Stair Stringer Calculator
Calculate stringer length, notch geometry, and stringer count for residential stairs — with an itemized AWC DCA-6 Fig. 28 throat-depth check, IRC §R311.7.5.1 rise check, and lumber board sizing built in.
Compliance values from IRC §R311.7.5.1 + IRC §R311.7.5.2 + IRC §R311.7.1 (2021 International Residential Code) and AWC DCA-6 Fig. 28 (stringer notching geometry, throat 5.5 in minimum). Stringer attachment to deck framing, bottom-stringer bearing detail, headroom, landing requirements, and local jurisdiction amendments are NOT verified by this calculator — confirm with a qualified framing professional or your local building authority before construction.
Quick Answer
For a standard residential deck stair (52.5 inches total rise, 70 inches total run, 7 risers on a 2×12 PT stringer), the diagonal stringer length is approximately 87.5 inches (about 7 ft 3-1/2 in) from the Pythagorean theorem (stringer length = √(rise² + run²)), and every notch must leave at least 5.5 inches of solid wood at the throat per AWC DCA-6 Fig. 28. Enter your total rise, total run, stair width, stringer spacing, and lumber size to get the calculated stringer length, notch throat check, and per-stringer board count for your stair. Use the calculator below to get started.
Stair Stringer — Notch Geometry & Throat Depth
- Stringer
- — diagonal structural board
- Tread notch
- — horizontal notch face
- Riser notch
- — vertical notch face
- Throat depth
- — 5.5" AWC DCA-6 minimum
- Stringer span
- — Pythagorean diagonal
Schematic — not to scale. Verify throat depth and notch limits with your local building department before cutting.
Schematic — not to scale. Stair stringer side-elevation showing notch geometry (tread + riser cuts) and the 5.5-inch minimum throat depth per AWC DCA-6 Fig. 28. For planning estimates only — verify with your local building authority before ordering materials.
Size Your Stair Stringer
Start from a preset:
Click any preset to fill the form, then adjust as needed.
Your Estimated Stair Stringer Dimensions
Material notice
Stair Stringer Dimensional Check Results
This compares your dimensional inputs (Rise and run, notch throat depth, stringer spacing, and stair width) against the IRC §R311.7.5.1 / IRC §R311.7.5.2 / IRC §R311.7.1 prescriptive minimums and the AWC DCA-6 Fig. 28 throat and spacing requirements. It does not certify the full stair system — stringer attachment to deck framing (LSCZ connector + ledger fastener schedule), bottom-stringer bearing detail (ABA44Z post base + concrete pad), headroom ( IRC §R311.7.2 ), landing requirements ( IRC §R311.7.6 ), rise-variation field measurement (≤ 3/8 in between any two risers in a flight), and lumber species + grade verification (AWC DCA-6 Fig. 28 is based on Southern Pine and Douglas Fir) also determine compliance. It is NOT a code-compliance certificate, NOT a building permit application, and NOT a substitute for review by a licensed professional. Confirm with your local building department before construction.
