How to Calculate and Cut a Stair Stringer
1. The Principle of Equal Risers
The human body relies heavily on rhythmic muscle memory when traversing stairs. If a single step in a flight differs by more than 3/8 of an inch (9.5 mm) from the others, it creates a significant trip hazard. The International Residential Code (IRC Section R311.7.5.1) mandates:
"The maximum riser height shall be 7-3/4 inches (197 mm). The greatest riser height within any flight of stairs shall not exceed the smallest by more than 3/8 inch (9.5 mm)."
2. The "Bottom Drop" Rule (Where DIYers Make Mistakes)
When you cut stringers, you must account for the physical thickness of the tread material. If you install a 1-inch thick tread board on the bottom step, that step will end up 1 inch too tall unless you cut 1 inch off the very bottom of the stringer.
$$\text{Bottom Cut} = \text{Unit Rise} - \text{Tread Thickness}$$ Trimming the bottom of the stringer by the tread thickness ensures every step—from the basement slab to the top landing—maintains an identical finished height.
3. Stringer Throat Depth Integrity
The "throat" is the remaining solid wood measured perpendicularly between the inner apex of a tread/riser notch and the bottom edge of the board. An undersized throat can cause a stringer to snap along the grain under heavy dynamic loads. Code requires a minimum of 3.5 inches of continuous solid lumber, which is why 2×12 lumber is the standard choice for cut stair stringers.