Mathematical Derivation & Field Specifications: 2-Step Garage (15" Rise)
For a finished floor-to-floor vertical elevation of 15" (1.25 ft / 381 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 2.04 raw steps. Locking the riser integer to 2 vertical risers establishes an exact unit rise of 7.500" (7-1/2" / 191 mm) per step.
Because this layout specifies a drop top connection with 1" finished tread stock, the stringer carriage requires 1 horizontal tread cuts spanning a total horizontal floor projection (Total Run) of 10.5" (0.88 ft) at a stair pitch angle of 35.5°. The bottom plumb cut must be shortened (dropped) by the 1" tread thickness so the finished first step finishes at exactly 7-1/2" above the lower landing: bottom notch rise = 6-1/2" (6.500"). To maintain the mandatory 80" minimum vertical headroom clearance through a 10.5" upper floor assembly, frame the stairwell rough opening to at least 127" (10.58 ft) and purchase 3 ft 2×12 Douglas Fir or Southern Yellow Pine stringer stock (true hypotenuse length: 30.3" across a 36" stair width).
Riser Count Sensitivity Matrix for 15" Total Vertical Rise
Comparing adjacent riser counts around the optimal 2-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 |
|---|---|---|---|---|---|
| 2 Risers (Selected) | 7-1/2" (7.500") | 191 mm | 10.5" (0.88 ft) | 35.5° | IRC R311.7 PASS |
| 3 Risers | 5" (5.000") | 127 mm | 21.0" (1.75 ft) | 25.5° | IRC R311.7 PASS |
| 4 Risers | 3-3/4" (3.750") | 95 mm | 31.5" (2.63 ft) | 19.7° | SUB-OPTIMAL |
Cumulative Framing Square & Tape Measure Layout Schedule (2 Steps)
To prevent cumulative rounding drift of up to 0.13" across 2 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) | 6-1/2" | 7-1/2" (7.50") | 191 mm | 10.50" | 12.90" |
| Step #2 | 7-1/2" | 15" (15.00") | 381 mm | 10.50" | 25.81" |
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 2-Step Garage (15" Rise)
1. Should You Buy Pre-Cut Stringers or Raw 2×12 Lumber for a 15" (2-Step) Staircase?
For a 15-inch total vertical rise (2 risers at 7-1/2" each), you should never buy off-the-shelf pre-cut 2-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 15" flight out of level and fail the IRC R311.7.5.1 3/8-inch riser variance inspection. Instead, purchase 4 boards of 3-foot #1 Prime KDAT (Kiln-Dried After Treatment) 2×12 Southern Yellow Pine or Select Structural Douglas Fir (true hypotenuse length: 30.3" across your 36" stair width).
2. Where to Buy, Exact Hardware SKUs & Manufacturer Warranty Protection
Source your 3 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 1 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 2-Step Layout
- Step 1 (Crown & Layout): Sight down each 3 ft 2×12, place the crown (hump) facing UP, and lock brass stair gauges at 7-1/2" (rise) and 10.5" (run).
- Step 2 (Bottom Heel Drop): Shorten the bottom plumb riser cut by 1" so the bottom notch measures 6-1/2"; once the 1" tread is installed, Step #1 returns to 7-1/2".
- Step 3 (Apex Over-Cut Protection): Stop your 7-1/4" circular saw 1/4" before the inside corner of all 1 notches and finish the cut with a handsaw to preserve the full 5.15" 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 10.5" (0.88 ft) horizontal projection.