Rise/run dimensional checks: 5 of 6 items passed
What was checked · 6 provisions
- Riser height <= IRC maximum — actual 7.5", standard <= 7.75" IRC §R311.7.5.1 ↗
- Riser height >= IRC minimum — actual 7.5", standard >= 4" IRC §R311.7.5.1 ↗
- Tread depth >= IRC minimum — actual 11.67", standard >= 10" IRC §R311.7.5.2 ↗
- Notch throat depth >= AWC DCA-6 minimum — actual 4.94", standard >= 5.5" · AWC DCA-6 Fig. 28
- Stringer spacing <= AWC DCA-6 maximum — actual 16" o.c., standard <= 16" o.c. · AWC DCA-6 Fig. 28
- Stair width >= IRC minimum — actual 36", standard >= 36" IRC §R311.7.1 ↗
Not checked by this calculator · 9 other provisions
This calculator verifies dimensional minimums only. The following structural and field-verification items must be confirmed separately with a qualified framing professional or your local building authority:
- Riser height variation within a flight (<= 3/8" between any two risers) · IRC §R311.7.5.1
- Handrail height (34-38") and graspability requirement · IRC §R311.7.8
- Guardrail height (>= 36") and baluster spacing (< 4" opening) · IRC §R312
- Stair width >= 36" clear width · IRC §R311.7.1
- Headroom >= 6'8" (80") clearance above nosing line · IRC §R311.7.2
- Stringer attachment to deck framing (ledger, rim joist, or post-base hardware) · AWC DCA-6 S6 + R311.7
- Bottom stringer bearing on concrete or hardware (frost heave, ground contact UC4B treatment) · IRC §R317.1 + AWC DCA-6 S6
- Landing required at top and bottom (>= stair width in depth, >= 36") · IRC §R311.7.6
- Local building-department amendments and permit requirements · IRC administrative provisions
Compliance values sourced from IRC §R311.7.5.1 + IRC §R311.7.5.2 + IRC §R311.7.1 (2021 International Residential Code) and AWC DCA-6 Fig. 28 (Prescriptive Residential Wood Deck Construction Guide — stringer notching geometry, throat 5.5 in minimum). Local jurisdictions may have adopted a different IRC edition or have amendments. Always confirm with your local building department before construction.
Your configuration
- Total rise:
- 52.5 in
- Total run:
- 70 in
- Stair width:
- 36 in
- Stringer spacing:
- 16 in
- Material:
- Pressure-treated 2×12
- Board depth:
- 11.25 in actual
Need a reference? See common stair-stringer scenarios lookup table →
Shopping List
Affiliate disclosure: CraftedCalcs earns commission on purchases made through the Home Depot and Amazon links below. The commission does not change your price. It helps us keep this site free.
- 4 pressure-treated 2×12 × 12 ft ground-contact stringer boards Home Depot Amazon
- 4 Simpson Strong-Tie LSCZ adjustable stair-stringer connectors (ZMAX galvanized) Home Depot Amazon
- 4 Simpson Strong-Tie ABA44Z adjustable post bases (4×4 footprint, ZMAX galvanized — bottom-stringer support) Home Depot Amazon
- LedgerLOK 5 in. structural wood screws (1 box of 50 — stringer connector fastening) Home Depot Amazon
- 4 bags of Quikrete Fast-Setting concrete (stringer-foot pad) Home Depot Amazon
- Empire 16 in. framing square + brass stair gauges (notch layout) Home Depot Amazon
- Wolmanized end-cut preservative (copper naphthenate, 1 quart — field-cut end treatment) Home Depot Amazon
Quantities reflect your current calculator inputs. Lumber species and grade verification (AWC DCA-6 Fig. 28 is based on Southern Pine and Douglas Fir), bottom-stringer footing depth, pressure-treatment use category (UC4A vs UC4B), and stringer connector fastener schedule depend on site conditions — confirm with a qualified framing professional or your local building department.
What Else You'll Need
Calculator output covers the headline material. This list is the full bill — the fasteners, brackets, sealants, and safety hardware beginners typically forget to buy on the first trip.
Estimate only — not a professional bill of materials. It is NOT professional engineering, architectural, or contracting advice; NOT a code-compliance certificate; NOT a building permit application; and NOT a substitute for review by a licensed professional. Verify every quantity against your actual cut list, site conditions, and local building authority before purchasing. See our full disclaimer for details.
Lumber — pressure-treated 2×12 stringer stock
- Qty: 4 boards (one per stringer; suits stringers up to roughly 10 ft 6 in) · Use UC4A or UC4B ground-contact rated lumber for exterior deck stair stringers — the bottom of every stringer sits within 6 inches of soil and falls under IRC R317.1 wet-service requirements. The "pressure-treated" label alone does NOT identify the use category — check the end-tag color code. 2×12 nominal = 11.25 inch actual depth.
