How this calculation works
The Staircase Rise & Run Calculator computes code-compliant riser heights, tread run dimensions, number of steps, total staircase run length, and diagonal stringer board lengths.
Mathematical formula and logic
Number of Risers = round(Total Rise / 7.5). Unit Riser Height = Total Rise / Number of Risers. Number of Treads = Risers - 1. Total Run = Treads × Tread Run. Stringer Length = sqrt(Total Rise^2 + Total Run^2).
Worked example
For a 108-inch floor-to-floor rise with 10.5-inch treads: Requires 14 Risers at 7.71 inches each, 13 Treads, a total horizontal run of 136.5 inches (11.38 ft), and a diagonal stringer length of 174.05 inches (14.5 ft). Blondel's Rule (2R + T = 25.92) confirms code compliance.
Calculation assumptions
- International Residential Code (IRC) maximum riser height is 7.75 inches; minimum tread depth is 10 inches.
- Blondel's Rule of stair comfort: 2 × Rise + Run should equal between 24 and 26 inches.
Frequently asked questions
What is the maximum stair riser height allowed by code?
Under the International Residential Code (IRC R311.7), the maximum riser height for residential stairs is 7.75 inches (197 mm).
What is the minimum stair tread depth allowed by code?
The minimum tread depth under IRC code is 10 inches (254 mm) measured from nosing to nosing.
Why is the number of treads always one less than the number of risers?
The top step lands directly onto the upper floor level, which acts as the final tread surface.
What is the standard angle for residential stairs?
A comfortable, code-compliant residential staircase has an incline angle between 34° and 38°.
What is minimum headroom clearance for stairs?
IRC building code mandates a minimum vertical headroom clearance of 6 feet 8 inches (80 inches / 2032 mm) measured from the sloped plane of the stair tread nosing to the ceiling above.