CarpentryInstant Tool
Stair Calculator
Calculate rise, run, number of risers, stringer length, and incline angle to meet building codes.
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IRC Building Code Compliant
2R + T = 24.9 inchesHow Stair Calculator Works
Number of Risers = Total Rise / Target Riser Height 7.75 in max | Stringer Length = √Total Rise² + Total Run²Calculates optimal stair geometry following IRC International Residential Code guidelines. Standard codes specify maximum riser height of 7.75 inches and minimum tread depth of 10 inches. The rule of thumb: 2 × Riser Height + Tread Depth should equal 24 to 25 inches for a comfortable stride.
Variable Breakdown
Total Rise
Vertical RiseHeight between lower and upper finished floor
Riser Height
Target RiserDesired individual step height - IRC max 7.75 in
Tread Depth
Step TreadHorizontal foot step surface depth - IRC min 10 in
Stringer
Stringer Length√ - Total Rise² + Total Run²
Example Calculation
Deck Stair Stringer Layout
A backyard deck with a 68-inch total rise and 10.5-inch target tread depth.
- Calculate risers: 68 in ÷ 7.5 in target = 9.07 -> round to 9 risers.
- Calculate exact riser height: 68 in ÷ 9 = 7.56 inches under 7.75 in code.
- Calculate tread count: 9 risers - 1 = 8 treads.
- Calculate total horizontal run: 8 treads × 10.5 in = 84 inches or 7.00 ft.
- Calculate stringer length: Square Root of 68 squared plus 84 squared = 108.07 inches requiring a 10 ft board.
Result:9 Risers at 7.56 inches - 108.1 inch Stringer Board
IRC Building Code Stair Standards
| Stair Parameter | IRC Code Rule | Comfort Standard | Safety Notes |
|---|---|---|---|
| Maximum Riser Height | 7.75 inches | 7.0 to 7.5 inches | Variance between steps must not exceed 0.375 in |
| Minimum Tread Depth | 10.0 inches | 10.5 to 11.0 inches | Measured horizontally from nosing to nosing |
| Minimum Stair Width | 36.0 inches | 36.0 to 42.0 inches | Clear width above handrail height |
| Stair Incline Angle | 30° to 37° | 32° to 35° | Angles over 42° violate residential code |
| Minimum Headroom | 80 inches | 84 to 90 inches | Vertical clearance from sloped stair plane |
Frequently Asked Questions
What is the standard residential stair riser height?
Under the International Residential Code IRC, the maximum riser height for residential stairs is 7.75 inches 197 mm, with the most comfortable standard being 7 to 7.5 inches.
What is the 7-11 stair rule?
The 7-11 rule is a common carpentry guideline where the ideal riser height is approximately 7 inches and the minimum tread depth is 11 inches.
What is a comfortable stair angle?
A comfortable stair incline angle is between 30 and 37 degrees. Angles steeper than 42 degrees feel like ladders, while angles below 25 degrees feel like ramps.
How do you calculate stringer length?
Using the Pythagorean theorem: Stringer Length = Square Root of Total Rise² + Total Run², plus allowances for top and bottom hangers.
Why is there one less tread than risers?
The top riser meets the upper finished floor platform, which acts as the final landing, meaning you always require one fewer tread than risers.
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