How to Calculate Stair Rise and Run
Designing stairs is mostly a math problem: divide your floor-to-floor height into equal steps, each safe enough to climb without tripping. The hard part is matching the IRC code requirements (rise ≤ 7.75 inches, tread ≥ 10 inches, width ≥ 36 inches) while staying within the constraints of your actual space.
Actual rise per step = Total rise ÷ riser count
Total run = (risers − 1) × tread depth
Stringer length = √(total rise² + total run²)
Stair angle = arctan(rise ÷ run) — typically 30-38°
The "minus 1" in the total-run formula trips up first-timers. If you have 14 risers (steps up), the top one ends at the upper floor — so you only build 13 horizontal treads. Walk up the stairs and count: you press your foot down 13 times before stepping onto the landing.
Worked example: typical residential stairs
Floor-to-floor height: 108 inches (9 ft including subfloor and finish flooring). Target: 7.5-inch rise, 10-inch tread.
- Number of risers: 108 ÷ 7.5 = 14.4 → round to 14 risers
- Actual rise: 108 ÷ 14 = 7.71 inches (under the 7.75-inch IRC max ✓)
- Number of treads: 14 − 1 = 13 treads
- Total run: 13 × 10 = 130 inches (10 ft 10 in)
- Stringer length: √(108² + 130²) = √(11,664 + 16,900) = √28,564 ≈ 169 inches (14 ft 1 in)
- Angle: arctan(108 ÷ 130) = 37.6° (comfortable, well under steep)
IRC Stair Code Requirements (2026)
The International Residential Code (IRC) is adopted with local modifications by nearly every US jurisdiction. Section R311.7 covers stairways. The main requirements that affect every residential stair design:
| Dimension | IRC requirement | Common practice |
|---|---|---|
| Maximum riser height | 7.75 inches | 7-7.5 inches typical |
| Minimum tread depth | 10 inches | 10-11 inches typical |
| Minimum stair width | 36 inches above handrail | 36-42 inches |
| Minimum headroom | 80 inches vertical clearance | 80+ inches |
| Maximum variation between risers | 0.375 inch (3/8) | Keep within 0.125 inch |
| Maximum variation between treads | 0.375 inch (3/8) | Keep within 0.125 inch |
| Nosing projection | 0.75-1.25 inches if treads < 11 inches | 1 inch typical |
| Handrail required | 4+ risers | Same |
| Handrail height | 34-38 inches above tread nosing | 36 inches typical |
The 3/8-inch tolerance on rise-to-rise variation is the most commonly violated rule. Even small inconsistencies (the bottom step a half-inch shorter because the slab is high, for example) increase trip rates dramatically — your foot expects each step to be identical.
Stair Anatomy
- Riser: The vertical part between two treads. Can be solid (closed riser) or left open.
- Tread: The horizontal surface you step on. Includes the nosing overhang.
- Nosing: The 0.75-1.25 inch overhang of the tread beyond the riser below it.
- Stringer: The diagonal board (or steel channel) that supports the steps. Usually 2x12 lumber.
- Total rise: Floor-to-floor height from finished surface to finished surface.
- Total run: Horizontal distance from the top step to the bottom of the bottom riser.
- Landing: A flat platform interrupting the stair — required for runs over 12 ft, or where direction changes.
- Handrail: Continuous gripping surface 34-38 inches above the tread nosing.
- Baluster: The vertical pickets in the guardrail. Spacing must be tight enough that a 4-inch sphere can't pass through.
- Newel post: The structural post at the top and bottom of a railing.
Stair Stringer Sizing and Materials
The stringer carries the entire load of the stairs and anyone walking on them. After cutting the notches for rise and run, at least 5 inches of solid wood must remain at the narrowest point (the throat). This is why 2x12 lumber (11.25 inches actual depth) is standard for residential stair stringers — 2x10 doesn't leave enough material.
Wood stringer rules
- 2x12 lumber — Standard for residential stairs. Allows safe notching for 7-8 inch rise.
- Pressure-treated — Required for exterior stairs and any stringer touching concrete.
- Maximum unsupported span: 13 feet 3 inches for 2x12 stringers at typical rise/run.
- Minimum 3 stringers for stairs 36 inches wide. Add a center stringer for stairs 4+ ft wide.
- Stringer spacing — Maximum 16 inches on center for 1-inch tread material; 24 inches OC for 2-inch treads.
- Hangers vs ledger — Top of stringer can be hung from a ledger board with joist hangers, or rested on a beam. Bottom rests on the slab or a footing pad.
Steel stringer notes
Pre-fabricated steel stringers (also called "stringer brackets") are available at home centers in common configurations: 3-step, 4-step, 5-step. They snap onto your 2x12 lumber and create the notches without precise cutting. Code-compliant when used per manufacturer instructions; useful for short outdoor stairs and decks.
