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C-01 · Carpentry

Stair stringer calculator

Enter the total rise to get the number of steps, riser and tread sizes, stringer length and a dimensioned cut diagram, checked against the IRC residential stair rules.

in

Finished surface below to finished deck or floor above. Fractions OK: 37 1/2.

in
in
in
in

Lowest point of the ceiling or beam above, measured straight up from the line of the nosings.

Result

5 risers

7 1/2″ rise · 4 treads at 10 1/4″

Total run
41″
Stringer length
50 3/16″
Angle
36.2°
Throat (2x12)
5 3/16″
Bottom riser after drop
6 1/2″

Code check · IRC 2021

  • Riser ≤ 7 3/4″R311.7.5.1
  • Tread ≥ 10″R311.7.5.2
  • Throat ≥ 5″AWC DCA 6
  • Unsupported run ≤ 6′-0″AWC DCA 6
  • 3/4″–1 1/4″ nosing (tread < 11″)R311.7.5.3
  • Headroom ≥ 6′-8″ (enter to check)R311.7.2
  • Handrail 34–38″ high (4+ risers)R311.7.8
  • Guards on open sides; open risers stop a 4″ ballR312.1.1
Cut diagram · 2x12 stringer
7 1/2″10 1/4″TOTAL RISE 37 1/2″TOTAL RUN 41″L = 50 3/16″36.2°THROAT 5 3/16″DROP 1″

How the layout is calculated

Divide the total rise by the tallest riser you'll allow and round up to get the number of risers. Every riser is then the same height. There is always one fewer tread than risers, because the deck or floor above is the last step.

Formula

Risers
n = ⌈total rise ÷ max riser⌉
Riser height
r = total rise ÷ n
Total run
(n − 1) × tread depth
Stringer length
(n − 1) × step − drop × r ÷ step
Angle
arctan(r ÷ tread depth)
Throat
board depth − r × t ÷ step

⌈ ⌉ means round up. Tread depth (t) is the run of each step, measured from one nosing to the next; step = √(r² + t²) is the diagonal of one step. The stringer length is measured along the board edge, from the bottom front corner to the end of the top seat. The throat is the wood left between the inside corner of each notch and the bottom edge of the board.

Worked example

A deck sits 37 1/2″ above the patio. 37.5 ÷ 7.75 = 4.84, so round up to 5 risers of exactly 7 1/2″. 4 treads at 10 1/4″ give a total run of 41″ at 36.2°. Each step's diagonal is 12.701″, so the 4 notches take up 50 13/16″ of board; cutting 1″ off the bottom, so the first step matches the others once the tread is on, brings the stringer to 50 3/16″. An 8 ft 2x12 covers it, and the notches leave a 5 3/16″ throat.

IRC stair rules

  • Risers no taller than 7 3/4″, measured between the leading edges of the treads (R311.7.5.1).
  • Treads at least 10″ deep, nosing to nosing (R311.7.5.2). Below 11″, each tread needs a nosing of 3/4″ to 1 1/4″ (R311.7.5.3).
  • In one flight the tallest riser may not beat the shortest by more than 3/8″, and the same goes for treads. That is why the bottom of the stringer is cut down by the tread thickness.
  • Headroom of at least 6′-8″, measured straight up from the line of the nosings (R311.7.2).
  • No more than 12′-7″ of rise in one flight (R311.7.3), and a landing at least 36″ deep at the top and bottom (R311.7.6).
  • A handrail on at least one side once there are 4 or more risers, 34″ to 38″ above the nosings (R311.7.8).
  • Guards on open sides more than 30″ above the ground (R312.1.1). Open risers that high must not let a 4″ ball through (R311.7.5.1).

The 2018 IRC has the same limits under the same section numbers. The 2024 IRC keeps the limits and moves the stair rules to R318.7 and guards to R321.

Cutting the stringer

Lay out each notch with a framing square set to the riser height on one arm and the tread depth on the other. The seat of each notch carries a tread, so take the tread thickness off the bottom riser only; the top riser is set by where the stringer meets the deck framing.

That drop assumes the stringer stands on the finished surface, such as a concrete pad. If it stands on a subfloor that gets finish flooring later, cut off the tread thickness less the finish thickness. Measure the total rise from finished floor to finished floor either way.

For deck stairs, the American Wood Council's deck guide (DCA 6) asks for 2x12 stringers with at least 5″ of throat, cut stringers no more than 18″ apart (at least 3 of them), and no more than 6′-0″ of horizontal span before a post or landing. A solid (uncut) stringer can span 13′-3″. The guide also wants an intermediate landing once the stairway rises more than 12′-0″, a little stricter than the IRC.

Assumptions

  • A straight flight with cut stringers, the same finished floor material at the top and bottom, and level ground.
  • The stringer length is the board the cut stringer takes up, from the bottom front corner to the end of the top seat. Buy the next standard length up, and allow extra if the stringer runs past the top seat to hang on the deck framing.
  • The span check uses the total run as the horizontal span; the guard note follows DCA 6, which calls for guards once the total rise is 30″ or more.

Local codes vary and can be stricter than the IRC. Check with your building department before you build.

References

  • ICC, International Residential Code 2021: R311.7 stairways (R311.7.2 headroom, R311.7.3 vertical rise, R311.7.5 treads, risers and nosings, R311.7.6 landings, R311.7.8 handrails), R312.1 guards.
  • ICC, International Residential Code 2024: R318.7 stairways, R321 guards.
  • American Wood Council, DCA 6: Prescriptive Residential Wood Deck Construction Guide (2015 IRC edition): stair requirements, Figures 28–30.
  • M. Dawson, “Better Stair Stringer Layout,” JLC Deck Builder, 2024: stringer length from the step diagonal, bottom drop.

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