Stair Calculator
Calculate rise, run, number of steps, stringer length, and all materials needed. Checks IRC and IBC building code compliance automatically. Includes a visual stair diagram. Updated .
Stair Calculator — Building Code & Design Guide ()
Building a staircase requires precise calculations to ensure safety, comfort, and code compliance. The relationship between rise (the vertical height of each step) and run (the horizontal depth of each tread) directly determines how comfortable and safe stairs are to climb. Stairs that are too steep feel tiring and dangerous; stairs that are too shallow waste space and feel awkward.
The Rise + Run Formula
The classic ergonomic formula for comfortable stairs is: 2 × Rise + Run = 24"–25". For a 7" rise: 2 × 7 = 14, so run should be 10–11". For a 6.5" rise: run should be 11"–12". This formula, developed by 17th-century French architect François Blondel, has been validated by centuries of stair building and remains the gold standard for comfortable stair design.
IRC Building Code Requirements
| Dimension | IRC Minimum / Maximum | Recommended | Notes |
|---|
| Riser height | Max 7¾" (7.75") | 6¾"–7¼" | All risers must be within 3/8" of each other |
| Tread depth | Min 10" | 11"–11½" | Measured from nosing to nosing |
| Stair width | Min 36" | 36"–42" | Clear width between handrails |
| Headroom | Min 6'8" (80") | 7'0" | Measured vertically above stair nosing |
| Nosing projection | ¾"–1¼" | 1" | Overhang of tread beyond riser below |
| Landing depth | Min 36" | Equal to width | At top and bottom of stair |
| Handrail height | 34"–38" | 36" | Required if 4+ risers |
| Guardrail height | Min 36" | 42" | Required if open side 30"+ above floor |
How to Measure Total Rise
Total rise is the vertical distance from the top surface of the lower floor to the top surface of the upper floor. For a deck, it's from the ground to the top of the decking. Measure this precisely — an error of even half an inch throws off all your riser heights. If your floor-to-floor measurement is, say, 108.5 inches, the calculator distributes that across the number of risers to give you even, code-compliant riser heights.
Stringer Length Formula
Stringer length = √(Total Rise² + Total Run²). This is the Pythagorean theorem applied to the hypotenuse of the right triangle formed by the stairs. A typical 9-foot ceiling stair with 11" treads: √(108² + 154²) = √(11664 + 23716) = √35380 ≈ 188" (about 15.7 feet). This is the minimum board length needed for each stringer — in practice you'll use a 16-foot 2×12.
How do I calculate the number of steps for stairs?
Divide the total rise (floor-to-floor height in inches) by your desired riser height. Round to the nearest whole number — that's your step count. Then divide the total rise by that step count to get the exact riser height. For example: 108 inches ÷ 7 inches = 15.43, round to 15 steps. Exact riser = 108 ÷ 15 = 7.2 inches per step. This ensures all risers are exactly equal, which is a code requirement and a safety issue — unequal risers are a major cause of stair falls.
What is the standard stair rise and run?
The standard residential stair rise is 7" to 7¾" per step, with a run (tread depth) of 10" to 11½". The IRC maximum riser height is 7¾" and minimum tread depth is 10". For comfort, most builders target 7" rise and 11" run, which satisfies the 2R+T = 25" ergonomic formula (2×7 + 11 = 25). Steeper stairs with 7¾" risers and 10" treads are code-compliant but less comfortable, especially for older adults.
How many stringers do I need?
The number of stringers depends on stair width. For stairs up to 30" wide, 2 stringers (one on each side) are sufficient. For 30"–48" wide stairs, 3 stringers are needed (two sides plus one center). For stairs wider than 48", use 4 or more stringers. Each stringer should be no more than 16"–18" apart. Stringers are typically cut from 2×12 lumber (the strongest option) or doubled 2×10. The notch depth should not reduce the remaining stringer depth below 3½".
What size lumber for stair stringers?
Stair stringers are typically cut from 2×12 dimensional lumber. After cutting the notches for the treads, the remaining "effective depth" of the stringer (the narrowest part) must be at least 3.5 inches per IRC code. A 2×12 (actual 11.25" wide) provides enough material for deep notches while maintaining this minimum. Never use 2×10 for notched stringers — there isn't enough material. Some builders use engineered lumber (LVL) for long spans.
How do I calculate stair stringer length?
Use the Pythagorean theorem: stringer length = √(total rise² + total run²). Total run = number of treads × tread depth (note: number of treads = number of risers minus 1, because the top landing is the floor itself). For example, 15 risers at 7.2" each = 108" total rise. 14 treads at 11" each = 154" total run. Stringer = √(108² + 154²) = √(11664 + 23716) = √35380 ≈ 188 inches (15.7 feet). Buy 16-foot 2×12s.
Do I need a permit to build stairs?
Most jurisdictions require a building permit for stair construction, especially for interior stairs and deck stairs attached to a house. Permits ensure your stairs are inspected for code compliance. Unpermitted stairs can cause problems when selling your home and may not be covered by insurance if someone is injured. Check with your local building department — deck stair permits typically cost $50–$150 and the inspection process is straightforward if you follow IRC requirements.