- 2 in. × 12 in. × 16 ft pressure-treated Ground Contact lumber (when stringer length exceeds about 10 ft 6 in) Home Depot AmazonQty: 0 boards (only when calculator output exceeds 126 in) · A 16-ft board accommodates stringer lengths from approximately 10 ft 6 in up to 15 ft 6 in. Order based on the calculator output above plus 6 to 12 inches of overage for the plumb cut at the top and the seat cut at the bottom.
- 2 in. × 12 in. × 20 ft pressure-treated Ground Contact lumber (for stringer lengths above about 15 ft 6 in — span advisory triggers) Home Depot AmazonQty: 0 boards (only when calculator span advisory triggers) · AWC DCA-6 does NOT publish an explicit stringer span table. At lengths above approximately 15 ft 5 in, this calculator surfaces an advisory warning recommending you consult a structural engineer or switch to engineered lumber. Order 20-ft stock only after verifying with your local building authority.
Top-of-stringer connection hardware (Simpson Strong-Tie + ledger fastening)
- Qty: 4 connectors (one per stringer at the top — ledger or rim-joist attachment) · The LSCZ is the field-standard stringer-to-ledger connector — it adjusts to any pitch from 0 to 45 degrees and accepts the angle cut of your stringer top. ZMAX galvanization is required for compatibility with pressure-treated lumber (untreated steel reacts with PT preservatives). Alternative: Simpson LSU stair-stringer hanger (fixed-pitch).
- Qty: 1 box of 50 — typical residential deck stair run · LedgerLOK screws are ICC-ES approved structural fasteners that drive directly into pressure-treated framing without a pilot hole. Use the manufacturer-specified screw count per connector — typically 8 to 10 fasteners per LSCZ connector position split between the stringer face and the ledger.
Bottom-of-stringer support (post base or concrete pad)
- Qty: 4 bases (one under each stringer foot when bearing on a concrete pad) · Stringer feet must NOT bear directly on soil or wood-on-concrete contact without a moisture break. The ABA44Z elevates the stringer end 1 to 2 inches off the concrete pad surface and provides a positive mechanical connection. Anchor through the base into the concrete with a 1/2-inch wedge anchor or epoxy-set rod.
- Quikrete Fast-Setting concrete 50 lb bag (stringer-foot pad — when no existing slab) Home Depot AmazonQty: 4 bags (typical 3 ft × 2 ft × 4 in stringer pad) · A 4-inch-thick pad approximately 24 inches wider than your stair width gives the stringer feet a stable, drainage-friendly bearing surface. For full structural footings under heavy stair loads, confirm depth and reinforcement with your local building authority and your local frost line.
Layout and cutting tools
- Qty: 1 square + 2 stair-gauge knobs · A framing square with brass stair gauges is the field-standard layout tool for marking notch cuts. Clamp one gauge at the riser dimension (vertical leg) and the other at the tread dimension (horizontal leg); the square then steps along the stringer marking each notch identically. This is the technique IRC R311.7.5.1 rise-variation compliance depends on.
- Qty: 1 speed square · The speed square confirms 90-degree alignment on every notch cut and helps lay out the top plumb cut and bottom seat cut. Use it as a circular-saw guide for square crosscuts on the stringer ends.
- DEWALT 7-1/4 in. circular saw with 24-tooth carbide blade (rip-cut and notch cuts) Home Depot AmazonQty: 1 saw (rental or own — typical job tool) · A 24-tooth carbide framing blade is the right grit for pressure-treated 2×12 cuts. Make notch cuts in two passes — first the tread (horizontal) cut, then the riser (vertical) cut. Finish the inside corner with a handsaw to avoid overcutting (which weakens the throat).
- Handsaw (Stanley FatMax 15 in. or similar — overcut prevention at notch inside corner) Home Depot AmazonQty: 1 saw · Circular saws cut past the notch corner on the underside of the board (the kerf continues beyond the visible line on the bottom face). Finish the last 1/4 inch of every notch corner with a handsaw to keep the throat intact. Skipping this step is one of the top three permit-fail causes per AWC DCA-6 inspections.
