Enter the total rise - finished floor to finished floor - and the calculator returns the riser count, the exact riser height to cut, the treads, total run, stair angle, and stringer length, flagging anything that breaks residential code.

Formula

$\text{risers}=\left\lceil\frac{\text{total rise}}{\text{max riser}}\right\rceil \qquad \text{riser height}=\frac{\text{total rise}}{\text{risers}}$

$\text{treads}=\text{risers}-1 \qquad \text{total run}=\text{treads}\times\text{tread depth} \qquad \text{stringer}=\sqrt{\text{rise}^2+\text{run}^2}$

Rounding up keeps every riser at or under the maximum; dividing by the final count makes all risers identical. The top "step" is the upper floor itself (a flush-mounted stringer needs one extra tread). The stringer is the hypotenuse of the rise-run triangle - the Pythagorean theorem at work.

A 105 in rise with the IRC maximum 7.75 in riser and 10 in treads: 14 risers at exactly 7.5 in, 13 treads, a 130 in run, a 36.9° angle, and a 167.1 in stringer (buy 16 ft boards to allow for cuts).

Residential code limits (2021 IRC)

Dimension	Limit	Section
Riser height	7.75 in max	R311.7.5.1
Riser variation	3/8 in max	R311.7.5.1
Tread depth	10 in min	R311.7.5.2
Stair width	36 in min	R311.7.1
Headroom	6 ft 8 in min	R311.7.2

These are the model-code numbers for dwellings; local jurisdictions amend them - check with your building department before cutting.

Pythagorean theorem calculator - the stringer math on its own.
Concrete calculator - for poured steps and landings.

Sources and further reading

2021 International Residential Code, Section R311.7 - the stairway provisions the warnings are based on.
Wikipedia: Stairs - terminology for risers, treads, and stringers.

Stair Calculator