Stair Stringer Calculator

How do you calculate stair stringers? Step by step

Everything starts from the total rise. Here is the full calculation for a 105″ rise with 10″ treads and risers capped at 7¾″ — the calculator’s own defaults, so you can type 105 into it and check every line.

1. Measure the total rise — finished floor to finished floor: 105″.
2. Count the risers. 105 ÷ 7.75 = 13.55; round up to 14 risers.
3. Find the riser height. 105 ÷ 14 = 7.5″ — every riser identical.
4. Count the treads. One fewer than the risers, because the upper floor is the last step: 14 − 1 = 13 treads.
5. Total run. 13 × 10″ = 130″ (10 ft 10 in).
6. Stringer length. √(105² + 130²) = 167.1″ (13 ft 11 in) of board along the nosing line, before end cuts.
7. Check it. 7.5″ is under the 7¾″ riser limit and 10″ meets the 10″ tread minimum; 2 × 7.5 + 10 = 25″ sits in the 24–25″ comfort window; and a 2×12 keeps 5.25″ at the throat (see below).

Why riser height is a division, not a choice

Stairs must land exactly on the upper floor, so riser height is always total rise ÷ number of risers — you pick the count, the height follows. Divide by the code maximum, round up, and every riser comes out identical and legal. A flight with one odd step at the top is the trip hazard building codes exist to prevent, which is why the 3/8″ variation rule gets measured.

From numbers to layout

• Set a framing square to riser × tread with stair gauges and walk it down the stringer — the calculator’s two numbers are exactly the square’s two legs.
• Drop the bottom riser by one tread-board thickness so the first step matches the rest after treads go on.
• Check the throat after marking: the wood left behind the notches carries the load.
• Dry-fit one stringer and check the top and bottom step heights in place before cutting its siblings.

IRC residential stair limits (R311.7)

These are the stair limits as written in R311.7 of the model code, before any state or local amendments:

Turn the first two rows into a layout rule: the fewest risers a rise can use is total rise ÷ 7.75, rounded up. A 105″ rise needs at least 14; a 30″ rise needs 4.

Check your jurisdiction before cutting. Fine Homebuilding’s 2024 stair-code article starts from the same 7¾″ and 10″ figures and points out that some government-amended codes allow risers of 8¼″ and even 9″. The calculator’s Max riser height field is editable for exactly that reason, and the inspector’s edition is the one that counts.

How long of a 2x12 do I need for a stair stringer?

Stringer length is the hypotenuse of the staircase triangle, so it grows with both rise and run. For a 105″ rise the minimum is 13.9 ft of 2×12. The table runs the same math for common rises, with 10″ treads and risers capped at 7¾″.

Treat the length as a minimum. It is the line along the nosings; the board also has to hold the plumb cut at the top and the seat cut at the bottom. In the 105″ example, a 14 ft board covers the 13.9 ft minimum with just 0.9″ to spare, which is not enough for the end cuts. Round up to the next length your yard stocks, and go one longer when the minimum lands close to a stock length.

The last column matters for decks. The AWC deck guide (DCA 6) limits a cut 2×12 stringer to about 6 ft of horizontal span between supports; past that, it says to shorten the span with a post under the stringer or an intermediate landing. Rises that need more than 6 ft of run are marked Yes. That is a deck-stair provision; interior stairs are supported by the framing around them and follow local code.

2x10 or 2x12 stair stringers?

Use 2×12s. A stringer is a beam with notches cut out of it, and the part that carries the load is the wood left behind the notch, the throat. The American Wood Council’s deck guide requires stringers of at least 2×12 and shows a minimum remaining depth of 5″ measured square to the board. (The IRC’s stair section, R311.7, sets riser and tread dimensions but, in the text we read, no stringer size or throat depth, so this rule comes from AWC.)

The throat is the board’s actual depth minus the notch depth, where notch depth is riser × tread ÷ √(riser² + tread²). At the code-maximum 7¾″ × 10″ notch that is 6.13″, and a 2×12 keeps 5.12″, matching the 5.1″ AWC uses for the same ratio in its commentary.

A 2×10 reaches 5″ only if the notch is shallower than 4.25″, which with a 10″ tread means risers under about 4.7″ — far below the 7¾″ code limit and the 7.5″ risers in the example. On ordinary stairs the 2×12 is the smallest board that works.

Count and spacing: for deck stairs, DCA 6 asks for at least three cut stringers on a 36″-wide stair, or cut and solid stringers no more than 18″ on center on wider ones. Pick straight stock, crown all the stringers the same way, and confirm the layout with a dry-fitted stringer before cutting the rest.

The comfort rules, and what the “27 rule” is

Code sets the limits; two stride rules tune the feel. 2 × riser + tread should land near 24–25″, and riser + tread near 17–18″. Fine Homebuilding puts the targets at 25″ and 18″ and notes that the code maximums of 7¾″ and 10″ give 17.75″ and 25.5″ — legal, but at the steep end. Your 105″ example scores 25″ and 17.5″. The 2R + T formula is usually credited to the 17th-century architect Nicolas-François Blondel.

What about the “27 rule”? It is not in the IRC’s stair provisions, and we found no standard that defines it. The one place that 27 appears as a requirement in the stair text we read is the minimum clear width at and below handrail height when handrails run on both sides (R311.7.1). Informal guides use the name for several unrelated rules, so if a source cites it, check what it means. For layout, use the code limits and the two comfort sums above.