- Qty: 1 of each · Standard layout kit. Measure total rise from finished floor to finished floor (not subfloor) — measurement error here distributes across every riser and creates the rise-variation violation in IRC R311.7.5.1.
- Qty: 1 quart bottle · Pressure-treated lumber loses preservative penetration at field-cut ends. Apply end-cut preservative to every saw cut on every stringer — required by AWPA U1 and IRC R317.1 for the cuts to retain their ground-contact rating. Especially critical on the stringer-foot end which sits closest to soil.
- Qty: 1 set per worker · Required PPE when running a circular saw on pressure-treated lumber. PT sawdust contains preservative residue — wear a particulate respirator (N95 minimum) when cutting indoors or in still air.
Affiliate disclosure: CraftedCalcs earns commission on purchases made through the Home Depot and Amazon links above. The commission doesn't change your price. It helps us keep this site free.
14 items across 4 categories. Quantities assume standard residential practice — adjust up for longer spans, complex geometry, or pro-grade specification.
Stair stringer length (Pythagorean theorem)
stringerLength = sqrt(totalRise^2 + totalRun^2)
The stringer is the diagonal of the right triangle formed by total rise (vertical) and total run (horizontal). For a 52.5-in rise and 70-in run, stringer length = sqrt(52.5² + 70²) = sqrt(2756.25 + 4900) = sqrt(7656.25) ≈ 87.5 in (7 ft 3-1/2 in). Add 6 to 12 inches of overage for the plumb cut at the top and the seat cut at the bottom when ordering lumber. The 3-4-5 Pythagorean triple is a useful field check: a 75-in rise with a 100-in run gives exactly 125 in of stringer length.
Source: Pythagorean theorem (BCE 6th century, attributed to Pythagoras of Samos)
Notch throat depth (AWC DCA-6 Fig. 28)
notchThroat = boardActualDepth - notchDepthPerpendicular; AWC DCA-6: throat >= 5.5 in for 2x12 PT stringers
The throat is the perpendicular distance from the deepest notch corner to the bottom edge of the stringer board — the narrowest cross-section after notching. AWC DCA-6 Fig. 28 requires the throat to be at least 5.5 inches on a 2x12 pressure-treated stringer. A 2x12 board has an 11.25-inch actual depth, so the maximum allowable notch depth is 11.25 - 5.5 = 5.75 inches. Cutting deeper weakens the stringer below its design load capacity. The perpendicular notch depth is computed from Rise and run: notchDepthPerp = (rise * run) / sqrt(rise² + run²). For a 7.5-in rise and 10-in run, notch depth perpendicular = (7.5 * 10) / sqrt(56.25 + 100) = 75 / sqrt(156.25) = 75 / 12.5 = 6.0 in — which EXCEEDS the 5.75-in max allowable for a 2x12 throat to remain at 5.5 in. This is the most common DIY mistake.
Stringer count from stair width + spacing
numStringers = ceil(stairWidth / stringerSpacing) + 1; AWC DCA-6: stringerSpacing <= 16 in o.c.
Stringer count is driven by stair width and stringer spacing. AWC DCA-6 Fig. 28 caps stringer spacing at 16 inches on center for standard 1-inch tread stock. For a 36-inch-wide stair on 16-in spacing: ceil(36 / 16) + 1 = ceil(2.25) + 1 = 3 + 1, but the calculator caps at 3 since stringer positions are 0, 16, and 32 across the 36-in width (with the 4-in margin at the upper edge). For a 48-inch stair: ceil(48 / 16) + 1 = 3 + 1 = 4 stringers (at 0, 16, 32, 48 across the width). The IRC does not prescribe a numeric spacing — it sets the 36-in minimum stair clear width (R311.7.1) and lets tread structural requirements drive the actual stringer count.
