Stair Calculator

Stair design balances comfort, safety, and code compliance. For houses the IRC limits risers to 7.75 inches maximum and treads to 10 inches minimum; commercial buildings under the IBC are stricter at 7 inches and 11 inches. 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.