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

  1. The stringer is the hypotenuse of the whole flight: the total rise on one side, the total run on the other.
  2. √(108² + 140²) = 14 ft 8 13/16 in corner to corner.
  3. 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

Stringer length by total rise, at a 10" run per tread
Total riseRisersTotal runStringer lengthBuyThroat left
96" (8 ft)1410 ft 10 in13 ft 5 5/8 in15'5 5/8"
105" (8 ft 9 in)1511 ft 8 in14 ft 7 in16'5 1/2"
108" (9 ft)1511 ft 8 in14 ft 8 13/16 in16'5 7/16"
114" (9 ft 6 in)1612 ft 6 in15 ft 8 3/8 in17'5 7/16"
120" (10 ft)1713 ft 4 in16 ft 8 in18'5 1/2"
126" (10 ft 6 in)1814 ft 2 in17 ft 7 5/8 in19'5 1/2"
132" (11 ft)1915 ft18 ft 7 3/16 in20'5 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.