Stair Calculator
Calculate stair risers, tread runs, stringer lumber length, total horizontal span, and slope angle with IRC building code compliance checks.
Calculation Results
Total number of vertical riser cuts needed to reach finished floor elevation.
The height of each riser cut (IRC code maximum is 7.75 inches).
Number of horizontal step treads (always 1 fewer than risers when top step is flush).
Total horizontal floor space required by the staircase stringers.
Minimum rough diagonal length of 2x12 lumber board required for stringers.
Incline angle of the staircase (ideal architectural range is 32° to 37°).
Ergonomic comfort check (2 × Riser + Tread should fall between 24 and 25.5 inches).
How This Calculator Works
Layout your staircase stringers in four simple steps:
- Measure the Total Rise: Use a level and tape measure to find the exact vertical distance between the lower finished floor level and the upper finished floor landing.
- Enter Target Riser & Tread: Standard comfortable values are 7.25" to 7.5" for risers and 10.5" to 11" for treads.
- Verify Code Compliance: Confirm that the calculated exact riser height does not exceed 7.75 inches and the incline angle sits between 32° and 37°.
- Cut Stringers: Buy 2x12 lumber boards matching the calculated diagonal stringer length. Remember to cut the bottom of the stringer by the thickness of the tread material to ensure consistent step heights.
Formula & Calculations
Stair layout and framing geometry are governed by Section R311.7 of the International Residential Code (IRC):
1. Step Counts and Riser Height
Number of Risers = round(Total Rise / Target Riser)
Exact Riser Height = Total Rise / Number of Risers
Number of Treads = Number of Risers - 1 (assuming the top step lands flush with the upper finished floor).
2. Total Run and Stringer Length
Total Run = Number of Treads × Tread Depth
Stringer Length = √(Total Rise² + Total Run²)
3. Building Code Safety Limits (IRC R311.7)
- Maximum Riser Height: 7.75 inches (197 mm).
- Minimum Tread Depth: 10.0 inches (254 mm) with a minimum 0.75" to 1.25" nosing overhang.
- Maximum Variance: The greatest riser height or tread depth within any flight shall not exceed the smallest by more than 3/8 inch (9.5 mm).
- Blondel's Ergonomic Rule:
2 × Riser + Tread = 24" to 25.5". This matches the natural human walking stride.
Step-by-Step Calculation Examples
Interior Second-Floor Stairs (105 in total rise)
Framing a standard 105-inch rise staircase with target 7.25" risers and 10.5" treads.
- total_rise: 105
- desired_riser: 7.25
- tread_depth: 10.5
- nosing: 1
- stair_width: 36
- number_of_risers: 14
- actual_riser_height: 7.50 in
- number_of_treads: 13
- total_run: 136.5 in
- stringer_length: 172.2 in
- stair_angle: 37.6
- blondel_comfort_score: 25.50 in
Frequently Asked Questions
What is the maximum legal riser height for residential stairs?
Under the International Residential Code (IRC Section R311.7.5.1), the maximum riser height for residential stairs is 7.75 inches (197 mm). In commercial applications under the IBC, the maximum riser height is 7.0 inches.
What is the minimum legal tread depth for stairs?
The IRC requires a minimum tread depth of 10.0 inches (254 mm) measured from nosing to nosing. If treads are less than 11 inches deep, a nosing projection of between 3/4 inch and 1-1/4 inches is mandatory.
Why is there one less tread than risers?
When a staircase connects two floor levels, the final "step" at the top of the flight is the floor surface of the upper landing itself. Therefore, a standard flight with 14 risers requires only 13 framing treads cut into the stringer.
How much minimum headroom is required above stairs?
The IRC mandates a minimum vertical headroom clearance of 6 feet, 8 inches (80 inches or 2,032 mm). This distance is measured vertically from the sloped plane adjoining the tread nosing to any ceiling or bulkhead obstruction above.
How many stringers do I need for my staircase width?
For standard 36-inch wide wooden staircases using 5/4" pine or 2x lumber treads, 3 stringers spaced roughly 16 inches on-center are standard. If using composite or PVC decking treads, stringers must be spaced 12 inches on-center (4 stringers for a 36-inch stair) to prevent tread sagging.
Why do you cut the bottom of the stair stringer?
You must deduct the thickness of the tread material (typically 1.0" to 1.5") from the bottom heel of the stringer where it rests on the lower floor. If you skip this drop cut, the bottom step will be too tall by the thickness of the tread, and the top step will be too short.