What the code lets you build
For US residential stairs, the 2021 International Residential Code sets the two numbers everything else follows from: riser height no more than 7¾ in (R311.7.5.1) and tread depth no less than 10 in (R311.7.5.2). The same section caps the variation between the tallest and shortest riser in a flight at 3/8 in, which in practice means every riser gets cut identical.
Commercial work under the IBC is stricter: 7 in maximum risers and 11 in minimum treads. The calculator defaults to the residential limits and lets you type in the commercial ones. Either way, local amendments override the model codes, so the number that finally matters is the one your building department enforces.
The riser-first method, worked through
Say the finished floor to finished floor rise is 9 ft, or 108 in. Divide by the 7.75 in maximum: 108 ÷ 7.75 = 13.94, round up to 14 risers. Rounding down would leave risers over the legal limit, which is why the direction of rounding is not a style choice.
Each riser is then 108 ÷ 14 = 7.714 in ≈ 7 11/16 in. A standard mount puts the top "tread" level with the upper floor, so a 14-riser stair has 13 treads. At a 10 in tread depth the total run is 130 in, and the stringer diagonal is √(108² + 130²) ≈ 169 in. Call it 14 ft 1 in of 2×12 before waste, so you are buying 16-footers.
The angle comes out to arctan(108/130) ≈ 39.7°, on the steep side of comfortable but fully legal. Deeper treads flatten the stair at the cost of run length.
Marking and cutting stringers
Set a framing square to riser height on one leg and tread depth on the other (stair gauges make this repeatable), then step it down the stringer once per tread. Two details catch first-timers: drop the bottom of the stringer by one tread-material thickness so the first step is not taller than the rest once treads go on, and keep the notches shallow enough that solid wood remains behind them; over-notched stringers are the classic wobbly-stair failure, and span tables assume the uncut depth.
Cut one stringer, test-fit it against the actual floors, and only then use it as the template for the rest. A stringer that is 1/4 in off multiplies its error across every step.
What an over-notched stringer actually looks like on inspection
Anthony Baldwin, a building inspector on the Gold Coast, described finding a stringer cut too deeply around the tread sections on an otherwise neat-looking finished stair. Walking on it showed noticeable movement, and closer inspection found too much timber removed from the notches, leaving insufficient solid wood to carry the stringer's strength. Tightening or re-securing the treads would not have fixed it; the stringers themselves needed to be rectified, since the problem was in the cut, not the fasteners.
The finished surface can look fine while hiding this. Working out riser and tread measurements before cutting, and stopping the notch depth well short of where it starts eating into the stringer's solid core, is what keeps a stair from ending up this way.
Legal is not the same as comfortable
Carpenters have used the rule attributed to François Blondel since the 1600s: twice the riser plus the tread should land near 24–25 in, matching a natural walking gait. The 7 11/16 in riser with a 10 in tread from the example gives 2(7.71) + 10 = 25.4 in, acceptable but slightly steep. A 7 in riser with an 11 in tread hits exactly 25 in and is noticeably easier to climb.
If the run space allows it, aim below the code maximums rather than at them. Stairs cut to the legal limit are the steepest stairs anyone is allowed to build, and they feel like it.