To calculate stairs, divide the total rise by your target riser height, round to a whole number of risers, then divide the rise by that number to get each step's exact height. A 108 in floor-to-floor rise works out to 15 risers of 7.20 in, 14 treads, about 12.3 ft of run and a 15.2 ft stringer.
Everything starts with one measurement: the total rise, from the finished floor at the bottom to the finished floor at the top. Not subfloor to subfloor, unless both levels will get the same flooring. If the top gets 3/4 in hardwood and the bottom stays bare concrete, that 3/4 in lands entirely on one step, and uneven steps are how people trip.
Once you have the rise, the math goes in three steps:
That's the same sequence our stair calculator runs: it rounds to the nearest whole riser, then checks the result against code. If rounding ever pushes a riser over your limit, add one more riser and redo step 3.
Because the top floor is the last "tread." Walk up a 15-riser stair and you'll step on 14 cut treads, then your 15th step lands on the upper floor. So the number of treads is always the riser count minus one, and that's what drives the length of the stair.
Total run = treads × tread depth. With 14 treads at 10.5 in, the run is 147 in, or about 12.3 ft of floor space measured from the face of the top riser to the face of the bottom one.
The stringer, the notched board the treads sit on, is the hypotenuse of that triangle: √(rise² + run²). For 108 in of rise and 147 in of run, that's √(11,664 + 21,609) = 182.4 in, or 15.2 ft. You'd buy 16 ft stock.
Here's the calculator's math run for common floor-to-floor heights at a 7.25 in target riser and a 10.5 in tread, which are the tool's defaults. Floor-to-floor height is usually the ceiling height plus the floor framing above it, so a house with 8 ft ceilings often lands around 105 to 108 in.
| Total rise | Risers | Riser height | Treads | Total run | Stringer length | Angle |
|---|---|---|---|---|---|---|
| 36 in (deck) | 5 | 7.20 in | 4 | 42.0 in (3.5 ft) | 55.3 in (4.6 ft) | 34.4° |
| 48 in | 7 | 6.86 in | 6 | 63.0 in (5.3 ft) | 79.2 in (6.6 ft) | 33.1° |
| 96 in | 13 | 7.38 in | 12 | 126.0 in (10.5 ft) | 158.4 in (13.2 ft) | 35.1° |
| 102 in | 14 | 7.29 in | 13 | 136.5 in (11.4 ft) | 170.4 in (14.2 ft) | 34.8° |
| 108 in | 15 | 7.20 in | 14 | 147.0 in (12.3 ft) | 182.4 in (15.2 ft) | 34.4° |
| 112 in | 15 | 7.47 in | 14 | 147.0 in (12.3 ft) | 184.8 in (15.4 ft) | 35.4° |
| 120 in | 17 | 7.06 in | 16 | 168.0 in (14.0 ft) | 206.5 in (17.2 ft) | 33.9° |
| 132 in | 18 | 7.33 in | 17 | 178.5 in (14.9 ft) | 222.0 in (18.5 ft) | 34.9° |
Most full-height interior stairs end up between 13 and 17 risers, and the angle barely moves from 33 to 35 degrees. The run is what surprises people: a typical stair between floors eats 11 to 14 ft of floor, plus a landing at each end.
Most US jurisdictions build on the International Residential Code (IRC). Your city or county may have amended it, so check with the local building department before you cut anything. These are the numbers that matter for a house:
| Rule | IRC residential limit | Section |
|---|---|---|
| Maximum riser height | 7¾ in | R311.7.5.1 |
| Minimum tread depth | 10 in | R311.7.5.2 |
| Largest vs smallest riser (or tread) | No more than ⅜ in difference | R311.7.5.1 / .2 |
| Minimum stair width | 36 in | R311.7.1 |
| Minimum headroom | 6 ft 8 in, measured from the nosing line | R311.7.2 |
| Maximum rise of one flight | 151 in between floors or landings | R311.7.3 |
| Nosing | ¾ to 1¼ in, required when treads are under 11 in | R311.7.5.3 |
| Handrail | Required with 4 or more risers, 34 to 38 in high | R311.7.8 |
Commercial buildings follow the International Building Code instead, which is stricter: 7 in maximum riser and 11 in minimum tread.
The ⅜ in tolerance is the one DIY builders fail most. It applies to the whole flight, including the top and bottom steps, which is exactly where flooring thickness and stringer cuts introduce errors.
Code tells you what's legal, not what feels good. For comfort, builders lean on two old rules of thumb:
In practice, 7 to 7.25 in risers with 10.5 to 11 in treads feel right to most adults. If you're building for older parents or small kids, drop the riser toward 6.5 to 7 in. You'll need an extra riser and a bit more run, but the stair gets noticeably easier. At 108 in of rise, a 7 in target with 11 in treads gives 15 risers at 7.20 in and a 154 in run, only 7 in longer than the default.
Use the stringer length from the formula, then buy the next lumber size up. Dimensional lumber comes in 2 ft steps (8, 10, 12, 14, 16 ft and so on), and you need a little extra for the plumb cut at the top and the level cut at the bottom.
So a 13.2 ft stringer comes out of 14 ft stock, and the 15.2 ft stringer for a 108 in rise comes out of a 16. Once you're past 18 ft of stringer, you're near the 151 in code limit for a single flight anyway, and it's time to think about a landing.
Most stringers are cut from 2×12s. After the notches come out, check the solid wood left below them (the "throat"). The American Wood Council's DCA 6 deck guide uses 5 in as the minimum for cut stringers. Spacing matters too: three stringers for a 36 in wide stair is the usual starting point, and thinner treads need them closer together.
One step people forget: drop the stringer at the bottom by the thickness of one tread. The first cut riser gets a tread on top of it but the floor doesn't, so without the drop your bottom step ends up a full tread-thickness taller than the rest. For a 1 in tread, trim 1 in off the bottom of the stringer.
If you're pricing out the whole job, our lumber calculator handles the board feet for stringers and treads. Building outside? The deck calculator works out the deck the stairs are coming off of.
Divide the total rise, from finished floor to finished floor, by your target riser height and round to a whole number. Then divide the rise by that whole number to get the actual riser height. For 108 in of rise and a 7.25 in target: 108 ÷ 7.25 = 14.9, so 15 risers at 7.20 in each.
A 9 ft ceiling usually means around 117 to 120 in of floor-to-floor rise once you add the floor framing. At 120 in and a 7.25 in target riser, that's 17 risers at 7.06 in with 16 treads. Measure your actual rise, because joist depth and flooring change it.
The IRC caps residential risers at 7¾ in and requires treads of at least 10 in. The biggest and smallest riser in a flight can't differ by more than ⅜ in. Commercial stairs under the IBC are stricter: 7 in maximum riser and 11 in minimum tread.
Eight risers at 7 in is 56 in of rise, with 7 treads. At 10.5 in treads the run is 73.5 in, so the stringer is √(56² + 73.5²) ≈ 92.4 in, about 7.7 ft. You'd cut it from 10 ft stock to leave room for the top and bottom cuts.
Under the IRC, any stair with four or more risers needs a handrail on at least one side, mounted 34 to 38 in above the tread nosings. Many decks and entry stairs with only a few steps still get one because it's cheap insurance against a fall.