Stair Stringer Calculator
Enter your total rise and get the numbers you need to lay out and cut a stringer: riser height, tread depth, stringer length, cut angle and throat depth — with an automatic check against the IRC stair code.
How to calculate a stair stringer
A stringer is the notched board that carries the treads. Everything about it follows from one number: the total rise — the vertical distance from the lower finished floor to the upper finished floor. Get that measurement wrong and every other number is wrong with it, so measure it twice, at the exact spot where the stairs will land.
From the total rise you work out how many risers you need. Divide the rise by a comfortable riser height — somewhere between 7 and 7½ inches — and round to a whole number. You cannot have a fraction of a step, so you round first and then divide again. That second division gives you the actual riser height, and every riser in the flight must be exactly that. Code allows no more than ⅜ inch of variation between the tallest and shortest riser in a single flight, which is a much tighter tolerance than most people expect. A quarter inch of slop at the bottom step is the difference between a staircase that feels solid and one that feels wrong every time you walk down it.
The number of treads is one less than the number of risers, because the upper floor serves as the final tread. Multiply the tread depth by the number of treads to get the total run — the horizontal distance the staircase eats up. This is where most layouts fail: the rise fits, but the run doesn't, and you end up either steepening the stairs past code or landing them further out into the room than you planned.
To find the stringer length, treat the rise and the run as the two legs of a right triangle. The stringer is the hypotenuse: the square root of the rise squared plus the run squared. That gives you the length of the cut line, but not the length of board you need to buy. Add 6 to 12 inches of extra stock so the stringer can extend past the top and bottom cuts where it gets fastened.
Throat depth is what actually breaks stringers
When you notch a board for treads, what's left behind each notch is the throat. A cut stringer almost never fails in bending — it fails in shear at the inside corner of a notch, because that corner concentrates stress. The throat is measured perpendicular to the bottom edge of the board, and it's the difference between the actual width of your lumber and the altitude of the triangular cut at each step. IRC R507.13.1 puts the floor at 5 inches, and it is a hard limit, not a guideline.
The thing that catches people out is that a deeper tread eats more throat, not less. Each notch is a triangle with a vertical leg equal to the riser and a horizontal leg equal to the tread; make that triangle longer and its altitude grows, so less wood is left under the corner. On a 2 × 12, a 7-inch riser with an 11-inch tread leaves about 5 3/8 inches — comfortable. Take the riser to the 7¾-inch maximum and that same 11-inch tread leaves only 4 15/16 inches, which fails. Hold the tread at the 10-inch code minimum with that tall riser and you're back up to 5 1/8, just legal.
So the steepest legal riser and the deepest legal tread don't go together on a 2 × 12. If you want 11-inch treads, plan on risers around 7 inches. If the rise forces you to 7¾, use 10-inch treads — or step up to a housed stringer, which carries the notches inside the board and keeps the full width of wood underneath.
Code requirements
These are the residential limits from the International Residential Code (IRC). Deck stairs are handled by R507.13, which sends you back to the stair dimensions in R311.7 and then adds its own rules for stringers — the 2 × 12 material, the 18-inch spacing, the 6-foot span and the 5-inch throat are all from R507.13.1, not from trade practice. Your local jurisdiction may amend them, so confirm with your building department before you cut.
One thing that surprises people: the IRC sets a maximum riser height but no minimum. You will see a 4-inch minimum quoted all over the internet, including on other stair calculators, but that figure belongs to the International Building Code — the commercial code. The IRC commentary says so in as many words. Four inches is still a sensible floor, because below that a step reads as a trip hazard, but it is not an IRC violation.
| Item | Requirement |
|---|---|
| Maximum riser height | 7¾ in |
| Minimum riser height | None. The IRC sets no minimum — 4 in is the IBC limit for commercial stairs, and roughly where a step stops being a trip hazard. |
| Minimum tread depth | 10 in |
| Riser variation in a flight | ⅜ in max between tallest and shortest |
| Tread nosing | ¾ in to 1¼ in past the riser, where the tread is less than 11 in deep |
| Handrail height | 34 in to 38 in above the nosing |
| Stringer material | Sawn or solid 2 × 12 |
| Cut stringer span | 6 ft 0 in measured horizontally, all species |
| Cut stringer spacing | 18 in on center max |
| Minimum throat depth | 5 in |
Worked example: deck stairs
Say you're building stairs off a deck with a total rise of 34 inches, and the stair is 36 inches wide. You want 11-inch treads.