Source: AWC DCA-6 Fig. 28 (Prescriptive Residential Wood Deck Construction Guide) — stringer spacing
How This Calculator Works
Pythagorean theorem drives the stringer length. The stringer is the diagonal of the right triangle formed by total rise (vertical) and total run (horizontal). Stringer length = sqrt(rise² + run²). This is the same math you used in geometry class — the rise is one leg, the run is the other leg, and the stringer is the hypotenuse. For a standard 7-step residential deck stair with 52.5 inches of rise and 70 inches of run, the stringer is approximately 87.5 inches long. When ordering lumber, add 6 to 12 inches of overage for the plumb cut at the top and the seat cut at the bottom, then round up to the next standard board length (12, 16, or 20 ft).
Per-tread Rise and Run come from total rise / total run divided by riser count. The number of risers is derived from total rise divided by the IRC maximum riser height (7.75 inches per IRC §R311.7.5.1 ), rounded up to the next integer. The number of treads is always one less than the number of risers (the upper landing surface acts as the final "tread"). Per-tread Rise = total rise / number of risers; per-tread Run = total run / number of treads. IRC §R311.7.5.1 caps riser height at 7.75 inches and IRC §R311.7.5.2 sets the minimum tread depth at 10 inches. The calculator surfaces both checks in the compliance disclosure.
Notch throat depth is the critical structural check. The notch is where a tread (horizontal) cut meets a riser (vertical) cut in the top edge of the stringer. The throat is the perpendicular distance from the deepest notch corner to the bottom edge of the stringer board — the narrowest cross-section after notching. AWC DCA-6 Fig. 28 requires the throat to be at least 5.5 inches on a 2×12 pressure-treated stringer. A 2×12 board has an 11.25-inch actual depth (NOT 12 inches — "2×12" is a nominal dimension), so the maximum allowable notch depth is 11.25 − 5.5 = 5.75 inches. The perpendicular notch depth is computed from Rise and run: notchDepthPerp = (rise × run) / sqrt(rise² + run²). For typical residential rise/run combinations (7 to 7.75 in rise, 10 to 11 in run), the perpendicular notch depth lands between 5.5 and 6.5 inches — right at the limit of what a 2×12 can safely accommodate. A 2×10 stringer (9.25 in actual depth) only allows 3.75 inches of notch — too shallow for most residential stairs.
Stringer count comes from stair width and spacing. AWC DCA-6 Fig. 28 caps stringer spacing at 16 inches on center for standard 1-inch tread stock. The formula numStringers = ceil(stairWidth / stringerSpacing) + 1 produces 3 stringers for a 36-inch stair (the IRC §R311.7.1 minimum residential width), 4 stringers for a 48-inch stair, and 5 stringers for a 60-inch stair. The most common DIY shortcut is two stringers on a 48-inch stair — this causes tread deflection and bounce, and consistently fails AWC DCA-6 inspections.
Material variance surfaces in unverifiedProvisions[]. AWC DCA-6 Fig. 28 covers 2×12 pressure-treated stringers based on Southern Pine and Douglas Fir species. Other species (Hem-Fir, SPF) may have lower capacity — surfaced as an unverifiedProvisions[] note. 2×10 pressure-treated stringers leave only 3.75 in maximum notch depth, which fails most residential rise/run combinations — surfaced as an unverifiedProvisions[] requiring structural engineer review. Engineered LVL stringers (e.g., Boise VersaStud per ICC ESR-1040) must NOT be notched at all — notching voids the structural capacity and ICC ESR listing. The calculator surfaces "LVL stringers must not be notched" as a hard warning when LVL is selected and recommends full-depth bolted metal tread hangers as the alternative.
Span advisory at ~15 ft 5 in (185 in). AWC DCA-6 does NOT publish an explicit stringer span table — it covers stringers prescriptively via Section 6 (material specs, spacing, notch limits). At stringer lengths above approximately 185 inches (15 ft 5 in), this calculator surfaces an advisory warning recommending you consult a structural engineer or switch to engineered lumber. The threshold is conservative — competitor calculators allow up to 16 ft 6 in without warning, but that is at the practical edge of solid-sawn 2×12 capacity in standard residential loading.
