How to Calculate Stair Dimensions
Building a staircase requires calculating risers (vertical steps), treads (horizontal walking surfaces), and the stringer (the angled board that supports them).
The method
- Divide total height by desired riser height → number of risers (rounded up).
- Divide total height by number of risers → actual riser height.
- Number of treads = risers − 1 (the top floor is the last "step").
- Total run = treads × tread depth.
- Stringer length = √(height² + run²) (Pythagorean theorem).
Worked example
108" total height (9 ft), 7.5" risers, 10" treads. Risers = ⌈108÷7.5⌉ = 15. Actual riser = 108÷15 = 7.2". Treads = 14. Total run = 14 × 10 = 140". Stringer = √(108² + 140²) = √(11664 + 19600) = √31264 ≈ 176.8" (14.7 ft).
Building code guidelines
- Maximum riser height: 7¾" (IRC residential)
- Minimum tread depth: 10" (IRC residential)
- Riser height variation: max ⅜" difference between tallest and shortest
- Minimum stair width: 36"
Always check your local building code — requirements vary by jurisdiction.