Stair Calculator — Risers, Treads, Stringer Length & Angle
Calculate number of risers and treads, actual riser height, total run, stringer length, and slope angle from your floor-to-floor rise. Includes IRC building-code check (max 7¾″ riser, min 10″ tread).
Stair Calculator
IRC Code Requirements (US Residential)
| Dimension | Imperial | Metric |
|---|---|---|
| Maximum riser height | 7¾″ | 197 mm |
| Minimum tread depth | 10″ | 254 mm |
| Minimum stair width | 36″ | 914 mm |
| Minimum headroom (clearance above) | 6 ft 8″ | 2032 mm |
| Maximum riser/tread variation | 3/8″ | 9.5 mm |
| Handrail height (above nose) | 34–38″ | 864–965 mm |
| Handrail required when | 4 or more risers | |
From the 2021 International Residential Code (IRC R311.7). Local codes may be stricter; commercial buildings follow IBC. Always confirm with your AHJ (Authority Having Jurisdiction) before building.
How to Calculate Stairs
- Measure total rise: floor-to-floor height (don’t forget the upper-floor thickness).
- Choose preferred riser height: 7″ (18 cm) is comfortable; 7¾″ (19.7 cm) is the IRC max.
- Number of risers: total rise ÷ preferred riser, rounded to nearest whole number.
- Actual riser height: total rise ÷ number of risers (will be slightly different from preferred).
- Number of treads: risers − 1. (The top floor is the last "tread" so it doesn’t count.)
- Total run: treads × tread depth. This is the horizontal length the stairs occupy.
- Stringer length: √(rise² + run²) using the Pythagorean theorem. Order one size up.
Imperial example: 96″ rise, prefer 7″ risers, 11″ treads. Risers = 96 ÷ 7 ≈ 14. Actual riser = 96 ÷ 14 = 6.86″. Treads = 13. Run = 13 × 11 = 143″ (11.92 ft). Stringer = √(9216 + 20449) = 172.2″ (14.35 ft). Angle = arctan(96/143) = 33.9°.
Metric example: 244 cm rise, prefer 18 cm risers, 28 cm treads. Risers = 244 ÷ 18 ≈ 14. Actual riser = 244 ÷ 14 = 17.4 cm. Treads = 13. Run = 13 × 28 = 364 cm (3.64 m). Stringer = √(244² + 364²) = 438 cm (4.38 m). Angle = 33.9°.
Stair Comfort Formulas
Three classic formulas help judge whether a stair pitch will feel comfortable:
- 2R + T = 24–25″ (rule of 25, residential). The most widely used: 2×riser + tread should be between 24 and 25 inches. Example: 7 + 7 + 11 = 25 ✓.
- R + T = 17–18″. Simpler check — rise plus tread between 17 and 18 inches.
- R × T = 72–75. Rise × tread should be in this range. Example: 7 × 11 = 77 (slightly steep but acceptable).
If your stair fails the 2R+T rule by more than 1 inch in either direction, the rhythm will feel "off" — either tippy-toe (steep) or shuffling (shallow).
Stringer Material Selection
- 2×12 SPF or pressure-treated: standard for indoor and outdoor stairs up to ~3 ft wide. Cut three for ≥36″ width to limit deflection.
- 2×10: works for short flights (4 risers or fewer); 2×12 preferred for longer.
- Engineered LVL/LSL: for very long open stairs (no mid-span support), use laminated veneer lumber rated for the load.
- Steel stringers: commercial and industrial — 4″/6″ channel sections, no deflection issues.
Always order stringers one nominal length up from your calculation. A 14-ft stringer needs at least a 16-ft 2×12 because the cut wastes material at both ends.
Frequently Asked Questions
How many stairs do I need for an 8-foot rise?
8 ft = 96 inches. Divided by a typical 7″ riser = 13.7, rounded to 14 risers. Actual riser height becomes 96 ÷ 14 = 6.86″. Number of treads = risers − 1 = 13. With 11″ treads, total run = 143″ (11.9 ft). Stringer length = √(96² + 143²) = 172″ (14.3 ft).
What is the standard riser height?
IRC maximum riser is 7¾″ (197 mm); minimum tread is 10″ (254 mm). Comfortable residential stairs typically use 7″ risers with 11″ treads. The "rule of 25": 2×Riser + Tread should fall between 24 and 25 inches for natural walking cadence.
How long should my stair stringer be?
Stringer length = √(total rise² + total run²). For an 8 ft rise (96″) with 11″ treads and 13 treads: total run = 143″, stringer = √(9216 + 20449) = 172″ (14 ft 4 in). Always order the next standard length up — 14 ft or 16 ft 2×12 boards are common. Add 6–12″ for the cuts at top and bottom.
What angle should stairs be?
Comfortable residential stairs have an angle of 30°–35°. The IRC allows up to 38° (about 7¾″ rise / 10″ tread). Angles above 42° are very steep and considered ladder-like. Below 25° is gentle but takes more horizontal space — common for outdoor or commercial stairs.
Related Calculators
- Board Foot Calculator — estimate lumber volume and cost for your stringers and treads
- Concrete Calculator — for concrete steps and landings (Steps mode)
- Rafter Length Calculator — same triangulation math for roof framing
- Decking Calculator — building stairs onto a deck?
- Rebar Calculator — reinforcement steel for concrete steps
- Slope (Degrees ↔ Percent) — stair angle vs rise-over-run slope
- All Construction Calculators
Code values from the 2021 IRC. Local building codes (IBC commercial, AHJ residential) may impose stricter limits. Stair design should also account for headroom, landings every 12 vertical feet, and handrail requirements above 4 risers. Consult a licensed contractor or engineer for structural designs.
