Building a sturdy, code-compliant set of stairs begins with understanding the geometric relationship between vertical rise and horizontal run.
The Right Triangle of Stair Building
Every straight flight of stairs forms a large right-angled triangle:
- Total Rise ($a$): The vertical distance from the finished lower floor or grade to the finished upper floor surface.
- Total Run ($b$): The horizontal distance from the face of the top riser to the face of the bottom riser.
- Stringer Length ($c$): The hypotenuse connecting the top and bottom support points.
Stringer Length = √(Total Rise² + Total Run²)Practical Stringer Length Allowance
When ordering dimensional lumber (such as 2×12 #1 Southern Pine or Douglas Fir), always add 12 to 18 inches to your calculated diagonal length. This extra material accommodates:
- The top plumb cut flush against the ledger board.
- The bottom level cut seating onto the concrete slab or footing.
- Waste and mill defects on board ends.