BuildCalc Guides · Stairs

How to Calculate Stair Stringers

Stair layout is the most code-loaded carpentry job most DIYers will ever tackle. Here is the math, the IRC limits, and a worked example for a typical 9 foot floor-to-floor rise.

The math

Every stair layout starts from a single measurement: the total rise from finished floor to finished floor. Everything else follows.

Number of risers = total rise ÷ target riser, rounded to a whole number. Aim for a target between 7.25″ and 7.5″.
Riser height = total rise ÷ number of risers (exact). This is what you mark on the stringer.
Number of treads = risers − 1. The top "tread" is the upper floor.
Tread depth = total run ÷ treads. If you have a fixed total run, this is locked. If not, pick a target (10″ minimum, 10.5–11″ is typical).
Stringer length = √(rise² + run²) — the diagonal hypotenuse. This is the lumber length you need to buy.
Angle = arctan(rise ÷ run). 30°–37° is the comfort band.
Bottom riser cut = riser height − tread thickness. Cutting the bottom of the stringer shorter by one tread thickness is what keeps every finished step equal once the treads sit on top.

IRC R311.7 in plain English

The International Residential Code section that governs stairs in houses is R311.7. The numbers that show up on every inspection:

Max riser height: 7-3/4″. Hard limit. Any layout above this fails.
Min tread depth: 10″, measured between the nosings. (Open-riser stairs are allowed to cheat the math, but most inspectors will still want 10″ of walking surface.)
Riser uniformity: 3/8″ max difference between the largest and smallest riser in a single flight. This is why a precise layout matters — uneven steps trip people.
Headroom: 6 ft 8 in measured plumb above the tread nosing. Easy to miss when framing a finished ceiling.
Comfort guideline: 2R + T between 24″ and 25″. Not a code limit, but a long-standing rule of thumb that produces a stair people enjoy using.

Worked example — 9 foot rise

A 9 foot floor-to-floor rise (108 inches) is one of the most common deck-to-grade or basement runs. With a 7.5″ target riser and a 10.5″ target tread:

108 ÷ 7.5 = 14.4 → round to 15 risers.
108 ÷ 15 = 7.20″ riser height (well under the 7.75″ max).
Treads = 15 − 1 = 14 treads.
Total run = 14 × 10.5 = 147″ (12 ft 3 in).
Stringer = √(108² + 147²) = √33 273 = ~182.4″ (15 ft 3 in). Buy 16 ft 2×12 stock.
Angle = arctan(108 / 147) = 36.3°. Within the 30°–37° comfort band.
2R + T = 14.4 + 10.5 = 24.9″ — right in the 24–25″ comfort window.
With 1″ tread thickness, bottom riser cut = 7.2 − 1 = 6.2″.

Laying it out cleanly

Clamp stair gauges to a framing square at the riser and tread marks. The gauges guarantee every cut you scribe matches every other one — no measure-and-mark drift down the length of the 2×12.
Cut the bottom riser short by exactly one tread thickness. The treads then bring every finished step back up to the same height.
Plan your attachment at the top before you cut anything — hanging the stringer off a rim joist usually means a notch at the top, while landing on a top plate or LVL means a flat cut.

Calculate for your stairs

BuildCalc's stair calculator turns one measurement — your total rise — into a complete cut list with riser height, tread depth, stringer length, angle and the bottom riser cut. Every layout is checked live against IRC R311.7.

Open the stair calculator →

FAQ

What is the maximum riser height per code?+

The International Residential Code (IRC R311.7.5) sets a maximum riser height of 7-3/4 inches for residential stairs. Any layout above that fails inspection. BuildCalc flags it automatically.

Is 10 inches really the minimum stair tread depth?+

Yes — IRC R311.7.5 requires a 10 inch minimum tread depth, measured between the nosings. Deeper treads are more comfortable; the calculator warns you if the layout falls below 10 inches.

What is the bottom riser cut, or stringer drop?+

Once finished treads are installed, each tread adds its own thickness on top of every step. To keep every finished step the same height as the first, the bottom of the stringer is cut shorter by exactly one tread thickness. That offset is called the bottom riser cut, or "dropping the stringer."

How do I keep every riser exactly the same height?+

Total rise divided by the number of risers gives the exact riser height — they will all be the same on paper. Real-world variance comes from layout and saw work: clamp stair gauges to a framing square at the riser-and-tread marks, scribe every notch from the same gauges, and recheck against the saw blade before each cut. IRC allows at most 3/8 inch difference between the largest and smallest riser in a flight.

What stair pitch is comfortable?+

Most comfortable stairs land between 30 and 37 degrees from horizontal. Steeper than about 37 starts to feel like a ladder; shallower than 30 eats a lot of floor space. The classic comfort rule is that twice the riser height plus the tread depth (2R + T) should be between 24 and 25 inches.

What length lumber do I need for a stringer?+

Stringer length is the diagonal — the square root of total rise squared plus total run squared. A 9 foot rise with a 12 foot 3 inch run works out to about 183 inches, so you would buy 16 foot 2x12 stock (and cut once). For a 9-or-12 foot run you can usually get away with 14 foot 2x12.

Related guides

How many bags of concrete for a 10×10 slab? — for the stair landing pad or footing.
How much paint for a 12×12 room? — finishing the basement at the bottom of the stairs.
How many bundles of shingles for 1,000 sq ft? — exterior stairs and the porch roof above them.