Stairs Stringer 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.
IRC R311.7.2 requires 6 ft 8 in (80 in) measured vertically from the nosing line.
Finished floor down to the underside of the ceiling, used to size the stairwell opening.
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
14
Tread depth used
10.0000 in
Total run
140.0000 in
Stringer length
179.2875 in
Stair angle
38.6598 deg
Stringer throat depth
5.2671 in
Stairwell opening needed
115.000 in
Comfort rule 2R + T
24.9333 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.
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 = 14; total run = 14 x 10 = 140 in
  3. Stringer = sqrt(112^2 + 140^2) = 179.28747864811976 in at 38.659808254090095 degrees
  4. Throat = 11.25 - (7.466666666666667 x 10) / sqrt(7.466666666666667^2 + 10^2) = 5.26710767515317 in
Checks against the limits enteredtable
Riser 7.467 in is within the 7.75 in maximum., Tread 10 in meets the 10 in minimum., Width 36 in meets the 36 in minimum., Nosing 0.75 in is within the 3/4 to 1 1/4 in range the IRC requires when the tread is under 11 in., Cut stringer keeps 5.267 in of throat, at or above the 3.5 in you required.

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