 - (2 × 7.2) = 10.1 in
Most residential codes separately cap riser height at 7¾ inches and set a 10-inch minimum tread depth, so the 2R+T rule and the hard code limits usually agree with each other for ordinary stairs — it's steep, space-constrained stairs (like a compact basement or loft stair) where the two can pull in different directions.
Why uniform steps matter more than the exact riser number
People stop consciously watching their feet after the first couple of steps on a staircase, walking the rest of the flight on muscle memory built from those first steps. A single riser that's even half an inch taller or shorter than the rest is a common cause of trips, precisely because it breaks a rhythm the body has already stopped paying attention to. That's the real reason building codes are strict about riser uniformity within a single flight — more than any specific height being inherently "correct."
Stringer length and stair angle
The stringer is the diagonal board the treads and risers attach to, and its length is the hypotenuse of a right triangle formed by total rise and total run — solved with the Pythagorean theorem.
Stringer length = √(Total rise² + Total run²)
108 in rise, 144 in run: √(108² + 144²) = √(11,664 + 20,736) = 180 in
That same rise and run also determine the stair angle (the incline from horizontal), which most residential guidance keeps between about 30 and 35 degrees — steeper starts to feel like a ladder, shallower starts eating up more floor space than typical homes have to spare.
Related building calculations
For a concrete stair landing or footing at the base of a staircase, the concrete calculator works out the mix and volume needed.