The height from floor to floor in. The number of risers and treads, their sizes, the run and the stringer out, with the code checks.
Result
The stair takes 14 risers of 7 11/16 inches and 13 treads of 10 inches.
The stairs run 10' 10" along the floor, on a stringer about 14' 1" long, at 37.6 degrees.
Against the code
Riser 7 11/16 in: within the code's 7 3/4 inch maximum.
Tread 10 in: at least the code's 10 inch minimum.
Total rise 9' 0": within the 12' 7" one flight can climb.
14 risers: a handrail on at least one side.
The stair
Total rise
9' 0"
Each riser
7 11/16"
Each tread
10"
Total run
10' 10"
Stringer
14' 1"
Measure the total rise from the finished floor at the bottom to the finished floor at the top. The tread depth is measured nosing to nosing.
How a stair is worked out
Risers: divide the total rise by the tallest riser allowed and round up. A 9 foot rise is 108 inches, and 108 ÷ 7.75 = 13.9, so 14 risers.
Riser height: the total rise divided by the risers, so every step is the same: 108 ÷ 14 = 7.714 inches, about 7 11/16.
Treads: one fewer than the risers, because the top floor is the last step: 13.
Total run: the treads times the tread depth: 13 × 10 = 130 inches, 10' 10".
Stringer: the diagonal of the rise and the run, √(108² + 130²) ≈ 169.0 inches.
Risers = total rise ÷ tallest riser, rounded upTreads = risers − 1Stringer = √(total rise² + total run²)
What the code asks of a stair
Riser height: 7 3/4 inches at most (R311.7.5.1).
Tread depth: 10 inches at least, nosing to nosing (R311.7.5.2).
Even steps: the tallest riser and the deepest tread in a flight within 3/8 inch of the smallest.
Nosing: 3/4 to 1 1/4 inches, where the treads are under 11 inches deep (R311.7.5.3).
Headroom: 6 feet 8 inches at least (R311.7.2).
Width: 36 inches at least (R311.7.1).
One flight: 12 feet 7 inches of rise at most between floors or landings (R311.7.3).
Handrail: on at least one side of a flight with four or more risers, 34 to 38 inches high (R311.7.8).
These are the 2021 International Residential Code's rules for houses; the local building department enforces the edition it has adopted.
Common questions
How many stairs for an 8 foot 9 inch rise?
105 inches ÷ 7.75 = 13.5, so 14 risers of 7 1/2 inches and 13 treads.
What is the maximum riser height?
7 3/4 inches for a house, under the residential code (IRC R311.7.5.1).
What is the minimum tread depth?
10 inches, measured nosing to nosing (IRC R311.7.5.2).
How long is a stair stringer?
The diagonal of the total rise and the total run: the square root of the rise squared plus the run squared. Buy the board long enough for that plus the cuts at each end.
Walk the job. Send the bid.
The phone measures every room. BluMatrix writes the estimate line by line, with labor and materials at current prices for the ZIP code. 3 days free.
Measure the roof. Send the bid.
The roof from the address, the estimate line by line at current prices for the ZIP code, and the client signs online. 3 days free.
Walk the loss. Send the estimate.
The phone measures every room. BluMatrix writes the estimate line by line at current prices for the ZIP code, with the ESX file for Xactimate. 3 days free.
Scope it on the visit.
Every room measured on the phone, the estimate written line by line at current prices for the ZIP code, and an ESX file that opens in Xactimate. 3 days free.
Know what the job should cost.
Scan the rooms with your phone. BluMatrix writes the estimate line by line, with labor and materials at current prices for the ZIP code. 3 days free.