Key terminology

Rise: the vertical height of a single step.
Run: the horizontal depth of a single step (tread depth).
Total rise: the vertical distance from floor to floor.
Total run: the total horizontal length the staircase covers.
Nosing: the overhang of the tread beyond the riser face, typically 3/4” to 1”.

Building code requirements (IRC 2021)

Maximum riser height: 7¾” (7.75 in)
Minimum tread depth: 10”
Uniformity: no single riser or tread may vary from the others by more than 3/8”
Minimum headroom: 6’ 8” clear above the stair nosing

The 7-11 rule

A common design guideline is that rise + run should equal approximately 17–18 inches for comfortable stair geometry. A 7” rise + 11” run = 18”, which is considered the ideal. Taller risers demand shallower treads to maintain ergonomic step proportion.

Number of risers = Total rise ÷ Riser height (round to nearest integer)
Actual riser height = Total rise ÷ Number of risers
Total run = (Number of risers − 1) × Tread depth

Subtract 1 from the number of risers because the top landing is a floor, not a tread.

Calculation walkthrough (9-foot rise)

Suppose you need stairs from a basement floor to the first floor with a total rise of 9 feet (108 inches):

Target riser height: 7 inches (within IRC maximum of 7¾")
Number of risers: 108 ÷ 7 = 15.43 -> round to 15 risers
Actual riser height: 108 ÷ 15 = 7.2 inches (well within the ⅜" uniformity rule)
Number of treads: 15 − 1 = 14 treads
Total run at 11" tread depth: 14 × 11 = 154 inches = 12 ft 10 in

Blondel's formula

The 17th-century architect François Blondel proposed an ergonomic formula based on human stride length:

2 × Rise + Run = 63–65 cm (approximately 24.8–25.6 inches)

This formula reflects the average human stride length and produces stairs that feel natural to ascend. A 7" (17.8 cm) rise with an 11" (28 cm) run gives 2 × 17.8 + 28 = 63.6 cm - squarely in the ideal range.

Open vs. closed risers

Closed risers have a vertical board (riser board) filling the gap between treads, making the staircase solid and enclosed. This is the standard for interior residential stairs.

Open risers have no vertical board - the space between treads is open. This modern aesthetic is popular for floating staircases, but building codes restrict the gap: openings must not allow passage of a 4-inch diameter sphere (per IRC), which protects young children from falling through or getting their heads trapped.