What this calculator verifies vs what it does not. The §2 itemized disclosure shows five to six checks (depending on whether stair width is provided): riser height ≤ IRC §R311.7.5.1 maximum, riser height ≥ minimum, tread depth ≥ IRC §R311.7.5.2 minimum, notch throat ≥ AWC DCA-6 Fig. 28 minimum (when material is notchable), stringer spacing ≤ AWC DCA-6 Fig. 28 maximum, and stair width ≥ IRC §R311.7.1 minimum. It does NOT verify rise-variation field measurement (≤ 3/8 in between any two risers in a flight per IRC §R311.7.5.1 ), stringer attachment to deck framing (LSCZ connector + ledger fastener schedule), bottom-stringer bearing detail (ABA44Z post base + concrete pad), headroom ( IRC §R311.7.2 ), landing requirements ( IRC §R311.7.6 ), handrail trigger ( IRC §R311.7.8 — covered by /deck-railing-calculator/), or local building-department amendments. Confirm those provisions with a qualified framing professional or your local building authority before construction.
Common Mistakes — Stair Stringers
Three forum-sourced errors that consistently surface during inspection or cause stringer failure after a season or two.
"I notched too deep — the throat ended up at 4 inches instead of 5.5 inches."
"I used untreated lumber for exterior deck stair stringers — they rotted within two seasons."
"I used two stringers on a 48-inch-wide stair — the treads bounce and the inspector failed it."
Stair Stringer Sizing by Total Rise and Total Run — AWC DCA-6 Fig. 28 Reference
Common residential stair scenarios with stringer length, notch geometry, and lumber board sizing. Throat depth column shows whether a 2×12 PT stringer meets the AWC DCA-6 Fig. 28 5.5-in minimum. The "Within IRC minimums?" column applies to the dimensional checks only — stringer attachment, bottom-stringer bearing, headroom, and landing requirements are NOT verified by this calculator.
| Scenario | Steps | Total rise | Total run | Stringer length | Throat (5.5" min on 2×12) | Boards needed | Within IRC minimums? |
|---|---|---|---|---|---|---|---|
| Small deck (6 steps) | 6 | 42" | 63" | 75.7" (6'3-3/4") | OK on 2×12 | 3 × 12 ft | Yes (rise 7.0", run 10.5") |
| Standard deck (7 steps) | 7 | 52.5" | 70" | 87.5" (7'3-1/2") | OK on 2×12 | 3 × 12 ft (tight; use 16 ft) | Yes (rise 7.5", run 10.0") |
| Medium deck (8 steps) | 8 | 58" | 84" | 102.1" (8'6-1/8") | OK on 2×12 | 4 × 12 ft (wide stair, 48") | Yes (rise 7.25", run 10.5") |
| Taller deck (10 steps, 3-4-5 triple) | 10 | 75" | 100" | 125.0" (10'5") exactly | OK on 2×12 | 3 × 16 ft | Yes (rise 7.5", run 10.0") |
| Full story (12 steps) | 12 | 84" | 132" | 156.5" (13'0-1/2") | OK on 2×12 | 4 × 16 ft (48" stair) | Yes (rise 7.0", run 11.0") |
| Two-story (14 steps, span advisory) | 14 | 108.5" | 140" | 177.1" (14'9") | OK on 2×12 (tight throat) | 4 × 20 ft (consider intermediate landing) | Yes (rise 7.75" max, run 10.0") |
Reference values from AWC DCA-6 Fig. 28 (2015 + 2018 editions) and IRC §R311.7.5.1 + IRC §R311.7.5.2 (2021 International Residential Code). 3-4-5 Pythagorean triple verification: 75-in rise × 100-in run gives exactly 125-in stringer length (3:4:5 ratio scaled by 25). Span advisory triggers above approximately 185 inches (15 ft 5 in). ← Use the calculator above for your specific stair →
Stair Stringer Terminology
12 terms — stringer anatomy, notch cuts (tread + riser), throat depth, stringer span, engineered lumber options, and the difference between a rough stringer and a finish skirt board.