The smallest number of risers that keeps you under 7¾ inches is five (34 ÷ 5 = 6.8 in). Going to six risers would give 5.67 inches, which is legal but shallow for an outdoor stair, so five is the better fit. That gives five risers at 6.8 inches each and four treads.
Four treads at 11 inches is a total run of 44 inches. The stringer length is the square root of 34² + 44², which comes out to 55.6 inches — so buy 2 × 12 stock at 6 feet. The saw angle is the arctangent of one riser divided by one tread, 6.8 ÷ 11, which is about 31.7 degrees off horizontal. Throat depth on a 2 × 12 works out to 5 7/16 inches, comfortably above the 5-inch minimum in R507.13.1.
At 36 inches wide, that stair needs three stringers, spaced 18 inches on center. If you widen it to 48 inches you need four, and the spacing stays at 16 inches.
Frequently asked questions
How many stringers do I need for my stairs?
For a stair up to 36 inches wide, two solid 2 × 12 stringers is the prescriptive path, and three cut stringers is the usual build. The rule to hold to is spacing: IRC R507.13.1 caps cut stringers at 18 inches on center, which puts a 36-inch stair at three stringers and a 48-inch stair at four. Wider stairs or stairs carrying heavy traffic are better built tighter than the minimum — 12 to 16 inches on center is common, and composite treads usually force it tighter still, so check the tread manufacturer's instructions.
How do I cut the bottom riser so all the steps match?
Subtract the thickness of your tread material from the bottom of the stringer. A 5/4 board is 1 inch thick, so take 1 inch off; 2 × material is 1½ inches, so take 1½. This makes the first riser — the one sitting on the ground — the same height as all the others. It's the single most common mistake in stringer layout.
What is the maximum riser height for stairs?
7¾ inches under the IRC. There is no minimum — the IRC sets only a ceiling. The 4-inch minimum you'll see quoted comes from the International Building Code, which governs commercial buildings, and it gets copied onto residential stair pages by mistake. As a practical matter, anything under about 4 inches reads as a trip hazard and 7 to 7½ inches is far more comfortable; steeper risers are legal all the way to 7¾ but feel like climbing a ladder.
Can I use a 2 × 10 instead of a 2 × 12 for a stringer?
No — not on a deck or an exterior stair. IRC R507.13.1 requires stringers to be sawn or solid 2 × 12, and it sets a 5-inch minimum throat. A 2 × 10 is only 9¼ inches wide, so a 7-inch riser leaves you about 3⅓ inches of throat, well under that limit and right around where a stringer starts to shear at the notch. The calculator will show you the number for a 2 × 10, but treat anything under 5 inches as a fail regardless of what the rest of the layout looks like.
How far can a cut stringer span?
6 feet 0 inches, measured horizontally between the centerlines of the bearings at each end, and that figure applies to every species. IRC R507.13.1 states it as a flat limit, and the AWC deck guide came to the same 6 feet after the 2013 revision to Southern Pine design values — an earlier edition allowed 7 feet for Southern Pine and you'll still see that number quoted. Past 6 feet the notches have removed so much wood that the board sags between supports. Longer runs need a landing, a 4 × 4 post under the middle of the stringer, or a housed (routed) stringer instead of a cut one — a solid stringer can span up to 13 ft 3 in in a 36-inch-wide stair because the notches are routed into the board rather than through its edge.
What angle do I set my saw to for the stair stringer cuts?
The stringer angle is the arctangent of the rise divided by the run. For a 6.8-inch riser and an 11-inch tread that's 31.7 degrees; for a steeper stair it climbs toward 40 degrees. Set your circular saw to that angle for the plumb (vertical) cuts. The seat cuts are horizontal — those are made with the saw set square and the board clamped at the stair angle.
Why is my stringer length different from my stringer cut length?
The calculated length is the length of the cut line — the hypotenuse from the bottom of the first riser to the top of the last. It does not include the material past the top and bottom cuts, where the stringer gets fastened to the deck rim or the floor framing. Add 6 to 12 inches of stock, then trim after dry-fitting.
Do stairs need a landing?
Yes, for interior stairs the IRC requires a landing at the top and bottom of every flight, and it requires a landing on any flight whose vertical rise exceeds 12 feet. A landing must be at least as wide as the stair and at least 36 inches deep. Landings also reset the ⅜-inch riser variation rule, which is sometimes the practical reason to add one.