Stair Calculator
Calculate the number of risers, tread depth, and stringer length for a complete staircase layout.
Formula & Explanation
The stair calculator determines the configuration of a complete staircase based on total vertical rise and desired riser height. **Number of Risers** = round(total rise ÷ target riser height) **Actual Riser Height** = total rise ÷ number of risers (may differ slightly from target to fit the rise evenly) **Number of Treads** = risers − 1 (the top riser lands on the upper floor, no tread needed) **Total Run** = number of treads × tread depth **Stringer Length** = √(total rise² + total run²) (using the Pythagorean theorem) The stringer is the diagonal board that supports the steps. Both rise and run dimensions are used to calculate its exact length, which is critical for cutting the stringer accurately.
Assumptions
- •Riser heights conform to typical residential building codes (7-7.75" common; 7" typical minimum, 7.75" typical maximum)
- •Tread depths conform to typical residential codes (10-11" minimum, measured from front of one riser to front of next)
- •Building codes vary by jurisdiction; local codes may have stricter limits. Accessibility ramps may have different requirements.
- •The stringer length assumes straight flights; landings or turns would require additional geometry
- •Open risers (where the step is visible underneath) may require additional structural support
- •Handrails and guardrails are subject to separate code requirements (typically 34-38" height, 4" sphere rule for baluster spacing)
Example Calculation
An 8-foot (96") rise with a 7.5" target riser results in 13 risers and 12 treads (the top riser lands on the upper floor). With 10.5" treads, the total run is 126", and the stringer diagonal measures about 161.56".
Inputs
Results
Common Staircase Configurations by Total Rise
| total rise | risers (at 7") | treads | tread depth (10") | stringer length |
|---|---|---|---|---|
| 7 ft (84") | 12 | 11 | 110" | ~145" |
| 8 ft (96") | 13 | 12 | 126" | ~162" |
| 9 ft (108") | 14 | 13 | 130" | ~173" |
| 10 ft (120") | 16 | 15 | 150" | ~195" |
| 10 ft (120") | 17 | 16 | 160" | ~207" |
| 11 ft (132") | 18 | 17 | 170" | ~218" |
| 12 ft (144") | 19 | 18 | 180" | ~230" |
Frequently Asked Questions
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