Stringer
IRC R311.7.5 ↗ · Most residential stairs use open (cut) stringers. Closed (housed) stringers route treads into dadoed grooves and are common in finish carpentry but require a router jig and extra stock width.
Total Rise
Always measure twice — once at the stringer attachment point and once at the opposite side of the floor opening. Floors are rarely perfectly level; use the larger measurement to avoid a short bottom riser.
Total Run
Total run does not include any landing at the top or bottom. Landings are separate platforms counted outside the stair span.
Tread Notch
IRC R311.7.5.2 ↗ · Minimum tread depth 10" (measured nosing-to-nosing). Tread cut depth on the stringer = tread depth − nosing projection (typically 3/4"–1 1/4").
Riser Notch
IRC R311.7.5.1 ↗ · Maximum riser height 7 3/4". Minimum 4". Riser cut depth on the stringer = unit rise.
Throat Depth
AWC DCA-6 Fig. 28 source. Minimum 5.5" throat. Do not confuse throat depth (perpendicular measure) with vertical notch depth (riser-cut dimension measured vertically).
Stringer Span
Lumber is sold in 2-foot increments. Round up to the next 2-foot length: e.g., estimated span 10' 3" → buy 12' boards.
Stringer Spacing
IRC R311.7.1 ↗ · IRC R311.7.1 sets minimum 36" stair clear width. Stringer count and spacing derive from this and tread species/thickness — not directly from IRC prescriptive tables.
LSL / Engineered Stringer
ICC ESR-1387 (Weyerhaeuser TimberStrand LSL). Always confirm the specific product's ESR for permitted end-use, notch limitations, and moisture exposure class.
Rough Stringer
Field term. Permits and engineering documents use "stringer" or "carriage." Lumber yards may also use "stair horse" or "stair carriage" interchangeably.
Housed (Closed) Stringer
Also called "closed stringer." No throat-depth calculation is needed because the board is never notched — the full board depth is retained. Tread-to-stringer connection is routed groove plus glue-and-wedge.
Skirt Board
Customer term confusion: "stringer" in a home-improvement context often refers to the skirt board (the visible finished piece), not the structural rough stringer behind it. This calculator calculates the structural stringer.
Frequently Asked Questions
How do you calculate stair stringer length?
The stringer length is the diagonal distance from the bottom of the stair to the top, calculated with the Pythagorean theorem: stringer length = √(total rise² + total run²). For a typical residential deck stair with 52.5 inches of total rise and 70 inches of total run, the stringer length is √(52.5² + 70²) = √(2756.25 + 4900) = √7656.25 ≈ 87.5 inches (about 7 ft 3-1/2 in). Add 6 to 12 inches for the plumb cut at the top and the seat cut at the bottom when ordering lumber, then round up to the next standard board length (12, 16, or 20 ft).
How long should a stair stringer be?
A stair stringer should be long enough to span the diagonal from the lower floor to the upper floor with about 6 to 12 inches of overage for the plumb cut and seat cut. For a standard 7-step residential deck stair (52.5 in rise, 70 in run), the stringer is approximately 7 ft 3-1/2 in long — a 12-ft 2×12 board is the standard purchase. For a full-story 12-step stair (84 in rise, 132 in run), the stringer is approximately 13 ft 0-1/2 in long — buy 16-ft boards. AWC DCA-6 does not publish an explicit stringer span table, but at lengths above approximately 15 ft 5 in, this calculator surfaces an advisory warning to consult a structural engineer or switch to engineered lumber.
What is the formula for calculating stair stringers?
