One measurement rules the flight
A straight stair is a chain of consequences, and the first link is a single tape-measure number: the total rise, floor surface to floor surface. Not the ceiling height — the rise includes the floor structure above, so a basement under an 8-ft ceiling typically measures about 105 inches once the joists and subfloor are counted, and a 9-ft ceiling lands near 119. Measure it where the stair will actually sit, because an inch of error here doesn’t stay an inch: it gets divided across every step and can flip a passing riser into a failing one.
Everything else in the flight is computed, not chosen. The riser count comes from the rise, the riser height comes from the count, the tread count comes from the risers, and the run and stringer come from the treads. The stair calculator runs that whole chain from the rise and a target riser height, then grades the result against the building-code limits — which is the right order of operations for a layout, and the order this guide follows.
Divide, round, and divide again
The riser count is the nearest whole number of steps to your target: n = round(rise ÷ target riser). At the common 7.5-inch target, the 105-inch basement rise gives round(105 ÷ 7.5) = 14 risers. Then — and this is the part hand layouts get wrong — the actual riser height is recomputed as rise ÷ count, so every step is exactly 105 ÷ 14 = 7.5 inches. You never stack fourteen 7.5-inch marks and absorb the remainder in the last step, because codes require riser uniformity: the variation within a flight is typically limited to 3/8 inch (9.5 mm), and an inspector’s level finds the odd step fast.
Because the count must be whole, it’s always worth looking one riser to either side. The same 119-inch rise works as 16 risers of 7.4 inches or 17 risers of 7.0 inches — both legal, one steeper and shorter, one gentler and longer. That trade is the core design decision in a straight flight, and it costs floor space, as the run numbers below show.
The 7¾-inch gate
The rounded count now faces the code check. For residential work under the IRC, R311.7.5 caps the riser at 7¾ inches (196 mm) and sets the minimum tread depth at 10 inches (254 mm); commercial stairs under the IBC are stricter at a 7-inch maximum riser on an 11-inch minimum tread, and OSHA standard industrial stairs allow 9.5 inches both ways. The check bites in real layouts: a 100-inch loft rise at 13 risers gives a 7.7-inch riser — passing, but with under a tenth of an inch to spare. Had the rounding produced a riser over 7.75, the fix is one more riser, which pushes the height back down and the run out.
Passing code is the floor, not the goal. The classical comfort rules score the step shape: Blondel’s 1675 stride formula wants 2R + T between 24 and 25 inches, the companion checks put R + T at 17–18 inches and R × T at 70–75 in², and the stair angle is most comfortable between 30° and 37°. The 14-riser basement flight on 10-inch treads lands at the top of every band — 2R + T = 25.0, R + T = 17.5, R × T = 75.0, angle 36.9° — a legal, compact stair that’s still on the steep side of comfortable.
What the flight costs in floor
Treads number one fewer than risers, and the run is treads × tread depth. Thirteen 10-inch treads put the basement flight at 130 inches of run — just under 11 feet of floor claimed before the bottom landing is counted. Move the same flight to 11-inch treads and the run grows to 143 inches while the angle eases from 36.9° to 34.3°; add that seventeenth riser to the 119-inch main stair and the run stretches from 150 to 160 inches. Deeper treads and softer risers are bought in inches of floor plan, which is why the fit check belongs early: measure the run you actually have before falling in love with a gentle stair.
Two more dimensions hang off the run. The stringer is the hypotenuse of the stair triangle, √(rise² + run²) — 167.1 inches for the basement flight, so buy a 16-ft board for cutting room; a 14-footer (168 inches) clears it by less than an inch. And headroom is checked along the flight under the floor opening above: both the IRC and IBC require 6 ft 8 in (2032 mm, 80 inches) of clearance from the nosing line, so a flight that fits the plan in run can still fail overhead, forcing a longer floor opening or a steeper pitch within the limits.
The guard finishes the job
A stair open on one side isn’t done when the treads are cut — the guard along the open side has its own code chain, and it starts where the stringer math ends. IRC R312.1.3 requires that no opening in the guard pass a 4-inch sphere, which turns the infill into a counting problem: for a clear opening between posts, the baluster spacing calculator computes the minimum count as ceil((opening − 4) ÷ (baluster width + 4)) and spaces them perfectly evenly. A 60-inch opening filled with 1½-inch (nominal 2×2) balusters needs 11 of them, producing an even 3.625-inch gap that clears the limit with 3/8 inch to spare.
The rounding boundary is just as sharp as the riser check: drop to 10 balusters in that opening and the gap opens to 4.09 inches — a failed inspection by about 3/32 of an inch. Stairs also carry their own allowances: openings in guards on the open sides of stair treads may reject a 4⅜-inch sphere instead, and the triangle formed by the tread, riser, and bottom rail may reject a 6-inch sphere. Layout marks come out of the same math — the first baluster center in that 60-inch opening falls 4.375 inches from the post face — so the rail can be drilled before it’s ever installed.
The chain in one pass
Run the basement stair through every link: a measured 105-inch rise at a 7.5-inch target gives 14 risers; recomputing puts each riser at exactly 7.5 inches, under the IRC’s 7¾-inch cap with the uniformity problem solved by construction. Thirteen 10-inch treads set the run at 130 inches and the stringer at 167.1 — one 16-ft board per carriage, bought for cutting room — at a 36.9° angle that grazes the top of the comfort band, with 2R + T sitting at 25.0 inches. If the open side gets a guard with a 60-inch clear opening, 11 balusters at a 3.625-inch gap close it out. One measurement, one rounding decision, and the rest is arithmetic — which is exactly what makes stairs unforgiving of a sloppy tape measure and kind to anyone who checks the chain before cutting.