Stair Stringer Calculator Formula
Understand the math behind the stair stringer calculator. Each variable explained with a worked example.
Formulas Used
Number of Risers
number_of_risers = num_risersActual Riser Height
actual_riser_height = actual_riserNumber of Treads
number_of_treads = num_treadsTotal Run (Horizontal)
total_run = num_treads * tread_depthStringer Length
stringer_length = sqrt(pow(total_rise, 2) + pow(num_treads * tread_depth, 2))Stringers Needed
num_stringers = stair_width <= 36 ? 3 : (floor(stair_width / 16) + 1)Variables
| Variable | Description | Default |
|---|---|---|
total_rise | Total Rise (Floor to Floor)(inches) | 108 |
desired_riser | Desired Riser Height(inches) | 7.5 |
tread_depth | Tread Depth(inches) | 10 |
stair_width | Stair Width(inches) | 36 |
num_risers | Derived value= round(total_rise / desired_riser) | calculated |
actual_riser | Derived value= total_rise / round(total_rise / desired_riser) | calculated |
num_treads | Derived value= round(total_rise / desired_riser) - 1 | calculated |
How It Works
How to Calculate Stair Stringers
Formula
Number of Risers = round(Total Rise / Desired Riser Height)
Actual Riser = Total Rise / Number of Risers
Number of Treads = Number of Risers - 1
Total Run = Number of Treads × Tread Depth
Stringer Length = sqrt(Total Rise² + Total Run²)
Building code typically requires: Max riser height 7-3/4 inches, min tread depth 10 inches, and the riser + tread combination should fall between 17 and 18 inches.
Worked Example
A staircase with 108 inches (9 feet) of total rise, 7.5" desired risers, 10" treads, 36" wide.
- 01Number of risers = round(108 / 7.5) = 14 risers
- 02Actual riser height = 108 / 14 = 7.714 inches
- 03Number of treads = 14 - 1 = 13 treads
- 04Total run = 13 × 10 = 130 inches (10.83 ft)
- 05Stringer length = sqrt(108² + 130²) = sqrt(28,564) = 169 inches (14.1 ft)
- 06Stringers needed = 3 (for 36" width)
Frequently Asked Questions
What is the maximum riser height allowed by code?
The IRC (International Residential Code) limits risers to 7-3/4 inches maximum. Local codes may vary. All risers in a flight must be uniform (within 3/8 inch).
What is the minimum tread depth?
The IRC requires a minimum tread depth of 10 inches (not including the nosing). The nosing should project 3/4 to 1-1/4 inches beyond the riser.
How many stringers do I need?
Use 3 stringers for stairs up to 36 inches wide. Add an additional stringer for every 16 inches of width beyond 36 inches.
Learn More
Guide
How to Calculate Stair Dimensions: Rise, Run, and Stringer Layout
Learn how to calculate stair dimensions including riser height, tread depth, stringer length, and total run. Covers building code requirements and layout techniques.
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Open Stair Stringer Calculator