Stair Calculator
Design safe stairs with IBC-compliant rise/run calculations. Computes number of steps, riser height, tread depth, stringer length and angle. Warns if measurements violate International Building Code standards.
Stair
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The Formula
Stair stringer layout follows the Pythagorean theorem. The number of risers is determined by dividing total rise by desired riser height and rounding up, then the exact riser height is recalculated.
Variable Definitions
Total Rise & Total Run
Rise is the total vertical height from finished floor to finished floor. Run is the total horizontal distance covered by the staircase. These two values determine the stair angle and stringer length.
Stringer Length
Diagonal length of the stair stringer board, typically a 2x12.
IBC Limits
International Building Code: max riser 7.75", min tread 10".
How to Use This Calculator
- 1
Measure the total vertical rise from finished floor to finished floor.
- 2
Enter your desired riser height (typically 7 inches).
- 3
Enter your desired tread depth (typically 11 inches).
- 4
Review the calculated number of steps, stringer dimensions, and IBC compliance status.
Stair geometry: riser = vertical, tread = horizontal, stringer = diagonal
Understanding the Concept
Stair design balances comfort, safety, and code compliance. The IBC limits risers to 7.75 inches maximum and treads to 10 inches minimum. The stringer is cut from a 2x12 board following the rise and run measurements. The stair angle typically falls between 30 and 50 degrees for comfortable ascent. Practical example: a total rise of 105 inches with a desired riser of 7 inches yields 105 / 7 = 15 risers exactly. With 14 treads at 11 inches depth, the total run is 14 × 11 = 154 inches (12 feet 10 inches). The stringer length is sqrt(105² + 154²) = sqrt(11025 + 23716) = sqrt(34741) = 186.4 inches (15 feet 6 inches). The angle is arctan(105/154) = 34.3 degrees, which falls in the comfortable range. Edge cases: for exterior stairs exposed to snow and ice, consider using open treads or adding heating elements to prevent ice buildup. For spiral or curved staircases, the inside radius must be at least twice the stair width to meet code. When the total rise results in fractional risers (e.g., 105.5 inch rise with 7 inch desired riser), the calculator rounds up to 16 risers, giving an actual riser of 6.59 inches. For basement stairs with limited headroom, a steeper angle up to 42 degrees may be acceptable, but any angle above 45 degrees should require a landing or an alternating tread design.
Frequently Asked Questions
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