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Stair Calculator,
rise, run, stringers & code.
Compute riser height, tread depth, stringer length, and stair angle from your total rise and run. Checks IRC and IBC building-code limits, flags the 2R + T comfort rule, and draws a scaled stair diagram — in imperial or metric.
Inputs
Stair dimensions
Units
Calculation mode
Building code
Vertical height from floor to landing (inches)
Horizontal distance available for stairs (inches)
Examples
- Steps (risers)
- 14
- Riser height
- 7.71"
- Tread depth
- 10.29"
- Stringer
- 180"
Step count
✓ Code compliant7.71" rise per step · 10.29" tread depth
Diagram
Side-view staircase profile
Compliance
✓ Meets building code
- Riser height7.71"
4"–7.75" per IRC Residential
- Tread depth10.29"
min 10" per IRC Residential
- 2R + T rule25.71"
target 24–25" for comfort
- Stringer angle36.87°
recommended 20°–38° (too steep or too shallow is awkward)
Stair-building guide
How stair geometry works — rise, run, and the comfort rule.
A flight of stairs is a deceptively precise geometry problem. The relationship between riser height and tread depth controls not just whether the stairs feel comfortable to walk, but whether they meet local building codes and both of those depend on the same two inputs: total rise (the vertical height you need to climb) and total run (the horizontal distance you have available).
Anatomy of a staircase
| Term | Definition | Typical range |
|---|---|---|
| Rise (riser height) | Vertical height of one step | 4"–7¾" (IRC) |
| Run (tread depth) | Horizontal depth of one step | 10"–18" |
| Total rise | Floor-to-floor vertical height | Varies |
| Total run | Horizontal footprint of the flight | Varies |
| Stringer | Diagonal structural board supporting the treads | — |
| Nosing | Tread overhang past the riser face | ¾"–1¼" |
| Headroom | Clearance above any tread to ceiling/obstruction | min 80" (IRC) |
The stair geometry formulas
Given n steps, total rise H, and total run R:
The stringer length is simply the hypotenuse of the right triangle formed by the total rise and total run, the same Pythagorean theorem you learned in school. The angle tells you how steep the flight is; code-comfortable stairs typically fall between 20° and 38°.
The 2R + T comfort rule
Building codes define minimums, but the classic ergonomics guideline goes a step further:
This rule, attributed to 17th-century French architect François Blondel, captures the natural stride length of a person climbing stairs. A riser of 7" and tread of 11" gives 2×7+11 = 25" — right in the sweet spot. Steeper stairs (large rise, narrow tread) and shallower ones (small rise, deep tread) both score outside that range and feel awkward or tiring.
Choosing the right number of steps
The number of steps n must satisfy two constraints simultaneously:
- Riser height ≤ code maximum: For IRC residential code, that is 7¾" (7.75"). For IBC commercial, 7". The minimum step count is therefore
⌈total rise / max riser⌉. - Riser height ≥ code minimum: The IRC minimum is 4". Adding too many steps makes each one tiny, which is a tripping hazard on the way down.
This calculator finds the smallest n that keeps the riser within both limits, then divides total run by n to get tread depth. In rise-only mode (when total run isn't known), it derives tread depth from the 2R+T midpoint (24.5" or 62.2 cm) or from your target tread depth override.
IRC vs. IBC building codes
| Requirement | IRC 2021 (Residential) | IBC 2021 (Commercial) |
|---|---|---|
| Max riser height | 7¾" (19.7 cm) | 7" (17.8 cm) |
| Min riser height | 4" (10.2 cm) | 4" (10.2 cm) |
| Min tread depth | 10" (25.4 cm) | 11" (27.9 cm) |
| Min headroom | 80" (203.2 cm) | 80" (203.2 cm) |
| Max riser variation | ⅜" between any two risers | ⅜" between any two risers |
| Nosing required | Yes (¾"–1¼") if tread < 11" | Yes (¾"–1¼") |
The IRC (International Residential Code) governs one- and two-family homes and townhouses up to three stories. The IBC (International Building Code) governs everything else — commercial buildings, multi-family housing, and most public spaces. Most U.S. states and municipalities adopt one of these codes, often with local amendments. Always verify with your local authority having jurisdiction (AHJ) before building.
Sizing the stringer
The stringer is the diagonal structural member that the treads rest on. Two types are common:
- Cut (open) stringer: The stringer board is notched to follow the stair profile. You can see the riser triangles from the side. Requires a minimum of 3½" of uncut wood remaining at the deepest notch (the "effective depth") to maintain structural integrity. For a standard 2×12 lumber stringer, this limits notch depth.
- Solid (closed) stringer: The stringer is not notched; treads are dadoed, bracketed, or cleat-mounted. Stronger and allows shallower lumber but more complex to fabricate.
For a cut stringer in typical residential construction, a 2×12 (actual 1.5" × 11.25") is the standard starting point. Longer flights or heavy loads may require a 3×12 or an LVL stringer.
Common stair scenarios
| Application | Typical total rise | Typical steps | Notes |
|---|---|---|---|
| Interior home stair | 8–9 ft (96–108") | 13–14 | IRC; 7¼" rise / 10" tread typical |
| Deck / exterior stairs | 2–4 ft (24–48") | 4–8 | 7" rise common; consider grading |
| Basement stairs | 8–9 ft (96–108") | 13–15 | IRC; often steeper due to space constraints |
| Commercial stair | 9–12 ft (108–144") | 15–20 | IBC; 7" max riser, 11" min tread |
| Porch / entry steps | 1.5–3 ft (18–36") | 3–5 | Low flights; check local frost heave rules |
Using metric measurements
This calculator works in both imperial (inches) and metric (centimetres). In metric mode, the same formulas apply and the comfort rule becomes:
The IRC/IBC code limits are converted to their exact metric equivalents. Most jurisdictions outside the United States use similar ergonomic guidelines but different code documents — consult your local building authority for jurisdiction-specific limits.