Stair calculator: rise, run, and stringer
Enter the total rise from finished floor to finished floor, and the total run if you already have one. You get the riser count, the rise and run of each step, the stair angle, the stringer length, and an IRC code check that marks each row pass or fail. It is the same math the CutOnce app runs, checked against the same IRC limits.
Updated
Type it the way your tape reads: 9 ft 1-1/2 in, 109.5, or 9′ 1½″
Leave blank for the ideal tread. Enter the run you have and the tread depth comes from it.
- Risers
- 15
- Riser height
- 7-5/16 in
- Treads
- 14
- Tread depth
- 10-3/8 in
- Total run
- 12 ft 1-5/8 in
- Stringer length
- 15 ft 2-3/16 in
- Stair angle
- 35.1°
IRC code check
Every row this page can check passes the IRC default.
| Check | Limit | This stair | Section | Result |
|---|---|---|---|---|
| Riser height | max 7-3/4 in | 7-5/16 in | IRC R311.7.5.1 | Pass |
| Tread depth | min 10 in | 10-7/16 in | IRC R311.7.5.2 | Pass |
| Rise between landings | max 12 ft 7 in | 9 ft 1-1/2 in | IRC R311.7.3 | Pass |
| Nosing | 3/4 in to 1-1/4 in on solid risers, treads under 11 in | 1 in | IRC R311.7.5.3 | Pass |
| Headroom | min 6 ft 8 in | in the app | IRC R311.7.2 | App |
| Riser variation | max 3/8 in | 0 in, equal risers | IRC R311.7.5.1 | Note |
| Guard triangle, open side | 6 in sphere | in the app | IRC R312.1.3 | App |
Every riser here is the same height, so designed variation is zero; keep the built risers within 3/8 in of each other. Headroom and the guard triangle need the stairwell opening, floor thickness, and rail height, so the CutOnce app checks those. The app also runs every check in metric.
A worked example
Say your total rise is 9 ft 1-1/2 in, floor to floor. Here is the whole layout and where each number comes from.
| Total rise | 9 ft 1-1/2 in | given |
| Risers | 15 | round(109.5 / 7.5) = 15, cap check ceil(109.5 / 7.75) = 15 |
| Riser height | 7-5/16 in | 109.5 / 15 |
| Treads | 14 | 15 - 1 |
| Tread depth | 10-3/8 in | 25 - 2 x 7.30 |
| Total run | 12 ft 1-5/8 in | 14 treads x tread depth |
| Stringer | 15 ft 2-3/16 in | sqrt(rise squared + run squared) |
| Angle | 35.1° | atan(riser / tread) |
Stair rise and run
Rise is the height of one step, measured between the leading edges of two treads. Run is the depth of one tread, measured nosing to nosing. The IRC allows a rise of 7-3/4 in at most and a run of 10 in or more, so the steepest stair it allows sits at 37.8°.
For a 9 ft 1-1/2 in total rise, the calculator gives 15 risers at 7-5/16 in and 14 treads at 10-3/8 in, a stair angle of 35.1°. Leave the run box blank and it picks the tread from the two-risers-plus-one-tread rule. Enter the run you have and each tread is that run divided by the tread count, which the code check then holds to the 10 in minimum.
How the layout is derived
- 01
Pick the riser count
Divide the total rise by a comfortable 7.5 in riser and round to the nearest whole number. Then check that count against the code maximum: if it puts the risers over 7-3/4 in, add one. Both rules run, and the larger count wins.
- 02
Divide the rise
Total rise divided by riser count gives the exact riser height. Every riser in a flight has to be within 3/8 in of the others, which is why you divide rather than measure up from the bottom.
- 03
Count the treads
A standard stringer mount has one fewer tread than risers. The top riser lands on the finished floor above, so it needs no tread.
- 04
Set the tread depth
The rule of thumb carpenters use is two risers plus one tread equals 25 in. That keeps the stair walkable. If the result would fall under the 10 in code minimum, the minimum wins.
- 05
Multiply out the run
Tread depth times tread count is the total run, the horizontal distance the stair eats. The stringer itself is the diagonal: the square root of rise squared plus run squared.
What the code requires
The limits below are the 2021 IRC residential defaults the app ships. The calculator above checks riser height, tread depth, total rise between landings, and nosing, and marks each row pass or fail. Every riser it lays out is the same height, so riser variation is zero by design. Headroom and the guard triangle need the stairwell opening, floor thickness, and rail height, so the app checks those. This page checks in imperial; the app runs the same checks in metric. Your jurisdiction can differ, so confirm locally before you cut.
| Requirement | Limit | Section | Checked |
|---|---|---|---|
| Maximum riser height | 7-3/4 in | IRC R311.7.5.1 | This page |
| Minimum tread depth | 10 in | IRC R311.7.5.2 | This page |
| Maximum rise between landings | 151 in | IRC R311.7.3 | This page |
| Nosing with solid risers, treads under 11 in | 3/4 in to 1-1/4 in | IRC R311.7.5.3 | This page |
| Maximum riser variation in a flight | 3/8 in | IRC R311.7.5.1 | By design |
| Minimum headroom | 6 ft 8 in | IRC R311.7.2 | In the app |
| Guard triangle under the bottom rail | blocks a 6 in sphere | IRC R312.1.3 | In the app |
Common questions
- Why does the riser count jump by one sometimes?
- Because two rules run at once. The comfort rule aims at 7.5 in risers; the code rule caps them at 7-3/4 in. On a 63 in rise the comfort rule alone suggests 8 risers at 7-7/8 in, which is over the cap, so the count goes to 9 and the risers drop to 7 in exactly.
- Do I measure the rise before or after finish flooring?
- After. Total rise is finished floor to finished floor. If the upper floor is getting 3/4 in hardwood and the lower slab is getting tile, both of those change your riser height, and a 3/4 in surprise at the bottom step is the classic failed inspection.
- Why is my tread depth exactly 10 in?
- That is the code minimum doing its job. On steep rises the two-risers-plus-a-tread rule would produce a tread under 10 in, so the calculator clamps to the minimum instead of returning something you cannot build.
- Is the stringer length the board length I should buy?
- It is the diagonal of the flight, not the board. Add for the top and bottom cuts and whatever your stringer attachment needs, and buy the next stock length up.
- What stair angle does the code allow?
- The angle comes from one step: the arctangent of rise over run. At the IRC limits of 7-3/4 in rise and 10 in run that is 37.8°, the steepest residential stair the code allows. The worked example above sits at 35.1°.
Cut the whole stair, not just the layout
This page solves the layout. The app does the rest of the stair: stringer notching with throat depth, headroom and stairwell opening, landing splits, and a printable cut plan you can hand to whoever is cutting.
CutOnce runs this same math on the jobsite, then prints the cut plan with the notches marked.
See also