A stair stringer calculator turns one measurement, the total rise from finished floor to finished floor, into the whole stair: how many risers, the exact height of each, the tread run, the total run the stair takes up, the stringer length from the hypotenuse, and the lumber to cut it from. Every stairs calculator does the same division and the same rounding, and the rounding is where a stair goes wrong, because the riser count has to be a whole number and every riser has to be the same height within the tolerance the code allows. This page works a 9-foot floor-to-floor stair, says where the code sets the limits, and shows the stair run calculator that gives the footprint; the free construction cost estimator on this site carries the stair as a line in the estimate at your own rates, with no account.
Risers from the total rise, and the exact riser height
Risers equals the total rise divided by the riser height you would like, rounded to the nearest whole number; the exact riser height is then the total rise divided by that count. A 9-foot floor-to-floor stair is 108 inches; at a target riser of 7.25 inches, 108 divided by 7.25 is 14.9, so 15 risers, and 108 divided by 15 is 7.2 inches each. The number of treads is one fewer than the risers, 14, because the top riser lands on the upper floor. The building codes the International Code Council publishes set the maximum riser height, the minimum tread depth and the variation allowed between risers; the calculator works to a target inside them and the code says where the limits are.
The stair run calculator: tread run and the stair's footprint
The total run equals the tread run times the number of treads. With a 10-inch run and 14 treads the stair takes 140 inches, 11 feet 8 inches, of floor before the landing, and a 10.5-inch run takes 147 inches. That is the number that decides whether the stair fits the opening, and a stairs calculator that gives the risers without the run has answered half the question. The run and rise together also give the stair's angle, which the tangent of rise over run supplies: 7.2 over 10 is an angle a little under 36 degrees, inside the range a comfortable stair sits in and the range OSHA's stairway rules, linked below, address for workplaces.
Stringer length and the lumber to cut it from
The stringer length is the hypotenuse of the total rise and the total run: the square root of 108 squared plus 140 squared is 176.8 inches, 14 feet 9 inches, so a 16-foot 2x12 cuts one stringer with the ends to spare. Three stringers for a 36-inch stair are three 16-foot 2x12s; wider stairs add a stringer at the spacing the tread material needs. The treads and risers are their own list: 14 treads at the stair's width plus 15 risers, in the stock chosen. The American Wood Council publishes the span and sizing tables the stringer's remaining depth after the cuts is checked against.
From the cut list to the estimate
The stair's line in the estimate is the lumber list at the yard's prices, the hardware, and the contractor's own labor rate to lay out, cut and set a stair of that size, marked up at the contractor's overhead and profit. On the worked stair: three 16-foot 2x12 stringers, 14 treads, 15 risers, the hangers and fasteners, and the labor, as one line the owner can read. The free construction cost estimator on this site carries that line at the contractor's own cost with site work, contingency and overhead and profit shown, and the schedule of values carries it as the value of the stair when it is billed.
Questions people ask about stair stringer calculator
How does a stair stringer calculator work out the risers?
Total rise divided by the target riser height, rounded to a whole number, then the total rise divided by that count for the exact riser. A 108-inch rise at a 7.25-inch target is 15 risers at 7.2 inches, with 14 treads.
What is the total run of a stair?
Tread run times the number of treads: 14 treads at 10 inches is 140 inches, 11 feet 8 inches, before the landing. The run decides whether the stair fits the opening.
How long a board does a stringer need?
The hypotenuse of total rise and total run: for 108 by 140 inches, 176.8 inches, so a 16-foot 2x12 per stringer, three for a 36-inch stair.