WoodCalc Pro

Stair Calculator

Enter the total rise and your target step size. You get the riser count, exact riser height, stringer length and angle, drawn to scale and checked against the 2021 IRC.

Measurements (inches)

Finished floor to finished floor. Feet OK: 9'
7–7½" is comfortable
Nosing to nosing, ≥ 10"
For headroom opening

Risers

14× 7 11/16"

Treads
13 × 10"
Exact riser
7.714"
Total run
10′ 10"
Angle
37.6°
Stringer length
14′ 1"
Buy stringers
4 × 16 ft
Throat left
5 1/8"
Headroom opening
≥ 9′ 8 11/16"
  • Riser 7.714" ≤ 7¾"
    IRC R311.7.5.1: maximum riser height 7¾ in.
  • Riser ≥ 4"
    IRC R311.7.5.1: risers must be at least 4 in.
  • Tread run 10" ≥ 10"
    IRC R311.7.5.2: minimum tread depth 10 in, nosing to nosing.
  • Nosing 1" between ¾" and 1¼"
    IRC R311.7.5.3: nosing required where tread depth is under 11 in with solid risers.
  • Rise between landings 108.0" ≤ 151"
    IRC R311.7.3: a single flight may not rise more than 12 ft 7 in without a landing.
  • Stair width 36" ≥ 36"
    IRC R311.7.1: 36 in clear width above the handrail height.
  • Stringer throat 5.14" ≥ 3½"
    Common framing practice (and many span guides): keep at least 3½ in, ideally 5 in, of solid wood below the notches.
  • Comfort: 2R + T = 25.43" (aim 24–25")
    Blondel's rule of thumb for a natural stride; not a code requirement.

How to lay out a stringer with a framing square

Your stringer, drawn to scale from the numbers above. Step through the four layout steps and watch where the framing square goes.

Clamp stair gauges (or tape) on a framing square: 7 11/16" on the tongue (short leg) for the rise and 10" on the body (long leg) for the run.

14 risers × 7 11/16" · 13 treads × 10" · bottom riser cut to 6 11/16"

How the stair math works

  1. Risers = total rise ÷ target riser, rounded up. 108" ÷ 7.5" → 14 risers.
  2. Exact riser = total rise ÷ risers = 7.714" (≈ 7 11/16").
  3. Treads = risers − 1, because the upper floor is the last step.
  4. Total run = treads × tread run.
  5. Stringer length = √(total rise² + total run²).
  6. Angle = arctan(riser ÷ run).

Measure the total rise at the spot where the stair will land, not at a wall: floors are rarely level, and a 1/2" error spreads over every step. If the finished flooring is not down yet, add its thickness at the top and bottom.

For every code rule in one place, including handrails, guards, headroom and winders, see the IRC stair code checker.

Ask the shop

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Questions people ask

How do I calculate the number of stairs?
Measure the total rise from finished floor to finished floor in inches and divide by a target riser height (7" to 7½" is comfortable). Round up to a whole number: that is the number of risers. The number of treads is one fewer, because the upper floor acts as the last tread. Divide the total rise by the number of risers for the exact riser height.
What is the maximum riser height under the IRC?
The 2021 IRC (R311.7.5.1) allows a maximum riser of 7¾" and a minimum tread depth of 10" (R311.7.5.2). Risers within a flight may not vary by more than 3/8" from the tallest to the shortest. Commercial stairs under the IBC are stricter: 7" maximum riser and 11" minimum tread.
How long does a stair stringer need to be?
The stringer length is the hypotenuse of the total rise and total run: √(rise² + run²). Buy a board at least one step longer than that to allow for the top and bottom cuts, then round up to the next standard length (8, 10, 12, 14, 16 ft).
What size lumber for stair stringers?
Use 2×12s for sawn (notched) stringers. After cutting a 7½" riser and 10" tread, a 2×12 (11¼" actual) leaves about 5" of throat, which is what most span guides want. The IRC does not set a stringer size; deck guides such as AWC DCA 6 limit sawn stringers at 16" on center to about 6 ft of horizontal span without mid-support.
Why is the bottom riser shorter?
The stringer is cut so every finished step is equal. Treads add height to each step, so you trim the tread thickness off the bottom of the stringer ("dropping the stringer"). Otherwise the first step would be taller than the rest, and the last one shorter.
How many stringers do I need?
Space stringers no more than 16" on center for 5/4 or 2× treads (12" for composite treads, per most manufacturers). A 36" wide stair needs three stringers; a 48" stair needs four.
What is the best stair angle?
Residential stairs are typically 30° to 37°. The IRC maximum (7¾" riser, 10" tread) works out to about 37.8°. Below about 30° a stair starts to feel like a ramp that trips you up; above 38° it is getting ladder-like.

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