Stair Calculator
Risers = total rise ÷ 7 3/4 in (the IRC maximum), rounded up, and there is one tread fewer than risers. A 108 in floor-to-floor rise gives 14 risers of 7 11/16 in and 13 treads; with 10 in treads, that is 130 in of run.
Risers (steps up)
14 risers of 7 11/16 in
13 treads of 10 in
Estimate only. Check dimensions, loads and local code requirements with a qualified professional before you build.
- Exact riser height
- 7.714 in
- Total run
- 10 ft 10 in (130 in)
- Stringer length (along the nosings)
- 14 ft 1 in (169 in)
- Stair angle
- 37.6°
- IRC checks
- Riser, tread and flight rise within IRC limits
IRC limits used: riser ≤ 7.75 in, tread ≥ 10 in, flight rise ≤ 151 in. Local codes can differ.
How it works
Risers = total rise ÷ maximum riser height, rounded up
Riser height = total rise ÷ risers
Treads = risers − 1 · total run = treads × tread depth
Stringer (along the nosings) = √(total rise² + total run²)
Angle = arctan(riser height ÷ tread depth)
Assumptions
- A straight flight from floor to floor, where the upper floor acts as the last step (so there is one tread fewer than risers).
- IRC 2021 limits: riser at most 7 3/4 in (R311.7.5.1), tread at least 10 in (R311.7.5.2), one flight rises at most 151 in before a landing (R311.7.3). Many towns amend these values.
- The stringer length is the straight line along the nosings; the board you cut from is longer.
Worked examples
A 9 ft (108 in) floor-to-floor rise, 10 in treads
- 108 ÷ 7.75 = 13.9, rounded up to 14 risers
- 108 ÷ 14 = 7.714 in per riser (about 7 11/16 in)
- 13 treads × 10 in = 130 in of run
- √(108² + 130²) = 169 in of stringer, angle 37.6°
Result: 14 risers of 7 11/16 in, 13 treads, 10 ft 10 in of run.
Checked by the automated test “stairs — 108 in rise → 14 risers of 7.71 in, 13 treads, 130 in run”.
A 30 in deck stair, 7 1/2 in max riser, 11 in treads
- 30 ÷ 7.5 = 4 risers of exactly 7.5 in
- 3 treads × 11 in = 33 in of run
Result: 4 risers, 3 treads, 33 in of run.
Checked by the automated test “stairs — 30 in deck rise → 4 risers of 7.5 in, 3 treads, 33 in run”.
Stairs are an estimate — confirm with a licensed professional and your building department before you cut: stringer size, support and local amendments are outside this calculator.
Rounding risers and treads
- Risers always round up. 13.9 risers is 14 risers; rounding down would push every riser over the limit.
- Divide the rise evenly. The calculator shows the exact riser height (7.714 in for a 108 in rise) and the nearest 1/16 in for your layout square.
- Check the floor space. Thirteen 10 in treads already need almost 11 ft of run, plus a clear landing at the bottom.
Common mistakes
- Measuring to the subfloor. Flooring added later changes the top or bottom riser. On the 108 in stair, 3/4 in of flooring added upstairs turns the top riser into about 8 7/16 in, over the 7 3/4 in limit.
- Forgetting headroom. IRC R311.7.2 asks for at least 6 ft 8 in of headroom above the nosings; check it against the floor opening above.
- Assuming the model code applies as written. Some jurisdictions amend riser and tread limits; your building department has the final word.
Frequently asked questions
How do I calculate stair rise and run?
Measure the total rise from finished floor to finished floor. Divide it by the tallest riser you allow (7 3/4 in under the IRC) and round up to get the number of risers; divide the rise by that number for the exact riser height. The run is one tread fewer than risers, times the tread depth.
How long does a stair stringer need to be?
At least the diagonal along the nosings: √(rise² + run²). For a 108 in rise and 130 in run that is 169 in, about 14 ft 1 in. The board must be longer than that to allow for the top and bottom cuts.
What is the maximum stair riser height under the IRC?
7 3/4 in, under section R311.7.5.1 of the 2021 International Residential Code. Within one flight the tallest riser may not exceed the shortest by more than 3/8 in, so all risers should be equal.
Does this work for deck stairs?
Yes: enter the height from the ground or landing to the deck surface as the total rise. The City of Philadelphia's deck checklist applies the same IRC limits: treads at least 10 in, risers at most 7 3/4 in, stairs at least 36 in wide.
Sources
Formula, examples and sources checked on by the Yardstick Math team. How we check our formulas.
- 2021 IRC R311.7.5.1 Risers — International Code Council
- 2021 IRC R311.7.2 Headroom (6 ft 8 in minimum) — International Code Council
- IRC Deck-Only Plan Review Checklist (tread 10 in min., riser 7-3/4 in max.) — City of Philadelphia
- R311.7.3 Vertical rise (151 in between floor levels or landings) — International Code Council (California Residential Code edition)