Stair Stringer Length Calculator
Calculate exact diagonal stringer hypotenuse length, incline angle, and required commercial board length.
Input Dimensions
Stringer Results
Enter dimensions and click Calculate Stringer to see results.
Interactive Cut Stringer Blueprint
Standard Staircase Worked Examples
Click any preset to automatically populate the calculator with proven dimensional specifications.
How Diagonal Stringer Length is Calculated
Trigonometric principles behind right-angle stair framing.
Measure Total Rise
Measure the exact vertical distance between finished floor surfaces using a plumb bob or laser level. Always account for finished flooring thickness.
Calculate Number of Steps
Divide total rise by your target riser height (typically 7.5"). Round to the nearest whole integer to find the exact number of equal risers.
Determine Riser & Run
Divide total rise by the number of risers for exact height. Select tread depth (minimum 10") and verify with Blondel’s comfort formula (2R + T = 24–25").
Layout & Deduct Bottom Foot
Step off cuts with a framing square and stair gauges. Deduct the thickness of one tread from the bottom cut so the finished first step matches the rest.
Rise and Run vs Stringer Length Quick Reference
Standard floor heights and corresponding stringer diagonal dimensions.
Building Code Comparison (IRC vs IBC vs OBC vs UK)
| Code Authority | Max Riser | Min Tread | Min Width | Min Throat |
|---|---|---|---|---|
| IRC Residential (US) | 7.75" (196 mm) | 10.0" (254 mm) | 36" (914 mm) | 3.5" (89 mm) |
| IBC Commercial (US) | 7.00" (178 mm) | 11.0" (279 mm) | 44" (1118 mm) | 3.5" (89 mm) |
| OBC (Ontario, Canada) | 8.25" (210 mm) | 8.25" (210 mm) | 33.5" (860 mm) | 3.5" (89 mm) |
| UK Approved Doc K | 8.66" (220 mm) | 8.66" (220 mm) | 31.5" (800 mm) | 3.5" (89 mm) |
Lumber Selection vs Notch & Throat Depth
| Nominal Size | Actual Width | Max Cut Notch | Remaining Throat | Recommendation |
|---|---|---|---|---|
| 2×8 | 7.25" (184 mm) | 4.50" | 2.75" (Deficient) | Not Code Compliant |
| 2×10 | 9.25" (235 mm) | 5.75" | 3.50" (Borderline) | Shallow stairs only |
| 2×12 | 11.25" (286 mm) | 6.25" | 5.00" (Excellent) | Standard / Best Choice |
| LVL / Engineered | 11.875" (302 mm) | 6.50" | 5.375" (Super-Duty) | Heavy Commercial / Long Spans |
Stringer Length FAQs
Common questions about hypotenuse calculations and stock lumber lengths.
What is the formula for stair stringer length?
Stringer Length is calculated using the Pythagorean theorem: Stringer Length = √(Total Rise² + Total Run²). This yields the exact hypotenuse along the pitch line.
How much extra lumber length should I purchase?
Always buy stringer boards at least 12 to 18 inches longer than the calculated diagonal length. This gives you ample room to cut the top plumb cut and bottom level cut.