Engineering calculator
Stair calculator
Divide the floor-to-floor rise into equal risers of no more than 7¾ in, give each tread at least 10 in of run, and you have the stair. A 9 ft rise, for example, takes 15 risers of about 7 3/16 in and 14 treads. Enter yours and this staircase calculator lays out the stringer, the floor opening for headroom and every code check, drawn to scale and in 3D.
Enter your riseMore in this series
Other stair layouts
This page lays out one straight flight. A stair that turns is worked out on its own page, with the same limits, drawing and 3D.
Tools for the job
What makes this job easier
Tools and materials that suit this kind of job. These are affiliate links: if you buy through one, Renovimo may earn a commission at no extra cost to you. It never changes the figures on this page.
Garvee
10 in table saw
Rips 2 × 12 tread stock and riser boards to width, and trims oak treads to the stair width.
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Garvee
Miter saw stand
Holds a 16 ft 2 × 12 level at the saw while you cut the stringer to length and square the treads.
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Garvee
Stair handrail, 6 ft
A graspable rail for a flight of four or more risers, mounted 34 to 38 in above the nosings.
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Dovoh
Cross-line laser level, green
Throws a level line for the header and the landing and a plumb line for the first riser, so every flight lands where the drawing says.
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Garvee
Folding work table and sawhorse
A cutting station beside the stair for notching stringers with a circular saw and finishing the cuts by hand.
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Garvee
Collapsible material cart, 1800 lb
Moves 2 × 12 stringer stock and a stack of treads from the truck to the stairwell in one trip.
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Not the tool you were after? Browse the whole range at Garvee or Dovoh — the stores these picks come from.
Based on your result
What you'll need
Lay out and cut one stringer, set it in place against the header and the floor, and only then use it as the pattern for the rest.
- 2 × 12 stringers
- Straight, with no large knots near the edge
- Calculate above
- Treads Amazon
- Oak stair treads or 2 × 12 lumber, cut to the stair width
- Calculate above
- Riser boards
- Primed 1 × 8, ripped to the riser height
- Calculate above
- Stringer connectors Amazon
- One per stringer at the header
- Calculate above
- Tread screws, 2½ in Amazon
- Two into every stringer under each tread
- Calculate above
- Construction adhesive Amazon
- A bead on every stringer cut before the tread goes down
- Calculate above
- Handrail brackets Amazon
- Once the stair has four or more risers
- Calculate above
- Stair gauges Amazon
- Clamped on the framing square at the riser and the run
- Calculate above
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The maths
How this stair stringer calculator works
Every riser in a flight has to match within ⅜ in, so the rise is divided into equal steps first and everything else follows from that one number: the run, the stringer, the angle and the opening above.
riser = rise ÷ risers
treads = risers − 1
total run = treads × run
stringer = the cut outline, tip to tip along the board (on the layout drawing)
throat = 11¼ − riser × run ÷ √(riser² + run²)
opening = (80 in + floor depth) × run ÷ riser + nosing
- 01
Divide the rise
Total rise over the riser you would like, rounded to whole steps. If that leaves a riser over 7¾ in, one more step goes in.
- 02
Count the treads
The upper floor is the top step, so a flight has one tread fewer than it has risers.
- 03
Lay out the stringer
Clamp the riser and the run on a framing square and step it down the 2 × 12, from the seat at the foot to the plumb cut at the top. The board must be at least that long plus a little to square the ends, and leave at least 5 in of solid wood under each notch.
- 04
Drop the stringer
Treads sit on the cuts, so take one tread thickness off the foot. Without it the bottom step comes out tall and the top step short.
- 05
Open the floor above
Headroom is 6 ft 8 in, measured plumb from the line of the nosings. The opening runs back from the header until the nosing line is that far below the underside of the floor.
Good to know
Stair calculator questions: rise, run and stair dimensions
At a 7¼ in target, 108 in divides into 15 risers of 7.2 in (7 3/16 in on the square) and 14 treads. With a 10 in run the flight is 140 in, or 11 ft 8 in, long, and each stringer is cut from a 16 ft 2 × 12.
The 2021 IRC allows a riser of no more than 7¾ in and a tread run of no less than 10 in, measured nosing to nosing. Within one flight the tallest and shortest riser may differ by no more than ⅜ in, and the same goes for tread runs.
Measured along the board from the tip of the seat cut at the foot to the plumb cut at the top — about the diagonal of the run and the rise, plus the two end cuts. For a 9 ft rise with 10 in treads that is 14 ft 4 in, so a 16 ft 2 × 12. The stringer layout drawing dimensions it; buy the next stock length up.
Long enough to leave 6 ft 8 in of headroom above the line of the nosings. Measured from the header back, that is (80 in + the depth of the floor) × run ÷ riser, plus the nosing at the top: for a 7.2 in riser, 10 in run, 1 in nosing and a 10 in deep floor, 126 in.
Yes, ¾ to 1¼ in — unless the tread run is at least 11 in, when the IRC drops the nosing requirement.
At least 36 in clear, wall to wall, above the handrail height. At and below the handrail the clear width may drop to 31½ in with one handrail or 27 in with two, and a handrail may project no more than 4½ in on either side.
For a house: risers of 7 to 7¾ in, tread runs of 10 to 11 in, a nosing of ¾ to 1¼ in, at least 36 in of width and 6 ft 8 in of headroom. A flight may rise no more than 151 in before it needs a landing.
Once it has four or more risers. The top of the rail goes 34 to 38 in above the nosings, measured straight up.