Stair Stringer Calculator — Length, Cut Angle & Layout
Calculate stair stringer length, the exact rise and run per step, and the cut angle. Enter the total rise, and get the number of steps, stringer board length and layout dimensions — for deck stairs, basement stairs and landings.
How long does a stair stringer need to be?
It is the hypotenuse: √(total rise² + total run²). A 2.75 m rise over a 4.29 m run needs a 5.11 m stringer; in feet, a 9 ft rise over 14 ft needs about 16 ft 8 in. Order the next stock length up — a stringer cut short is firewood, and the offcut is useful.
How do I mark out the cuts?
Set a framing square to the riser on one arm and the tread on the other, then step it along the board — every triangle is identical, which is the point of fixing the riser height first. Then drop the bottom cut by one tread thickness, or the first step ends up that much taller than the rest.
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How the stringer is calculated
- 1Risers: total rise ÷ target riser height (≈ 175 mm / 7 in), rounded to whole risers
- 2Actual riser: total rise ÷ riser count — every step must be equal within 5 mm, under ¼ in
- 3Tread run: comfort rule 2 × riser + tread ≈ 600–640 mm, or 24–25 in
- 4Total run: (risers − 1) × tread run
- 5Stringer length: √(total rise² + total run²) — add ~300 mm (12 in) for bearing at each end
- 6Cut angle: arctan(rise ÷ run), typically 32–38°
Worked example
Deck stairs: total rise 1.05 m (41½ in) from grade to deck. Target riser 175 mm, about 7 in.
6 risers of exactly 175 mm (6⅞ in), 5 treads of 260 mm (10¼ in). Total run: 1.30 m (51 in). Stringer: √(1.05² + 1.30²) = 1.67 m — 5 ft 6 in — cut from a 2.0 m board. Angle: 38.9°.
Frequently asked questions
How long a stringer do I need for an 8-foot rise?
A 2.44 m rise needs 14 risers of 174 mm. With 265 mm treads the run is 3.45 m, so the stringer is √(2.44² + 3.45²) = 4.22 m — cut it from a 16 ft (4.9 m) board.
What lumber do I use for stair stringers?
Cut stringers come from 2×12 (47×286 mm) structural-grade stock — smaller boards leave too little wood (the "throat") behind the notches. Keep at least 90 mm (3½ in) of uncut depth, and use treated lumber outdoors.
How many stringers do stairs need?
Three for a standard 900 mm (36 in) wide staircase — one each side plus centre. Two only for narrow stairs with thick treads. Wider stairs add a stringer per ~400 mm of width.
Can risers be different heights?
No — building codes limit the variation between the tallest and shortest riser (typically 5–10 mm, or ¼–⅜ in) because uneven steps cause falls. That's why you divide the total rise into equal risers rather than using a fixed 175 mm.
What is the maximum stair angle?
Comfortable stairs run 30–38°. Most codes cap private stairs around 42° via the max riser / min tread limits. Steeper than that is ladder territory and not code-compliant as a staircase.