Stair Calculator
With total rise 108 inch, target riser height 7.5 inch, tread depth 10 inch, stair comes to 7 11/16 in — actual riser height. It is reached in 6 steps, the last of which is 108 / 14, and each one is printed on the page with its numbers filled in. The formula is the one published by International Residential Code R311.7, not an approximation fitted to it.
Riser height, tread count, total run and stringer length from a total rise — checked against the code limits.
Formula and sources checked · How we check
Total rise 108 inch, Target riser height 7.5 inch, Tread depth 10 inch
7 11/16 in
Actual riser height for the example below. Editing a field recomputes the calculator below; this figure holds the answer the page was loaded with.
It is written into the HTML rather than drawn by a script, so a search engine reading this page without running JavaScript still finds an answer.
- Number of risers
max(round(108 / 7.5), 1)14 risers- Actual riser height
108 / 147.714 in- Number of treads
14 - 113 treads- Total run
13 * 10130 in- Stringer length
sqrt(pow(108, 2) + pow(130, 2))169.009 in- Stair angle
atan(108 / 130) * 180 / pi39.719 °
Worked example
A 9 ft rise divides into 14 risers of 7 11/16 in — just inside the 7 3/4 in cap. That gives 13 treads, a 130 in total run and a 39.7° stair. Try 15 risers if the run has to fit a shorter opening.
How to work it out yourself
- 1.Measure the total rise from finished floor to finished floor — not from subfloor, or every riser will be wrong by the flooring thickness.
- 2.Divide the total rise by your target riser height and round to the nearest whole number. That is the riser count.
- 3.Divide the total rise by that count for the actual riser height. It must be 7 3/4 in or less, and every riser must match within 3/8 in.
- 4.Treads are always one fewer than risers. Multiply treads by tread depth for the total run, and check it fits the opening.
- 5.The stringer length is the diagonal of rise and run. Buy a board longer than that to allow for the cuts.
Riser height and run by total rise
| Total rise (inch) | Actual riser height | Number of risers | Total run |
|---|---|---|---|
| 84 | 7 5/8 in | 11 risers | 100 in |
| 90 | 7 1/2 in | 12 risers | 110 in |
| 96 | 7 3/8 in | 13 risers | 120 in |
| 102 | 7 5/16 in | 14 risers | 130 in |
| 108 | 7 11/16 in | 14 risers | 130 in |
| 114 | 7 5/8 in | 15 risers | 140 in |
| 120 | 7 1/2 in | 16 risers | 150 in |
At a 7.5 in target with 10 in treads. Total rise is in inches — 96 in is a standard 8 ft floor-to-floor.
The formula
- Number of risers
max(round(108 / 7.5), 1) - Actual riser height
108 / 14 - Number of treads
14 - 1 - Total run
13 * 10 - Stringer length
sqrt(pow(108, 2) + pow(130, 2)) - Stair angle
atan(108 / 130) * 180 / pi
Source: International Residential Code R311.7 — stairways, American Wood Council — residential construction guides
Questions people actually ask
- Why must every riser be the same height?
- People climb from muscle memory after the first two steps. The IRC allows no more than 3/8 in variation across a flight because a single odd riser is the classic trip. Divide the total rise evenly and accept whatever height it lands on.
- What are the code limits?
- IRC R311.7: maximum riser 7 3/4 in, minimum tread depth 10 in, minimum headroom 6 ft 8 in, minimum width 36 in. Commercial stairs under the IBC are stricter at 7 in and 11 in.
- Is the stringer length what I should buy?
- No. This is the diagonal of the rise-and-run triangle — the minimum board length before the top hanger cut, the bottom riser deduction and waste. Add a foot before you order.
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Part of a job
- Building a deck — 7 pages, in the order the questions arrive
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