A stairs calculator starts from the one number that cannot be changed, the total rise from finished floor to finished floor, and works everything else from it: how many risers, how tall each one is, how many treads, how far the stair runs, and whether there is headroom under the floor above. The stair stringer calculator on this site takes the result into a cut list; this page is the stair itself, the numbers that decide whether it fits the opening before anyone buys a 2x12. It is worked on a 9 foot floor-to-floor stair with a 10 inch tread, and it says where the code's limits sit, with the rules linked below rather than repeated.
Risers: divide the total rise by a target and round
The total rise on the worked stair is 108 inches. Divide by a target riser, 7.25 inches on the example, to get 14.9, and round to a whole number of risers, 15. The exact riser is then the total rise over that count, 108 over 15, 7.2 inches, and every riser is that height, because a stair with one odd riser is a stair people trip on. Rounding down to 14 would give 7.71 inches, taller and steeper; rounding up to 16 gives 6.75, shallower and longer. The residential code's egress chapter, linked below, sets the maximum riser and the tolerance between risers for a dwelling, and the construction standard sets the same for stairs on a site. The stairs calculator on this site applies the target and shows both roundings.
Treads and the total run: the stair run calculator
There is one fewer tread than risers, because the top floor is the last tread: 14 treads on the worked stair. Total run is the tread count times the tread depth, 14 times 10 inches, 140 inches, 11 feet 8 inches measured horizontally from the bottom riser's face to the top riser's face. That is the number the stair run calculator part of this page exists for, since it decides whether the stair lands in the room or in the wall. A nosing overhangs each tread and does not change the run. If 140 inches does not fit, the choices are a deeper riser within the code's limit, a shallower tread within it, or a landing and a turn, and each is a new run to check.
Headroom: the floor above and where the stair passes under it
Headroom is measured plumb from the nosing line to the underside of the floor or ceiling above, and the residential code sets a minimum a stair has to clear along its whole length. On the worked stair the floor above is 108 inches up and the framing opening is where the stair passes under it; the point to check is the nosing directly below the opening's edge. With 7.2 inch risers, each tread back from the top loses 7.2 inches of height, so the headroom at the nosing six treads down is the floor-to-floor height less the joist depth and finish, less 6 times 7.2. If it fails, the opening is lengthened or the stair is moved, not the risers, because the risers are already set by the rise.
From the stair to the stringer, the lumber and the price
Once risers, treads and run are fixed, the stringer is a right triangle: 108 inches of rise and 140 of run, a hypotenuse near 177 inches, so 2x12 stock at 16 feet, three stringers for a stair up to about 36 inches wide and more for a wider one. The stair stringer calculator on this site prints the cut list from these numbers, and the construction cost estimator prices the stringers, treads, risers and the landing at your own rates. The stair's numbers are decided here first; a cut list from the wrong riser count is firewood.
Questions people ask about stairs calculator
How many risers does a 9 foot stair have?
Fifteen on the worked example: 108 inches over a 7.25 inch target is 14.9, rounded to 15, giving an exact riser of 7.2 inches. Fourteen at 7.71 is within many limits but steeper; sixteen at 6.75 is shallower and 10 inches longer in run.
How is the total run of a stair calculated?
Treads times tread depth. There is one fewer tread than risers, so 15 risers with a 10 inch tread is 14 treads and 140 inches of run, measured horizontally between the faces of the bottom and top risers. The nosing does not add to it.
What if the stair does not fit the room?
Change the riser within the code's limit, change the tread depth within it, or add a landing and a turn. The risers stay equal to each other in every case; a single odd riser is the one thing the calculator will not produce.