The Structural Backbone of Stairs
When you walk up a wooden staircase, the horizontal boards you step on are called treads, and the vertical boards your toes kick are called risers. However, the heavy structural beams underneath that support the entire system are called Stringers.
A stringer is typically a massive 2x12 piece of dimensional lumber. Carpenters use a framing square to draw a jagged, sawtooth pattern on the 2x12, and then use a circular saw to cut out the triangles. The treads and risers are then nailed directly into these cutouts.
To build a staircase, you must know exactly how long of a 2x12 you need to buy at the lumber yard. Because the stringer runs diagonally from the upper floor down to the lower floor, calculating its length requires finding the hypotenuse of a large right triangle.
Understanding the Stair Triangle
A staircase forms a massive right triangle in the room.
- Total Rise (Height): The vertical distance from the lower floor to the upper floor.
- Total Run (Length): The horizontal distance across the floor from the start of the stairs to the end of the stairs.
- The Stringer (Hypotenuse): The true diagonal length of the 2x12 lumber.
How to Calculate Stringer Length
To find the diagonal length of the stringer, you use the Pythagorean theorem (A² + B² = C²).
(Note: Before you can calculate the Total Run, you must use our Stair Rise & Run Calculator to determine exactly how many steps you have, and how deep each tread is).
The Formula
- Determine the Total Rise of the staircase in inches.
- Determine the Total Run of the staircase in inches. (Multiply the depth of a single tread by the total number of treads).
- Square the Total Rise (Rise × Rise).
- Square the Total Run (Run × Run).
- Add the two squared numbers together.
- Take the Square Root of that sum. This gives you the exact diagonal length in inches.
- Divide by 12 to convert to feet, and add a 10% to 15% Waste Factor (because you need extra wood at the top and bottom to make the final mounting cuts).
Stringer Length = Square Root (Total Rise² + Total Run²)
Example Calculation
You are building deck stairs. The total vertical drop to the grass is 48 inches (Total Rise). You have 6 treads, each 10 inches deep, so the stairs will extend out into the yard exactly 60 inches (Total Run).
- Square the Rise:
48 × 48 = 2,304 - Square the Run:
60 × 60 = 3,600 - Add them together:
2,304 + 3,600 = 5,904 - Take the Square Root:
√5,904 = 76.83 inches - Convert to feet:
76.83 ÷ 12 = 6.4 feet - Add Waste: You need roughly 1.5 extra feet for mounting cuts.
6.4 + 1.5 = 7.9 feet.
You must purchase 8-foot 2x12s to cut your stringers.
The "Dropped Stringer" Rule
When cutting the sawtooth pattern into the 2x12, carpenters must perform a critical final step called "Dropping the Stringer."
Because you are adding a thick wooden tread (usually 1 inch thick) to every step, the very first step at the bottom of the stairs will suddenly become 1 inch taller than all the others. To fix this, you must cut exactly the thickness of one tread (e.g., 1 inch) off the absolute bottom flat edge of the entire 2x12 stringer where it rests on the floor. This drops the entire staircase down 1 inch, making all the math perfect again.