Stair Calculator
Rise to code-compliant flight — risers by the 7¾-in IRC law, even risers to the ⅜ inch, stringer length and the board to buy.
Stair Calculator
Results recalculate instantly on every keystroke. Nothing you type is transmitted.
What this result does not account for
- Straight flights — winders and spirals are their own geometry.
- No landing take-off; split tall flights yourself.
- Finish-floor thickness assumed included in the rise.
In short: A 105-in floor-to-floor rise: 14 risers at exactly 7.5 in (ceil 105 ÷ 7.75), 13 treads at 10 in, 130 in of run, a 167.1077-in stringer — 13.93 ft, so buy 14-ft 2×12 stringers, three for a 36-in stair. The 2R+T lands on 25.0, dead center of the comfort rule.
Formula
risers = ⌈total rise ÷ 7.75⌉ — riser = rise ÷ risers, exact
treads = risers − 1; run = treads × tread
stringer = √(rise² + run²)
comfort: 2R + T = 24-25 in; θ = atan(rise ÷ run)
[('7¾ in', 'IRC max riser (R311.7.5.1)'), ('10 in', 'IRC min tread (R311.7.5.2)'), ('⅜ in', 'allowed riser-to-riser variance — exact division beats it'), ('2×12', 'stringer stock; buy the next standard length up')]
Worked Example
- Measure finished floor to finished floor — the total rise.
- Divide by 7.75 and round up for the riser count.
- Divide exactly for the riser each layout marks.
- Multiply treads by tread depth for the run; Pythagoras for the stringer.
- Buy the next standard 2×12 length; three stringers at 36 in.
105-in rise, 10-in treads: 14 risers at 7.5 exact, 13 treads, 130-in run, stringer 167.1077 in = 13.93 ft → 14-ft 2×12s × 3; 2R+T = 25.0; angle 38.93° — legal everywhere, a touch steep to the comfort line.
Strengths & Limits Of This Model
Where this engine is strong
- Exact even risers — the ⅜-in law by construction
- Stringer to the fourth decimal plus the board to buy
- Comfort (2R+T, angle) shown next to code, honestly
Where it stops
- Straight flights only
- No tread overhang or nosing model
Practical Use Cases
Deck stairs
Same IRC law outdoors in PT lumber.
Basement flights
Low-rise legs under 7¾.
Framing layouts
Riser marks to the third decimal.
Stringer orders
The board length before the yard run.
Remodel checks
Existing stairs measured against code.
Methodology & Editorial Standards
Risers come from ceil(rise ÷ 7.75) so no riser can exceed the IRC cap, then the riser height is the EXACT quotient — uniformity is the ⅜-in law, and exact division is the only way to keep it. Treads are risers − 1; run = treads × the chosen depth (10-in floor enforced); stringer = √(rise² + run²), bumped to the next standard board and counted three-per-36-in. Zero rise, rises past 240 in, treads outside 10-14 and widths under 36 are refused.
Computation runs in IEEE-754 double precision at full internal precision; rounding to two decimal places occurs strictly at the display layer, so no cumulative drift enters the result. All monetary outputs use accounting presentation — grouped thousands, two decimals, negatives in parentheses — so figures can be transcribed directly into a model or working paper. Division-by-zero and out-of-domain inputs return an em-dash rather than a misleading number.
This engine was reconciled against an independent reference implementation and hand-verified for the worked example above before release. Our full five-stage review process is published on the About Us page.
Disclaimer. This calculator is provided for informational and modelling purposes only and does not constitute financial, tax, legal, medical, or engineering advice. Verify all figures with a qualified professional before acting on them.
Stair Calculator — 8 Expert FAQs
8 analyst-written answers to the questions practitioners actually ask — optimised for voice and answer-engine retrieval.
How do I calculate the number of risers?
Divide the total rise by the 7¾-in code maximum and round UP — ceil(105 ÷ 7.75) = 14. Then each riser is the rise divided evenly: 105 ÷ 14 = 7.5 in, the same on every step.
What is the 2R + T rule?
Twice the riser plus the tread should land between 24 and 25 inches — the stride the leg expects. 2 × 7.5 + 10 = 25.0 is textbook. Outside the band stairs feel cramped or strung out.
Why is there one fewer tread than risers?
The top floor is the last tread. N risers lift you through N rises but only N−1 treads are hung — 14 risers, 13 treads, 130 in of run at 10-in treads.
How long is the stringer?
The Pythagorean diagonal: √(105² + 130²) = 167.1077 in ≈ 13.93 ft. Buy the next standard length — a 14-ft 2×12 — and let the yard keep the corner offcuts.
How many stringers does a stair need?
Three under a 36-in stair — one each side plus a carrier in the middle; wider stairs add one per 16 in of width beyond that.
What headroom and width does code require?
6 ft 8 in of headroom above the nose line and 36 in of clear width minimum, with a handrail once the flight hits four risers and a guard where the drop exceeds 30 in.
Do deck stairs follow the same math?
Yes — same IRC caps outdoors. Builders often hold outdoor risers a touch shallower for ice and mud, but the geometry and the stringer law are identical.
What rise needs a landing?
This page refuses single flights past 240 in of rise — a 20-foot climb without a landing is a fall ladder, not a stair. Split the rise and compute each leg separately.