Stair Calculator
Enter the floor-to-floor rise and the limits you build to. You get the risers and treads, the run, the stringer and the stairwell opening, with a side view of the flight.
Stringer and stairwell— stock depth, tread thickness, headroom
Risers
14 × 7-1/2"
13 treads · total run 10' 10" · 36.87°
- Risers
- 14
- Riser height
- 7-1/2"
- Treads
- 13
- Tread stock depthtread depth plus the nosing
- 11"
- Total run
- 10' 10"
- Stair angle
- 36.87°
- 2R + Tcomfort rule: two risers plus a tread
- 25" (within 24" to 25")
- IRC check
- Within R311.7 limits
- Stringer length
- 13' 11-1/8"
- Stock to buy
- 14 ft
- Throat leftwood left under the cut-outs
- 5-1/4"
- First riser cutshort by one tread thickness
- 6-1/2"
- Stairwell opening
- 10' 0"
- Treads under the opening
- 12
Side view
Kalku is coming to iPhone and Android
In the app the stair is a 3D model you can turn round as you type, your riser limit, tread depth and headroom are stored once and used on every job, and there is a Stair key on the feet-inch keypad for working it out on the spot. It works with no signal and saves every flight to share as a PDF.
How the stair is worked out
Everything starts from the total rise, measured from finished floor to finished floor. Divide it by the tallest riser you are allowed and round up: that is the number of risers, and the rise divided by that number is the exact riser height. Treads are one fewer, because the upper floor is the last step, and the total run is the treads times the tread depth.
The stringer is the diagonal of the total run and the total rise. The throat is the wood left under the cut-outs: the stock depth less riser × tread ÷ the step's diagonal. Too little and the stringer is weak, which is why the calculator says so when the stock is too shallow. The first riser is cut short by one tread thickness so that, once the treads are on, every step comes out the same. The stairwell opening is how much floor has to be left open above the flight so that nobody hits their head: enough treads to climb the headroom plus the floor's thickness.
Worked example: 105 inches floor to floor
This is the stair the calculator opens with: an 8' 9" rise, 7-3/4" maximum risers and 10" treads.
- Risers: 105 ÷ 7.75 = 13.55, rounded up to 14.
- Riser height: 105 ÷ 14 = 7-1/2".
- Treads: 14 − 1 = 13, so the total run is 13 × 10" = 10' 10".
- Stair angle: arctan(7.5 ÷ 10) = 36.87°; 2R + T = 15 + 10 = 25".
- Stringer: √(130² + 105²) = 167.1", which is 13' 11-1/8": a 14 ft board.
- Throat on a 2x12 (11-1/4" deep): 11.25 − 7.5 × 10 ÷ 12.5 = 5-1/4".
- Stairwell opening for 6' 8" of headroom under a 10" floor: (80 + 10) ÷ 7.5 = 12 treads, so 10' 0".
Measuring the rise
Measure where the stair will actually land, from the finished surface below to the finished surface above. If the floor covering is not down yet, add its thickness: a 3/4 inch hardwood floor laid upstairs after the stair is built makes the top riser 3/4 inch taller than the rest, and uneven risers are exactly what trips people. Every inch of the rise is shared out across the risers, so a small measuring error spreads; a large one changes the count.
Questions
How do I work out how many steps I need?
Divide the total rise, finished floor to finished floor, by the tallest riser you are allowed, and round up. Rounding up is what keeps every riser at or under the limit: 105 inches at a 7-3/4 inch maximum is 13.55, so 14 risers of exactly 7-1/2 inches. Rounding to the nearest would give 13 risers of 8.08 inches, over the limit.
Why is there one tread fewer than risers?
The upper floor is the last step. You climb 14 risers but only stand on 13 treads before you step onto the landing, so the total run is 13 × the tread depth, not 14.
What are the code limits for residential stairs?
Under the International Residential Code (R311.7): risers no taller than 7-3/4 inches, treads at least 10 inches deep, a nosing of 3/4 to 1-1/4 inches where the tread is under 11 inches, and 6 feet 8 inches of headroom. The calculator flags any of these it sees broken. Commercial stairs under the IBC are stricter, and many places adopt their own amendments, so check the code where you build.
Why is the stair angle not rise ÷ run?
Because a stair has one more riser than treads. The angle shown is riser height over tread depth, the line the nosings, the handrail and the stringer follow: 36.87° for 7-1/2 inch risers on 10 inch treads. The total rise over the total run is steeper, since the last riser has no tread under it.
What is the 2R + T rule?
A comfort check that goes back centuries: two risers plus one tread should come to about 24 to 25 inches, roughly the length of a step on the flat. 7-1/2 inch risers and 10 inch treads give 25. It is a guide to a stair that feels right, not a code requirement.
