Stair Stringer Length Calculator

A stringer is a right triangle: the total rise is the vertical leg, the total run is the horizontal leg, and the stringer itself is the hypotenuse. Length = √(rise² + run²).

For a 108 in total rise with 14 treads at 10.5 in (147 in total run), length = √(108² + 147²) = √(11,664 + 21,609) = √33,273 ≈ 182.4 in, or 15.2 ft.

Notice the stringer is longer than either leg but shorter than the sum of them — 108 + 147 = 255 in, well above the 182.4 in actual diagonal. That gap is exactly why a stringer uses less board than people first assume.

The 182.4 in figure is the layout length — the straight-line distance between the top outside corner and bottom outside corner of the notched zigzag. It is not the length of board you should buy.

You need extra material at both ends: enough at the top for the plumb cut to land past the header without the corner disappearing into a knife-edge, and enough at the bottom for the tread-thickness drop plus a stable foot. Most carpenters add 2–4 in of working margin beyond the raw diagonal.

182.4 in plus margin lands comfortably inside a 16 ft (192 in) board, so that's what you order — not a 15 ft board, which isn't standard stock anyway.

*Assumes a roughly 7 in riser and 10–11 in tread, which puts the stair angle near 32–35°. Steeper or shallower stairs shift the run-to-rise ratio and change how much rise a given board length can cover — always run your own numbers rather than reading straight off this table.

Beyond the plumb cut and bottom drop margin, lumber lengths aren't continuous — you can't buy a 15.4 ft board, so you round up to the next stocked length regardless of how close your math lands to the shorter size.

There's also a practical reason: a board cut exactly to the theoretical diagonal leaves you no room to adjust if the actual framed opening differs by even half an inch from the plan. A little extra length at the top is cheap insurance against a stringer that's a hair too short to reach the header.

This is why length alone doesn't tell you the shape of a stair — a steep, short-run flight and a shallow, long-run flight can need almost the same board. Angle and riser count matter just as much as the length number for figuring out whether a stringer actually fits your stairwell.

If you're building into a limited stairwell opening, you often know the available run before you know the exact rise. Work backward: divide the available run by your target tread depth to get a tread count, add one for the riser count, then divide total rise by that riser count to check the resulting riser height falls in an acceptable range.

If the resulting riser height is too tall or too short, you'll need to change tread depth, add a winder, or reconsider the stairwell opening rather than force the numbers.

For the full notch-by-notch layout once you know your board length, use the stair stringer calculator or the layout-focused version.

If limited headroom or run is the actual constraint, the stair run calculator and stair headroom calculator dig into those separately.