TryBuildCalcStair Stringer Throat Depth Calculator (IRC & AWC DCA-6 Check)
Check your stringer's throat depth instantly.
🕒 Last updated: September 4, 2026
Inputs
ℹ️Finished floor to finished floor height, measured on site — every riser height downstream depends on this being accurate.
ℹ️A starting point — the actual riser height is found by dividing total rise evenly across the nearest whole number of risers (IRC maximum is 7.75in).
ℹ️By Tread Depth: design from scratch, pick a comfortable tread. By Total Run: work backward from a fixed floor opening.
ℹ️IRC minimum is 10in — a common comfortable choice is 10.5-11in.
ℹ️Clear width — IRC minimum is 36in. Determines how many stringers are needed.
ℹ️2x12 gives the most throat-depth margin; 2x10 can work for a shallower stair but leaves less margin.
Waste
ℹ️Accounts for damaged pieces and cut waste on tread/riser boards — 10% is a common estimating default. Not applied to the fixed stringer count.
Cost
Risers / Treads
12 / 11
7" riser × 10.5" tread
Stringers Needed
4
12.48 ft cut length each (14 ft stock)
Advisory (not an IRC violation): throat depth (5.43") meets the IRC 3.5" code floor but falls short of the AWC DCA-6 recommended 5.5" — worth a deeper stringer board, especially for a deck stair.
Stringer Geometry
Angle: 33.69° from horizontal
Diagonal length: 142.82" (11.90 ft)
Cut length (with 7" layout allowance): 149.82"
Total rise / run: 84" / 115.5"
Throat Depth (2x12)
Board actual depth: 11.25"
Notch depth removed: 5.82"
Remaining throat: 5.43"
IRC code-floor minimum: 3.5" (met). AWC DCA-6 recommended minimum: 5.5" (not met) — these are two genuinely different, both commonly-cited figures; verify which applies to your project.
Tread & Riser Boards
Tread boards: 13 (+10% waste)
Riser boards: 14 (+10% waste)
Stair Comfort (Blondel's Formula)
2 × riser + tread = 24.5"
Within the widely-used 24-25" comfort target — a well-proportioned stair.
Assumptions Used
Standard US light-frame stick construction. Total rise is divided evenly across the entered target riser height (rounding to the nearest whole number of risers), so every riser in the flight is exactly the same height — this automatically satisfies the IRC's 3/8" riser/tread uniformity rule without needing a separate check. Stringer count follows the widely-cited "one stringer per spacing increment, minimum 2" rule for solid 2x lumber treads; tighten the spacing for composite or thin decking. This calculator gives stringer count, length, and throat depth only — it does not verify beam/ledger support sizing, landing requirements for tall flights, guard/handrail requirements, or local amendments to the adopted code edition.
Bill of Materials
Main material: 4 pcs + recommended tools
+−
Bill of Materials
Main material: 4 pcs + recommended tools
Computed items reflect your entered rise, run, and width; consumables below are general recommendations — actual needs vary by product and site conditions.
For Your Job
Stringers
Tread Boards
Riser Boards
Stringer Hangers / Connectors
General Tools & Consumables
Stringer hangers / angle brackets
Structural screws / joist hanger nails
Pressure-treated kick plate / concrete pad
Construction adhesive
Speed square / rafter square
Circular saw + jigsaw
Tape measure
Framing nailer or hammer
Safety glasses & hearing protection
Diagram simplified for clarity (not to scale, 4 steps shown regardless of actual count) — the highlighted point is the notch's deepest corner, where throat depth is measured.
Looking for the verification checklist, reference tables, tips, or common mistakes?See the complete Wood Stair Stringer Calculator.
Throat depth for a cut stringer
Throat depth is the net wood remaining below a cut stringer's deepest notch corner — the material that actually carries the load. This calculator checks it against two genuinely different commonly-cited minimums: 3.5" (IRC code floor) and 5.5" (AWC DCA-6 recommended).
This page defaults to a 7" riser / 10.5" tread on a 2x12 stringer — a commonly-referenced borderline case that passes the IRC minimum but falls just short of the AWC-recommended figure. Edit the inputs above to match your actual stair.
Wood Stair Stringer Calculator Formula: How Is It Determined?
Riser/tread count, stringer geometry, and throat depth, calculated separately and combined into a takeoff and code check.
Step 1 — Risers & Treads
Number of Risers = round(Total Rise ÷ Target Riser Height)
Actual Riser Height = Total Rise ÷ Number of Risers
Number of Treads = Number of Risers − 1
Dividing evenly guarantees every riser in the flight is exactly the same height, automatically satisfying the IRC's 3/8" riser-uniformity rule without a separate check.
Step 2 — Stringer Geometry
Angle = arctan(Riser Height ÷ Tread Depth)
Diagonal Length = √(Total Run² + Total Rise²)
Cut Length = Diagonal Length + 1 Riser Height (layout allowance)
Direct trigonometry on your entered rise and run — not a code-table lookup — with a small practical allowance for the bottom kick cut and top flush cut beyond the pure theoretical diagonal.
Step 3 — Throat Depth
Notch Depth Removed = Riser Height × cos(Angle)
Throat Depth = Stringer Board Depth − Notch Depth Removed
Every step notch's inside corner lies exactly on the stringer's own rise/run diagonal, so this perpendicular depth is the same fixed value for every step — checked against both the IRC 3.5" code floor and the AWC DCA-6 5.5" recommended minimum.
Worked Example
This example walks through your current inputs above, using the same steps as the Formula section.
Input Values Used
| Input | Value | Why it is used |
|---|---|---|
| Total rise | 84" | Sets riser count and height |
| Tread depth / total run | 10.5" / 115.5" | Sets stringer angle and length |
| Stringer lumber size | 2x12 (11.25") | Sets throat depth |
Step 1 — Risers & Treads
| Calculation | Result |
|---|---|
| Number of risers | 12 |
| Actual riser height | 7" |
| Number of treads | 11 |
Step 2 — Stringer Geometry
| Calculation | Result |
|---|---|
| Angle | 33.69° |
| Diagonal length | 142.82" |
| Cut length | 149.82" (14 ft stock) |
Step 3 — Throat Depth & Stringer Count
| Calculation | Result |
|---|---|
| Notch depth removed | 5.82" |
| Throat depth | 5.43" (IRC min met: yes) |
| Stringer count | 4 |
Therefore, this 84" rise stair needs 12 risers at 7" each, 4 stringers cut from 14 ft 2x12 stock, with a 5.43" throat depth.
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Disclaimer: This calculator provides approximate results for planning and estimation purposes only. Actual requirements may vary based on site conditions, materials, workmanship, and local building regulations. Always consult a qualified engineer, architect, or construction professional before making final decisions.