Mathematical Derivation & Field Specifications: 5-Step Deck (36" Rise)
For a finished floor-to-floor vertical elevation of 36" (3.00 ft / 914 mm) using a Standard Sub-Riser Drop Ledger Mount and 10.5" tread depth, dividing the total rise by the ergonomic target riser height of 7.35" yields 4.90 raw steps. Locking the riser integer to 5 vertical risers establishes an exact unit rise of 7.200" (7-3/16" / 183 mm) per step.
Because this layout specifies a drop top connection with 1" finished tread stock, the stringer carriage requires 4 horizontal tread cuts spanning a total horizontal floor projection (Total Run) of 42.0" (3.50 ft) at a stair pitch angle of 34.4°. The bottom plumb cut must be shortened (dropped) by the 1" tread thickness so the finished first step finishes at exactly 7-3/16" above the lower landing: bottom notch rise = 6-3/16" (6.200"). To maintain the mandatory 80" minimum vertical headroom clearance through a 10.5" upper floor assembly, frame the stairwell rough opening to at least 132" (11.00 ft) and purchase 6 ft 2×12 Douglas Fir or Southern Yellow Pine stringer stock (true hypotenuse length: 67.3" across a 48" stair width).
Riser Count Sensitivity Matrix for 36" Total Vertical Rise
Comparing adjacent riser counts around the optimal 5-riser configuration demonstrates why adding or removing steps shifts the unit rise toward the 7.75" building code ceiling or expands floor run footprint:
| Riser Count | Unit Rise (Frac / Dec) | Metric Rise | Total Run (10.5" Tread) | Slope Pitch | Code Verdict |
|---|---|---|---|---|---|
| 3 Risers | 12" (12.000") | 305 mm | 21.0" (1.75 ft) | 48.8° | EXCEEDS 7.75" MAX |
| 4 Risers | 9" (9.000") | 229 mm | 31.5" (2.63 ft) | 40.6° | EXCEEDS 7.75" MAX |
| 5 Risers (Selected) | 7-3/16" (7.200") | 183 mm | 42.0" (3.50 ft) | 34.4° | IRC R311.7 PASS |
| 6 Risers | 6" (6.000") | 152 mm | 52.5" (4.38 ft) | 29.7° | IRC R311.7 PASS |
| 7 Risers | 5-1/8" (5.143") | 131 mm | 63.0" (5.25 ft) | 26.1° | IRC R311.7 PASS |
Cumulative Framing Square & Tape Measure Layout Schedule (5 Steps)
To prevent cumulative rounding drift of up to 0.31" across 5 steps, hook your tape measure at the bottom stringer heel and mark the cumulative hypotenuse and elevation points below:
| Step # | Notch Rise Cut | Cumulative Elevation | Metric Elev | Cumulative Run | Stringer Edge Hypotenuse |
|---|---|---|---|---|---|
| Step #1 (Bottom Drop) | 6-3/16" | 7-3/16" (7.20") | 183 mm | 10.50" | 12.73" |
| Step #2 | 7-3/16" | 14-3/8" (14.40") | 366 mm | 21.00" | 25.46" |
| Step #3 | 7-3/16" | 21-5/8" (21.60") | 549 mm | 31.50" | 38.19" |
| Step #4 | 7-3/16" | 28-13/16" (28.80") | 732 mm | 42.00" | 50.93" |
| Step #5 | 7-3/16" | 36" (36.00") | 914 mm | 42.00" | 63.66" |
Official Building Code & Industry Standard Citations
- ICC International Residential Code (IRC R311.7) Governs maximum 7.75" riser height, minimum 10" tread depth, 3/8" riser variance, and 80" minimum stair headroom. Reference: ICC Digital Codes (codes.iccsafe.org).
- NFPA 70 / National Electrical Code (NEC Article 690) Governs photovoltaic maximum system voltage temperature correction (690.7) and 156% continuous OCPD sizing (690.8). Reference: National Fire Protection Association (nfpa.org).
- TCNA Handbook & ANSI A108.02 Tile Standards Establishes symmetrical perimeter cut layout rules, 33% max offset for 24"+ rectified porcelain, and mortar coverage. Reference: Tile Council of North America (tcnatile.com).
- APA Engineered Wood & AWC NDS Span Standards Governs structural panel thickness, kerf tolerance, and Southern Pine / Douglas Fir stringer throat bending capacity. Reference: APA Engineered Wood Association (apawood.org).
Material Buying Guide, Where to Buy, Warranty Protection & Installation Protocol for 5-Step Deck (36" Rise)
1. Should You Buy Pre-Cut Stringers or Raw 2×12 Lumber for a 36" (5-Step) Staircase?
For a 36-inch total vertical rise (5 risers at 7-3/16" each), you should never buy off-the-shelf pre-cut 5-step stringers from a big-box store. Retail pre-cut stringers are milled to a fixed 7.50" × 10.00" step without a bottom heel drop for your 1" tread stock—which would throw your finished 36" flight out of level and fail the IRC R311.7.5.1 3/8-inch riser variance inspection. Instead, purchase 4 boards of 6-foot #1 Prime KDAT (Kiln-Dried After Treatment) 2×12 Southern Yellow Pine or Select Structural Douglas Fir (true hypotenuse length: 67.3" across your 48" stair width).
2. Where to Buy, Exact Hardware SKUs & Manufacturer Warranty Protection
Source your 6 ft 2×12 stringer blanks from a local contractor lumberyard rather than picking through wet #2 grade boards at a retail center. Check the butt-end plastic tag to confirm UC4A/UC4B Ground Contact retention. To preserve the lumber treater's Lifetime Limited Rot Warranty (AWPA M4), you must brush two coats of 2% copper naphthenate end-cut preservative onto all 4 saw-cut notches before fastening treads. Anchor the top of all 4 stringers using Simpson Strong-Tie LSCZ (ZMAX G185) Adjustable Stringer Connectors fastened exclusively with hot-dip galvanized or `#9 × 1-1/2" SD9112` structural connector screws (using drywall or deck screws in structural hangers voids Simpson Strong-Tie's load rating and warranty).
3. Step-by-Step Jobsite Installation Checklist for This 5-Step Layout
- Step 1 (Crown & Layout): Sight down each 6 ft 2×12, place the crown (hump) facing UP, and lock brass stair gauges at 7-3/16" (rise) and 10.5" (run).
- Step 2 (Bottom Heel Drop): Shorten the bottom plumb riser cut by 1" so the bottom notch measures 6-3/16"; once the 1" tread is installed, Step #1 returns to 7-3/16".
- Step 3 (Apex Over-Cut Protection): Stop your 7-1/4" circular saw 1/4" before the inside corner of all 4 notches and finish the cut with a handsaw to preserve the full 5.31" structural throat spine.
- Step 4 (Ledger & Landing Bearing): Mount via sub-riser drop ledger framing and set the bottom heel on a pressure-treated sleeper plate or concrete pad at exactly 42.0" (3.50 ft) horizontal projection.