Stair Materials and Cost Breakdown 2026
| Component | Typical cost | Notes |
|---|---|---|
| 2x12 SPF lumber (16 ft) | $35-55 | For stringers |
| 2x12 pressure-treated (16 ft) | $55-90 | Exterior stringers |
| 2x10 tread material (10 ft) | $20-35 | Pine or fir |
| Oak tread (pre-cut, 36 in) | $30-50 each | Interior, finish-grade |
| Pre-cut riser board | $15-25 each | Pine, primed |
| Stair tread brackets (steel) | $8-15 each step | For prebuilt design |
| Handrail (8 ft section) | $25-60 | Pine, oak, or aluminum |
| Baluster (each) | $3-12 | Wood or iron |
| Newel post (turned) | $40-150 | Wood, varies by style |
| Total DIY material (12-step interior) | $400-800 | Add carpet or hardwood |
| Total DIY material (deck stairs) | $200-400 | Pressure-treated, 3-5 steps |
| Pro installation (interior) | $1,500-4,500 | Open-tread, varies by finish |
How to Build Stairs: Step by Step
- Measure total rise. Top of upper finished floor to top of lower finished floor. If lower floor isn't poured yet, factor in slab thickness and finish flooring.
- Calculate rise/run. Use this calculator. Adjust target rise to land on a whole-number riser count that fits IRC limits.
- Check the horizontal run. Make sure your stair fits in the available space. Reduce tread depth or add a landing if needed.
- Verify headroom. 80 inches minimum from any tread nosing to the ceiling above.
- Buy stringer stock. 2x12 pressure-treated for exterior, 2x12 SPF or fir for interior. Get one extra board — measuring errors are common.
- Mark stringer cuts. Use a framing square set to your rise and run dimensions. Mark all cuts before any are made — verify the sum equals your total rise.
- Cut the stringers. Circular saw for the long cuts, hand saw to finish the corners (don't overcut — it weakens the stringer).
- Subtract for tread thickness at the bottom. Bottom of the first stringer must be cut shorter by the tread thickness so the first step ends up the right height.
- Install stringers. Top hung from ledger board with stringer hangers, or rested on a 2x4 ledger. Bottom rests on slab or treated 2x4 pad.
- Install risers, then treads. Risers first (back of step), then treads (where you walk). Glue and screw — no nails — to prevent squeaks.
- Add handrail and balusters. Required for 4+ risers. Handrail 34-38 inches above tread nosings, continuous from top to bottom.
Common Stair Mistakes
- Forgetting to subtract tread thickness at the bottom: Bottom step ends up 1-inch taller than the rest. Major code violation and trip hazard.
- Inconsistent rise heights: Each step must be within 3/8 inch. Even small inconsistencies cause trips.
- Stringer notched too deeply: Less than 5 inches of throat remaining = weak stringer that can split. Upsize to 2x12.
- No nosing: Treads less than 11 inches deep must have a 0.75-1.25 inch nosing for foot placement.
- Headroom too low: Stair under a soffit or doorway often clips the 80-inch minimum. Plan early.
- Handrail too short: Must extend the full length of the stair plus 12 inches at top and bottom for ADA, or simply continuous start-to-finish for residential.
- Wrong tread material for outdoor: Untreated lumber outdoors rots within 2-3 years. Use pressure-treated, cedar, or composite.
- Open risers in homes with kids: A 4-inch sphere can't pass through any opening. Open risers fail this — close them with riser boards.
Special Stair Types
Deck stairs
Most decks are 24-36 inches above grade — 4 to 5 risers. Use 2x12 pressure-treated stringers, pressure-treated 2x6 or 2x10 treads (no risers needed for open deck stairs), and a galvanized or stainless steel hardware kit. Footings required at the bottom — concrete pier or buried 4x4 post.
Spiral stairs
Code allows 26-inch minimum diameter, 6.75-inch minimum tread depth measured 12 inches from the narrow end, and 9.5-inch maximum rise. Most spirals are 5-6 ft diameter. Pre-fabricated steel kits run $1,500-5,000; custom wood spirals $8,000-25,000+. Spiral stairs cannot serve as the only means of egress from a habitable area in most jurisdictions.
Winder stairs
Wedge-shaped treads that turn a corner without a landing. Used to save space in tight footprints. IRC requires the tread depth at the walk line (12 inches from the narrow end) to meet the same minimums as straight stairs. Each winder tread must have at least 10-inch run at the walk line and at least 6 inches at the narrow end.
Basement stairs
Often steeper than IRC ideal due to space constraints, but still must meet the 7.75-inch rise max and 10-inch tread min. Most jurisdictions enforce IRC stairs to basements. Older homes were often built before current code — you can usually leave existing as-is, but any replacement must meet current code.