How long a board do I need for a stair stringer?
A 9-foot rise needs a 16-foot 2x12 — the sloped length is longer than either the rise or the run. The arithmetic, plus the throat check that decides whether a 2x12 is enough.
108" of rise over 11 ft 8 in of run gives a stringer 14 ft 8 13/16 in long — buy 16'.
Notched for 15 risers it leaves 5 7/16" of throat under the deepest notch, and this stair needs 4 stringers at 36" wide.
How that is worked out
- The stringer is the hypotenuse of the whole flight: the total rise on one side, the total run on the other.
- √(108² + 140²) = 14 ft 8 13/16 in corner to corner.
- Then round up to stock, allowing for the end cuts: 16'. A stringer cut a hair short is firewood, so this always rounds up.
Stringer length by total rise, at a 10" run per tread
| Total rise | Risers | Total run | Stringer length | Buy | Throat left |
|---|---|---|---|---|---|
| 96" (8 ft) | 14 | 10 ft 10 in | 13 ft 5 5/8 in | 15' | 5 5/8" |
| 105" (8 ft 9 in) | 15 | 11 ft 8 in | 14 ft 7 in | 16' | 5 1/2" |
| 108" (9 ft) | 15 | 11 ft 8 in | 14 ft 8 13/16 in | 16' | 5 7/16" |
| 114" (9 ft 6 in) | 16 | 12 ft 6 in | 15 ft 8 3/8 in | 17' | 5 7/16" |
| 120" (10 ft) | 17 | 13 ft 4 in | 16 ft 8 in | 18' | 5 1/2" |
| 126" (10 ft 6 in) | 18 | 14 ft 2 in | 17 ft 7 5/8 in | 19' | 5 1/2" |
| 132" (11 ft) | 19 | 15 ft | 18 ft 7 3/16 in | 20' | 5 9/16" |
Worth knowing
- The throat — what is left under the deepest notch — is the number that decides whether a 2x12 is enough. 5" of sound material is the usual minimum, and a deep run or a shallow riser eats into it fast.
- Cut one stringer, then use it as the template for the rest. Stringers marked independently will not match, and a tread that rocks is the result.
- The bottom of the stringer has to come down by the thickness of the tread stock, or the bottom riser ends up a full tread taller than the others — which is the riser-variation rule failed on the first step.
- 2021 IRC figures, and defaults rather than law. Your jurisdiction amends them and the building department decides.
Work out your own numbers
- Stair stringers
Divide the rise into even risers, lay out the notches, and check the result against the code.
- Board cut calculator
How many pieces of one length come out of a board of another, with the kerf charged between cuts and the leftover shown.
Related questions
- What size board do I need for a stair stringer?
- A 2x12 is the standard, because it is the only common dimensional stock wide enough to leave sound material under the notches. For length, take the sloped length of the flight and round up to stock — a 9-foot rise typically needs a 16-footer.
- How do I calculate stringer length?
- It is the hypotenuse of the whole flight: square the total rise, square the total run, add them and take the square root. For 108" of rise over 140" of run that is about 177", or 14'9" — then round up to the next stock length you can buy.
- How many stringers does a staircase need?
- Enough that the tread material spans between them without flexing — this site's convention (16" maximum stringer spacing) puts that at four for a 36" stair, the same count the worked example above computes, and more again for a wider stair or thinner tread stock. Spacing is set by what the tread carries, not by the stair width itself.