MathBench

Stair Stringer Calculator

Enter the total rise and get an even riser height, the number of treads, total run, and the stringer length to cut, checked against typical residential code limits.

Your stringer layout

—riser height
—risers
—treads
—total run
—stringer length
—2R + T comfort (24–25″)

How this calculator works

Give the calculator one number (the total vertical rise from lower finished floor to upper finished floor) and it works out the rest. It divides the rise by your maximum allowed riser to find how many steps are needed, then spreads the rise evenly so every riser is identical (uneven steps are both a trip hazard and a code violation). Tread count, total horizontal run, and the diagonal stringer length follow from there.

The tread depth and max riser fields default to common residential values (a 10½″ run per step and the IRC's 7¾″ riser cap), but both are editable, because deck stairs, commercial work, and local amendments all shift the numbers. The result panel shows the code checks explicitly.

The formula

Risers        = ceil(total rise ÷ max riser)
Riser height  = total rise ÷ risers
Treads        = risers − 1
Total run     = treads × tread depth
Stringer      = √(total rise² + total run²)

Rounding the riser count up is what keeps every riser at or under the limit. The division then makes them all equal. The stringer length is the hypotenuse of the rise-run triangle (Pythagorean theorem). The lumber must be at least that long before the plumb and level end cuts. Code limits referenced: IRC R311.7.5 (7¾″ max riser, 10″ min tread, ⅜″ max variation).

Worked example

Say your basement stairs have a total rise of 105 inches, with 10½″ treads and the 7¾″ code limit:

  1. Risers: 105 ÷ 7.75 = 13.5 → round up to 14 risers
  2. Riser height: 105 ÷ 14 = 7½″ exactly
  3. Treads: 14 − 1 = 13
  4. Total run: 13 × 10.5 = 136.5″ = 11′ 4½″
  5. Stringer: √(105² + 136.5²) = 172.2″ ≈ 14′ 4¼″. Buy 16-foot 2×12s

Check the comfort rule: 2 × 7.5 + 10.5 = 25½″, a touch over the 24–25″ ideal, typical for space-saving basement stairs.

Assumptions & tips

  • Drop the stringer. After layout, trim one tread thickness off the bottom of the stringer. Skip this and the first step is one tread thicker than the rest, the most common stringer mistake there is.
  • Account for finish floors before cutting. Tile at the top or a slab coating at the bottom changes the effective rise. Measure to finished surfaces, or add the flooring thickness where it's missing.
  • Use a framing square with stair gauges. Clamp the gauges at your riser and tread values and step the square down the 2×12: layout takes minutes and every notch is identical.
  • Mind the throat. The wood left behind the notches carries the load. Keep at least 5″ or use a third stringer for spans over 36″ wide. Engineered or dropped-notch stringers need their own design.
  • This sizes lumber. Permits size stairs. Stairways involve headroom, width, handrail, and guard rules beyond riser/tread math. For anything more than replacing an existing stringer, talk to your building department. Inspections on stairs are cheap insurance.

Frequently asked questions

What is the maximum riser height allowed by code?

The International Residential Code (IRC R311.7.5) caps risers at 7¾ inches for homes, and requires treads at least 10 inches deep. Commercial stairs under the IBC are stricter: 7-inch max risers and 11-inch treads. Local amendments vary (a few jurisdictions allow 8¼-inch risers), so confirm with your building department before cutting stringers.

How do I measure total rise correctly?

Measure vertically from the finished floor at the bottom to the finished floor at the top, not to the subfloor. If the finish flooring is not installed yet, add its thickness to whichever level is missing it. An error here shows up as one uneven step, and code allows no more than 3/8 inch of variation between the tallest and shortest riser.

What is the comfortable riser-tread ratio?

The classic rule: twice the riser plus the tread should land between 24 and 25 inches. A 7½-inch riser with a 10-inch tread gives 25, right at the comfortable edge. Very short risers with deep treads feel like a ramp. Tall risers with shallow treads feel like a ladder. The rule is a comfort guide, not a code requirement.

What lumber do I need for stringers?

Use 2×12s. After the riser-and-tread notches are cut, code requires at least 5 inches of solid wood (the "throat") remaining. A 2×12 with a 7½ × 10 notch leaves just about that, so narrower stock is not an option. Buy stringers a size longer than the calculated length so you can cut the level and plumb ends cleanly.

Sources

  1. 2021 International Residential Code, Section R311.7.5 — Stair treads and risers. International Code Council. The limits the results panel checks every layout against: riser height not more than 7¾ inches, tread depth not less than 10 inches, and no more than ⅜ inch between the tallest and shortest riser in a flight.
  2. IRC Code Handout #437: Stair Treads and Risers. City of Boise Planning and Development Services, February 2022. cityofboise.orgA building department's openly readable restatement of R311.7.5, including how riser height and tread depth are measured: useful for confirming the numbers this page defaults to.
  3. DCA 6: Prescriptive Residential Wood Deck Construction Guide, based on the 2015 IRC. American Wood Council, 2018. awc.orgRequires all stair stringers to be a minimum of 2×12, three cut stringers for a 36-inch-wide stair, and no more than 18 inches between stringers: the stringer stock and spacing advice in the tips. Its commentary analyses cut stringers at 5.1 inches of remaining depth for a 7.75-to-10 rise-and-run, which is where the 5-inch throat figure comes from.
  4. Guidelines for Stair Safety, NBS Building Science Series 120. J. Archea, B. L. Collins and F. I. Stahl, National Bureau of Standards (now NIST), 1979. nvlpubs.nist.govReports the stair-proportion rule 2r + t = 63 cm (24.8 in.), which the report credits to Grandjean (1973): the basis for the 2R + T comfort readout and its 24 to 25 inch target.
  5. 2021 International Building Code, Section 1011.5.2 — Riser height and tread depth. International Code Council. The stricter commercial limits quoted in the FAQ (7-inch maximum riser and 11-inch minimum tread), which differ from the residential defaults this calculator ships with.

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