A stair with a total rise of 9 ft (108 in) needs 14 risers of 7 ¹¹⁄₁₆ in and 13 treads. With 10 in treads that takes 10 ft 10 in of floor, the stringers run 14 ft 1 in on the slope, and the stair climbs at 37.6°. Divide the rise into equal risers no taller than 7¾ in, then multiply the treads (one fewer than the risers) by the tread depth.
How the stair is calculated
The riser count comes first. The calculator divides the total rise by your target riser and rounds to the nearest whole number, then makes sure no riser comes out taller than the 7¾ in the IRC allows in R311.7.5.1. Every riser is then the rise divided by that count, so all of them match. The top floor counts as the last step, which is why there is always one tread fewer than risers.
Risers = total rise ÷ target riser, rounded (at least total rise ÷ 7¾ in). Riser height = total rise ÷ risers. Total run = (risers − 1) × tread depth. Stringer = √(run² + rise²).
Worked through for the default 9 ft floor to floor: 108 ÷ 7.5 = 14.4, which rounds to 14 risers. 108 ÷ 14 = 7.71 in, just under 7 ¾ in. Thirteen treads of 10 in give 130 in of run, and √(130² + 108²) = 169 in, the 14 ft 1 in stringer. The angle is the arctangent of 7.71 ÷ 10, 37.6°.
Stair rise and run for common heights
With a 7½ in target riser and 10 in treads:
| Total rise | Risers | Riser height | Treads | Total run | Stringer |
|---|---|---|---|---|---|
| 2 ft 6 in | 4 | 7 ½ in | 3 | 2 ft 6 in | 3 ft 6 ⁷⁄₁₆ in |
| 3 ft | 5 | 7 ³⁄₁₆ in | 4 | 3 ft 4 in | 4 ft 5 ¹³⁄₁₆ in |
| 4 ft | 7 | 6 ⅞ in | 6 | 5 ft | 6 ft 4 ¹³⁄₁₆ in |
| 6 ft | 10 | 7 ³⁄₁₆ in | 9 | 7 ft 6 in | 9 ft 7 ¼ in |
| 8 ft | 13 | 7 ⅜ in | 12 | 10 ft | 12 ft 9 ¹¹⁄₁₆ in |
| 9 ft | 14 | 7 ¹¹⁄₁₆ in | 13 | 10 ft 10 in | 14 ft 1 in |
| 10 ft | 16 | 7 ½ in | 15 | 12 ft 6 in | 16 ft ¹⁄₁₆ in |
Stair calculator by height, by run or with risers
By height is the usual case: you know floor to floor and want the stair. Measure plumb from finished floor to finished floor, since a floor covering added later changes the first or last riser.
Rise and run fits the stair into the floor space you have. The calculator takes the fewest risers the code allows, which leaves the deepest treads. For 9 ft of rise in 11 ft of run, that is 14 risers of 7 ¹¹⁄₁₆ in and 13 treads of 10 ⅛ in. If the tread comes out under 10 in, the space is too short for a code stair.
With risers lets you pick the count yourself. Fifteen risers on the same 9 ft rise give 7 ³⁄₁₆ in steps, a gentler 35.8° stair that needs 11 ft 8 in of run.
In metric, a 2.70 m rise with a 19 cm target riser and 25.5 cm treads gives 14 risers of 19.3 cm and 3.32 m of run.
Stair code limits (IRC R311.7)
The 2021 International Residential Code sets these limits for stairs in homes, and the Saint Paul building department's homeowner sheet restates them:
| Rule | Limit | Section |
|---|---|---|
| Riser height | 7¾ in max, within ⅜ in of each other | R311.7.5.1 |
| Tread depth | 10 in min, within ⅜ in of each other | R311.7.5.2 |
| Nosing | ¾ to 1¼ in, not needed with 11 in treads | R311.7.5.3 |
| Headroom | 6 ft 8 in above the nosing line | R311.7.2 |
| Width | 36 in clear | R311.7.1 |
| One flight | 12 ft 7 in of rise max | R311.7.3 |
| Handrail | 34 to 38 in, on flights with 4 or more risers | R311.7.8 |
Tread depth is measured nosing to nosing, so a 10 in tread with a 1 in nosing is an 11 in board.
Headroom and the stairwell opening
Headroom is measured straight up from the line through the tread noses. The opening in the floor above has to reach back far enough that the ceiling edge sits 6 ft 8 in over that line. For the 9 ft example with a 10 in deep floor, that takes an opening at least 9 ft 9 ¹¹⁄₁₆ in long, measured back from the top riser. A 10 ft opening leaves 6 ft 9 ¹³⁄₁₆ in. The header across that opening is sized with the beam span calculator.
Is the stair comfortable?
Codes set limits; comfort is a stride. NIST's review of stair research traces the rule twice the riser plus the tread back to Blondel, who set it at 24 in, and notes that the familiar 7 in riser with an 11 in tread gives 25 in. The default 9 ft stair comes to 25.4 in (2 × 7.71 + 10), a slightly long stride. One more riser shortens it: 15 risers of 7.2 in give 2 × 7.2 + 10 = 24.4 in, at the cost of 10 in more run. Deeper treads lengthen the stride, so pair them with shorter risers.
Deck stairs
Choose the deck preset to measure from the top of the decking down to the landing pad. Two 2×6 boards make an 11¼ in tread. A 3 ft deck gets 5 risers of 7 ³⁄₁₆ in and 3 ft 9 in of run. The American Wood Council's DCA 6 guide asks for 2×12 stringers, a guard once the stair rises 30 in, and stringers bearing on a footing, not on a patio slab. Plan the deck itself with the deck calculator and the post footings with the deck footing calculator. For masonry steps, the concrete steps calculator gives the yards.
Calculators for each part of the job
- Buy the boards: the stair tread calculator turns the risers and treads into tread and riser boards with cut lengths, and the stair runner calculator sizes the runner.
- Cut the stringers: the stair stringer calculator gives framing square settings, every mark and the throat.
- More than 12 ft 7 in of rise, or a turn: the stair calculator with landing splits the flights for straight, L and U stairs.
- Little floor space: the spiral staircase calculator checks treads and headroom for a spiral.
- Framing the walls around the stairwell: the framing calculator and the stud calculator.