🪜 How to Calculate Stair Stringers

What a Stringer Is

A stringer is the diagonal, sawtooth-cut 2x12 that carries the treads and risers of a staircase. Cutting one accurately comes down to four numbers: how many steps, how tall each riser is, how deep each tread is, and how long the board needs to be.

The Stair Stringer Formula

• Number of risers = total rise ÷ 7.5 in, rounded to a whole number.
• Riser height = total rise ÷ number of risers (keep it at or below the 7.75 in code max).
• Number of treads = risers − 1.
• Total run = treads × tread depth (usually 10–11 in).
• Stringer length = √(rise² + run²) — the diagonal of the whole run.

Worked Example: 9-Foot Floor-to-Floor

Say your total rise is 108 inches (9 ft) and you want a 10.5 in tread:

• Risers = 108 ÷ 7.5 = 14.4 → 14 risers
• Riser height = 108 ÷ 14 = 7.71 in (under the 7.75 in max ✓)
• Treads = 14 − 1 = 13 treads
• Total run = 13 × 10.5 = 136.5 in
• Stringer length = √(108² + 136.5²) = ≈ 174 in (14.5 ft) — buy a 16 ft board

Marking the Cuts With a Framing Square

Clamp two stair gauges to a framing square — one at your riser height on the narrow tongue, one at your tread depth on the wide blade. Then:

• Step it down the board: trace the riser and tread for each of the 14 steps, keeping the gauges tight to the edge.
• Top plumb cut: square off the top so the stringer meets the header vertically.
• Bottom level cut: cut the bottom flat so it sits on the landing.

Common Mistakes

• Forgetting the bottom drop — the number one stair inspection failure.
• Uneven risers — code allows only 3/8 in variation between the tallest and shortest riser.
• Too little throat — leave at least 3.5 in of solid wood behind the notches; that's why you use a 2x12, not a 2x10.
• Cutting all stringers first — cut one, test-fit it, then trace the rest from it.

Frequently Asked Questions

How do you calculate a stair stringer length?

Stringer length is the diagonal of the staircase: the square root of the total rise squared plus the total run squared. For a 108-inch rise and a 130-inch run, the stringer is about 169 inches, and you would buy the next standard board length up.

What is the formula for stair stringers?

Number of risers = total rise ÷ 7.5, rounded. Riser height = total rise ÷ number of risers. Total run = (risers − 1) × tread depth. Stringer length = √(rise² + run²).

How do you mark stair stringers with a framing square?

Clamp stair gauges to the framing square at your riser height on the tongue and your tread depth on the blade. Step the square down the board, tracing the riser and tread for each step, then square off the top plumb cut and bottom level cut.

What is the bottom drop on a stair stringer?

Subtract one tread thickness from the bottom riser cut so the finished first step ends up the same height as the rest. Skipping this makes the bottom step too tall.

How many stringers do I need?

Space stringers no more than 18 inches apart for 2x wood treads, or 12 to 16 inches for composite. A standard 36-inch stair uses 3 stringers.