How to Calculate Stair Stringer Length

1. Get the total rise (floor to finished floor) and the total run ((treads) × (run)) from the stair rise and run calculator.
2. Square each: total rise² and total run².
3. Add them together.
4. Take the square root of the sum — that is the diagonal stringer length, corner to corner.
5. Add a few inches for the top and bottom plumb cuts and a margin to trim to fit.

Take the example flight: total rise 9′-7″ (2.921 m) and total run 13′-8¾″ (4.185 m). Square the rise — about 8.53 m² — and the run — about 17.51 m². Add them for roughly 26.04, and the square root is about 5.10 m, or 16′-9″. That diagonal is the bare geometric length of the stringer, edge to edge along the slope.

It is worth noticing how much longer the stringer is than either floor dimension: nearly seventeen feet of board for a stair that is under ten feet tall and under fourteen feet long. That is why a stringer almost always has to be cut from a single long 2×12 (or two scarfed together for very tall flights) and why ordering the board too short is such a common, costly mistake. The stair stringer calculator runs this exact formula for you and reports the length, so you can buy the right board the first time.

The diagonal length tells you how long the board is, but not how wide it has to be. Notching the steps removes material from one edge, and the strip of solid wood left behind the deepest notch — the throat — is what actually carries the load. Cut the throat too thin and the stringer cracks. The throat works out to: throat = board width − (rise × run) ÷ √(rise² + run²), and you want to keep at least 3½″ of it.

In practice this is what decides 2×10 versus 2×12. A 2×12 (about 11¼″ of real width) leaves a healthy throat at typical rise-and-run; a 2×10 may not once you notch a deep step. Steeper stairs make the throat worse, not better: a taller rise and a longer run both cut deeper into the board, so a flight that is steep enough to feel like a ladder is also the flight most likely to leave a dangerously thin throat. The stair stringer calculator computes the throat for your exact numbers and flags when it is getting thin, which is your signal to step up a board size rather than cutting deeper into a board that is too narrow. When even a 2×12 cannot leave a safe throat, the answer is a solid (housed) stringer — where the steps slot into routed grooves and nothing is removed from the load path — rather than forcing a deeper notch.

The √-formula gives the corner-to-corner diagonal of the step triangles, but a real stringer needs a little more board than that at both ends. The bottom gets a plumb cut and a seat cut where it meets the floor or footing, and the top gets a plumb cut where it hangs off the framing — and you also drop the bottom by one tread thickness so the finished risers come out equal (the bottom-riser drop covered in the cutting-stringers guide). None of that is in the bare hypotenuse, so add a few inches of length when you buy.

The cardinal rule with stringers: buy long and trim to fit. A board cut an inch short is firewood, while a board cut an inch long is a thirty-second pass with a saw. Order to the calculated diagonal plus a margin for the end cuts and a safety trim, and confirm the figure with the stair stringer calculator before you head to the lumber yard.

The same two legs that set the stringer length also set the stair angle: angle = atan(rise ÷ run). A steeper stair (more rise per run) has a shorter total run, a shorter stringer, and a smaller footprint — but a steeper, less comfortable climb. A shallower stair eats more floor and a longer stringer but walks easier. The example flight lands at 9′-7″ over 13′-8¾″, a pitch of 33.2°, squarely inside the comfortable 30–37° band.

So before you lock in a stringer length, make sure the rise and run that feed it are themselves comfortable and legal. Check the pitch with the stair angle calculator and the steps with the stair rise and run calculator; for an outdoor flight off a deck, the deck stairs calculator runs the same stringer math with pressure-treated material and footing notes built in.

Once you have the length, the width (board size), and a comfortable pitch, the rest is layout and cutting — stepping off each rise and run with a framing square, keeping the throat, dropping the bottom riser, and cutting the notches clean. Our companion guide on cutting stair stringers walks that layout in full, and the stair stringer calculator prints a full-scale template you can lay straight on the 2×12 and trace.

Plan three stringers for a standard 36″-wide flight, four if you go wider or use thinner tread stock. Then price the boards, treads, and fasteners with the stairs cost calculator so the lumber order — the right length and the right count — is settled before you buy.