Updated · Built and checked by the PlinzoTools team, formulas tested against published sources
Calculate the diagonal stair stringer board length from total rise and run, rounded to a common stock lumber size.
A stair stringer is cut from a single board along the diagonal hypotenuse of the stair's rise-and-run triangle, not simply the sum of the rise and run. This calculator computes that real diagonal length using the Pythagorean theorem, then rounds up to the nearest length lumber yards actually stock, so the answer matches what you can buy.
Enter your total rise and total run in inches -- both available directly from the Stair Calculator, or from your own measurements.
Diagonal Length = √(Total Rise² + Total Run²)
This is the same Pythagorean relationship used for a roof's slope factor -- a stringer is essentially the "rafter" of a stair's triangle.
This is the raw diagonal length only -- a real stringer layout also needs enough extra board width to cut the actual riser/tread notches without weakening the board, so professional stringer layout typically starts from a 2x12 (not a narrower board) regardless of the calculated diagonal length.
Use the recommended board length when ordering stringer lumber, keeping in mind most staircases need 2 or 3 parallel stringers depending on tread material and span.
Take a stair with 96 inches of total rise and 120 inches of total run. Squaring each gives 9,216 and 14,400, which sum to 23,616. The square root is about 153.7 inches, or roughly 12.8 feet. A 14-foot board would technically be long enough for the raw diagonal, but you should also account for cut waste, the plumb cut at the top and the level cut at the bottom, so it is sensible to look at the next stock length up if the diagonal is close to a board length.
The number this calculator returns is the geometric hypotenuse between two points. A finished stringer, however, is a board with notches cut into its edge. The board must be long enough that the notched section fits within it, and the layout starts from the board edge rather than from a perfect line. Rounding up to the next stock length gives you working margin. If you are between sizes, choosing the longer board is generally the safer purchase because you cannot add length back to a short board.
If you do not have these figures yet, work them out first with the Stair Calculator so the stringer length is based on evenly divided risers.
How much wood remains under the deepest notch determines strength. Span, tread material, and load requirements are governed by local code, and long or wide stairs may need additional support. For anything beyond a simple short flight, confirm the design with your building department or a qualified carpenter or engineer before cutting.
Because it's the diagonal hypotenuse connecting both, not either measurement by itself -- the same reason a ramp or roof rafter is longer than its horizontal footprint.
Typically 2 for stairs up to about 36in wide with solid tread material, and 3 for wider stairs or when treads need more mid-span support -- check your local code and tread material's span rating.
No, it is the pure diagonal. The rounding to stock lengths adds some margin, but check your layout if the result sits just under a board length.
The geometry is the same right triangle, so the diagonal is correct for a ramp surface. Ramps have their own slope and code requirements that this tool does not evaluate.
Notching leaves less material in a narrower board. Most stringer layouts start from a 2x12 for that reason, but confirm what your local code and inspector expect.