Stair Calculator
Design staircases by finding the number of risers, tread details, run distances, and stringer lengths.
| Total Run Length | 130.00 Inches |
| Stringer Board Length | 164.01 Inches |
| Incline Angle | 37.56° |
| Code Check | Meets IRC Code Limits |
The Mathematics of Staircase Design
Designing stairs requires balancing the overall vertical rise with a comfortable horizontal walk (run). The layout is calculated using the following equations:
1. Calculate Count of Risers:
Divide the total rise by your target riser height and round to the nearest whole integer:
2. Solve Exact Riser Height & Treads Count:
Since you cannot build a partial step, the riser height must adjust slightly to fit the rounded step count. If the stair terminates at the upper landing floor height, you need one less tread than risers:
Treads Count = Risers Count - 1
3. Solve Total Run, Stringer, and Angle:
The total stringer board length represents the hypotenuse of the stair triangle (Rise and Run):
Stringer Length = Sqrt(Total Rise^2 + Total Run^2)
Incline Angle = Arctan(Total Rise / Total Run) * (180 / π)
IRC Residential Building Code Standards
Standard building code (International Residential Code - IRC) dictates specific dimensions to prevent tripping hazards:
- Maximum Riser Height: 7.75 inches (196 mm)
- Minimum Tread Depth: 10 inches (254 mm)
- Standard Comfort Rule: Riser + Tread should ideally sum to between 17 and 18 inches.