Stair math
Divide total rise by the maximum riser height and round up to get the number of risers; then divide total rise by that number for the actual (equal) riser height. Treads = risers − 1 when the top floor acts as the last step. Total run = treads × tread depth, and the stringer is roughly √(rise² + run²).
Example: 108 in rise ÷ 7.75 = 13.9 → 14 risers of 7.71 in; 13 treads × 10 in = 130 in run; stringer ≈ √(108² + 130²) = 169 in.
Code limits (IRC residential)
- Maximum riser height 7¾ in; minimum tread depth 10 in
- Variation between risers or treads no more than 3/8 in
- Minimum headroom 6 ft 8 in
Local codes may differ—check with your building department before cutting stringers. Add stringer length for the top connection and bottom cut.