Deck Stair Calculator

Finished floor to finished floor, measured vertically.
Leave blank to use the fewest risers that stay within the maximum riser height.
IRC R311.7.5.1 sets 7 3/4 in for dwellings. Commercial and some state codes are lower.
Nosing to nosing. Leave blank to use the minimum tread depth below.
IRC R311.7.5.2 sets 10 in for dwellings.
Actual dressed width of the stringer stock. A 2x12 is 11 1/4 in.
Least remaining depth behind the notch that your code or engineer requires on a cut stringer.
Riser height
7.4667 in
Stair Calculator
Risers
15
Treads
15
Tread depth used
11.0000 in
Total run
165.0000 in
Stringer length
199.4217 in
Stair angle
34.1682 deg
Stringer throat depth
5.0721 in
Stairwell opening needed
135.536 in
Comfort rule 2R + T
25.9333 in
Worked out from 2021 International Residential Code Section R311.7, Stairways: R311.7.1 minimum width 36 in, R311.7.2 minimum headroom 6 ft 8 in, R311.7.5.1 maximum riser 7 3/4 in, R311.7.5.2 minimum tread depth 10 in, R311.7.5.3 nosing 3/4 in to 1 1/4 in where tread depth is less than 11 in, and the 3/8 in maximum variation between the largest and smallest riser or tread in a flight and 3 other sources.
2R + T is 25.933 in, outside the 24-25 in band that walks comfortably. The flight is legal if the checks pass, but it will feel steep or shallow.
Stair dimensions are life-safety requirements enforced by the building code your jurisdiction has adopted, and local amendments are common. The limits here are pre-filled with the 2021 IRC values for one- and two-family dwellings; confirm the governing code and edition with your building department, and have the design reviewed before you cut a stringer.

How this is worked out

4 steps
  1. Risers = ceil(112 / 7.75) = 15; riser height = 112 / 15 = 7.466666666666667 in
  2. Treads = 15; total run = 15 x 11 = 165 in
  3. Stringer = sqrt(112^2 + 165^2) = 199.42166381815193 in at 34.16818532502535 degrees
  4. Throat = 11.25 - (7.466666666666667 x 11) / sqrt(7.466666666666667^2 + 11^2) = 5.072135587418261 in
Checks against the limits enteredtable
Riser 7.467 in is within the 7.75 in maximum., Tread 11 in meets the 10 in minimum., Width 36 in meets the 36 in minimum., Tread is 11 in or deeper, so the IRC does not require a nosing., Cut stringer keeps 5.072 in of throat, at or above the 3.5 in you required.

Results are general information, not financial, tax, legal, medical or engineering advice.