Stair rise and run: how to calculate a staircase

Planning workflow

1. Measure total rise from finished floor to finished floor, including the thickness of both finished surfaces.
2. Choose a target riser height, divide, and round to a whole riser count.
3. Recalculate the actual riser from that count so every riser in the flight is identical.
4. Multiply treads by tread depth to get total run, then add landings and check the run against the available floor length.
5. Check headroom along the whole flight, and confirm width, handrail, and guard requirements with the locally adopted code.

Formula or decision logic

Risers = round(total rise / target riser); actual riser = total rise / risers; treads = risers - 1 for a straight flight landing at the upper floor; total run = treads x tread depth. Riser and tread are inversely coupled: a taller riser reduces the riser count and shortens the run, while a deeper tread lengthens it. Rounding direction matters - rounding the riser count down makes each riser taller, rounding up makes each shorter. Every riser within a flight must be equal, because unequal risers are a recognized trip hazard and are limited to a small tolerance by code.

Worked planning example

A floor-to-floor height of 9 ft is 108 in. At a 7.5 in target, 108 / 7.5 = 14.4 risers. Rounding to 14 gives an actual riser of 108 / 14 = 7.714 in; rounding to 15 gives 7.2 in. Choosing 14 risers produces 13 treads, so at 10 in per tread the flight needs 130 in - 10 ft 10 in - of floor length. If only 10 ft is available, either the tread depth drops, a landing turns the flight, or the plan changes. Adding a mid-flight landing adds its own depth to the total run, so a 3 ft landing pushes the same flight to about 13 ft 10 in of combined run.

Limitations and review boundary

• Maximum riser, minimum tread, minimum width, headroom, handrail, and guard requirements come from the locally adopted code and are not established by this arithmetic.
• Winders, curved flights, and spiral stairs are measured differently and are treated separately by code.
• Structural support, stringer sizing, and connection details require a qualified designer.

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