Construction · Architecture · Building
Stair
Calculator
Calculate number of steps, rise height, run depth, stringer length, and stair angle. Includes IRC/IBC building code compliance check, SVG diagram, and material estimator.
—
Steps
—
Rise (in)
—
Angle
Find Number of Steps
Enter your total rise and preferred rise/run dimensions. The calculator finds the optimal number of steps.
in
in
in
in
in
in
Find Rise & Run per Step
Enter total rise and your desired number of steps to find the optimal rise and run dimensions.
in
steps
in
in
Number of Steps
—
risers
Rise each
—
Run each
—
Stair Diagram
Steps
—
Stringer Len.
—
Angle
—
Total Run
—
Stair Dimensions
🏛️ IRC / IBC Building Code Check
🪵 Material Estimate
Stair Design Fundamentals
Properly designed stairs balance safety, comfort, and building code requirements. The key relationship is the "rise + run rule": Rise + Run should be between 17–18 inches for comfortable climbing. Another rule: 2×Rise + Run = 24–25 inches.
Key Formulas & Building Code (IRC)
Number of risers = ceil(Total Rise / Preferred Rise)
Actual Rise per step = Total Rise / Number of Risers
Total Run = (Number of Risers - 1) × Tread Depth
Stringer Length = √(Total Rise² + Total Run²)
Stair Angle = arctan(Total Rise / Total Run)
IRC Residential Code Minimums:
Max rise per step: 7¾ inches (196mm)
Min rise per step: 4 inches (102mm)
Min tread depth: 10 inches (254mm)
Min stair width: 36 inches (914mm)
Min headroom: 6'8" = 80 inches (2032mm)
Max nosing: 1¼ inches (32mm)
Comfortable range: rise 6.5–7.5 in, tread 10–11 in
What is the ideal rise and run for stairs?
The most comfortable stairs follow the "rise + run = 17–18 inches" rule. A 7-inch rise with an 11-inch run (7+11=18) is widely considered ideal for residential stairs. The complementary formula is 2×rise + run = 24–25 inches (2×7+11=25). Too steep (high rise) is tiring and dangerous going down. Too shallow (low rise, long run) wastes floor space and feels awkward. The sweet spot for comfort is rise 6.5–7.5 inches, run 10–12 inches.
How do I calculate the number of stairs?
Divide total rise (floor to floor height) by your preferred rise per step. Round to the nearest whole number — that's your number of risers. Then divide total rise by that number for the exact rise per step. Example: 9-foot ceiling = 108 inches. 108 ÷ 7 = 15.4, round to 15 risers. Actual rise = 108/15 = 7.2 inches per step. Note: number of treads = number of risers − 1, because the top floor acts as the last "tread."
What is a stringer and how long should it be?
A stringer is the diagonal structural member that supports the treads and risers. Its length is calculated using the Pythagorean theorem: stringer length = √(total rise² + total run²). For example, total rise = 108 inches, total run = 14 × 11 = 154 inches. Stringer = √(108² + 154²) = √(11664 + 23716) = √35380 ≈ 188 inches = 15.7 feet. Most residential stairs use 2×12 lumber for stringers. A standard 16-foot 2×12 can handle most runs, but very long staircases may need a center stringer for support.
Does stair angle matter?
Yes — stair angle affects both safety and comfort. Comfortable residential stairs: 30°–37°. Steeper than 45° is considered a "ship's ladder" and may not meet code. Shallower than 20° feels very gradual and wastes floor space. The most common residential angle is around 32°–38°. Commercial and public stairs tend toward the lower end (around 27°–32°) for accessibility. ADA-compliant ramps must be 1:12 slope (4.8°) or less.