A stair is the one job on this site where you do not get to choose the answer. The rise is whatever the building gives you, and every riser in the flight has to be the same height, so the only decision is how many steps to divide that rise into. Everything else follows: the riser height, the run, the stringer, the angle. This stair calculator starts from the step count for that reason, rather than asking you to guess a riser height first.
Why it starts with the step count
The whole stair from one division
risers = total rise ÷ maximum riser, rounded up
Then riser height = total rise ÷ risers, and the flight is uniform by construction
Rounding up is what keeps you legal. Divide a 108 inch rise by a 7.75 inch maximum and you get 13.9, so the flight needs 14 risers, each 7.71 inches. Round down to 13 and every riser is 8.31 inches, which is over the limit in most of the country. Sharing the rise equally between whole steps is also how the uniformity rule is satisfied without trying: the code allows the tallest riser to exceed the shortest by 3/8 inch, and a stair cut from one division has no variation at all.
One more riser than tread
A flight of 14 risers has 13 treads, because the floor you arrive at is the last tread. That is the single most common mistake in stair arithmetic, and it is worth 10 inches of run, which is often the difference between a stair that fits the opening and one that does not.
It also changes the angle. The pitch of a stair is one riser over one tread, so 7.71 over 10 is 37.6 degrees. Take the whole opening instead, 108 over 130, and you get 39.7, which is not the angle of anything on the drawing.
The limits are inputs, not constants
The model IRC puts the maximum riser at 7.75 inches and the minimum tread at 10, with headroom of 6 feet 8 inches and a hard stop at 147 inches of rise for a single flight. States amend those numbers: Michigan allows a 8.25 inch riser and a 9 inch tread. This calculator asks for the limits rather than assuming them, and tells you whether the geometry sits inside the ones you entered. That is an arithmetic check against your own figures, not a code compliance opinion, and your building department is the authority.
What the stringer needs
The stringer spans the whole opening, so its cut length is the diagonal of the total rise and the total run: 108 by 130 inches is 169 inches, or 14.1 feet, which means 16 foot stock because lumber comes in even lengths. Cutting a 14 foot board for a 14.1 foot stringer is a mistake you make exactly once.
Stair calculator FAQ
Fourteen risers and thirteen treads. A 108 inch rise divided by a 7.75 inch maximum is 13.9, which rounds up to 14 steps of 7.71 inches each, and the run works out at 130 inches on a 10 inch tread.
The diagonal of the total rise and the total run. For a 108 inch rise and a 130 inch run that is 169 inches, or 14.1 feet, so you buy 16 foot stock because lumber comes in even lengths.
The model IRC allows 7.75 inches in a dwelling, with a minimum 10 inch tread, and the tallest riser in a flight may not exceed the shortest by more than 3/8 inch. States amend these figures, so check what your jurisdiction has adopted.
Three for a 36 inch stair at 16 inch centers: one at each edge and one in the middle. Wider flights, thinner treads or composite material want them closer together.