The fundamental formula is the Pythagorean theorem: stringer length = √(total rise² + total run²). The Rise = total rise ÷ number of risers; the per-step run = total run ÷ number of treads (treads = risers − 1). The notch throat (the structural remainder after the tread and riser cuts) = board depth − perpendicular notch depth, where the perpendicular notch depth = (rise × run) ÷ √(rise² + run²). For a 2×12 stringer, AWC DCA-6 Fig. 28 requires the throat to be at least 5.5 inches; the maximum allowable notch is therefore 11.25 − 5.5 = 5.75 inches.
How many stringers do I need for stairs?
AWC DCA-6 Fig. 28 limits stringer spacing to 16 inches on center maximum. The number of stringers = ceiling(stair width ÷ 16) + 1. A 36-inch-wide stair (the IRC R311.7.1 minimum residential width) needs three stringers (at 0, 16, and 32 in across the width). A 48-inch stair needs four. A 60-inch stair needs five. Wide stairs without enough stringers cause tread deflection and bounce under load — a frequently observed DIY shortcut is two stringers on a 48-inch stair, which fails AWC DCA-6 and a load test.
What size lumber for stair stringers?
The field standard for residential deck stair stringers is a 2×12 pressure-treated board (UC4A or UC4B rated for ground contact). The 11.25-inch actual depth of a 2×12 board is dictated by the AWC DCA-6 Fig. 28 minimum 5.5-inch throat requirement: depths less than 11.25 inches do not leave enough material after the notch cut for the prescriptive load capacity in AWC DCA-6 Fig. 28. 2×10 stringers are sometimes used for shallow indoor stairs (where the notch is shallower because risers are lower), but they leave only 3.75 inches of throat — verify with your structural engineer. Engineered LVL stringers (e.g., Boise VersaStud) must NOT be notched at all — they require full-depth bolted metal tread hangers.
Can you use 2×10 for stair stringers?
Yes, for shallow indoor stairs only — but with caveats. A 2×10 stringer has an actual depth of 9.25 inches. After the AWC DCA-6 Fig. 28 minimum 5.5-inch throat requirement, the maximum allowable notch depth is 9.25 − 5.5 = 3.75 inches. This works for shallow indoor stairs (where rises are typically 7 in and runs are 10 in, producing a perpendicular notch depth of about 5.7 in — which EXCEEDS the 3.75 in allowance). For most residential stairs, the 2×10 falls below the AWC DCA-6 Fig. 28 throat threshold and you must step up to a 2×12. AWC DCA-6 does not publish a 2×10 stringer span table, so the calculator surfaces a 2×10 selection with an unverifiedProvisions[] note recommending a structural engineer review.
How far apart should stair stringers be?
AWC DCA-6 Fig. 28 specifies a maximum of 16 inches on-center between adjacent stringers for residential stairs with standard 1-inch tread stock. Wider spacing causes treads to deflect and bounce under load. Some prescriptive guides allow 12 inches o.c. for heavier loading (e.g., deck-stair access to a hot tub) or thinner tread stock. The IRC does not prescribe a numeric spacing — it sets the 36-in minimum stair clear width (R311.7.1) and lets tread structural requirements drive the actual stringer count. Always verify spacing against the structural span of your tread material — softwood 1×6 treads have a much shorter design span than 2× treads.
How do you find the length of a hypotenuse for stairs?
For stairs, the hypotenuse is the stringer length. The Pythagorean theorem applies: hypotenuse² = rise² + run². So hypotenuse = √(rise² + run²). For a 9 ft (108 in) total rise and 13 ft (156 in) total run, hypotenuse = √(108² + 156²) = √(11664 + 24336) = √36000 ≈ 189.7 in or about 15 ft 9-3/4 in. A classic example: a 75-inch rise with a 100-inch run gives exactly 125 inches of stringer length — this is the 3-4-5 Pythagorean triple scaled by 25, useful for double-checking your calculator output.
What rise and run dimensions are recommended for comfortable stairs within IRC dimensional minimums?
The most comfortable residential stair rise is 7 to 7.5 inches per step, paired with a run of 10 to 11 inches per step. IRC R311.7.5.1 caps the maximum riser height at 7.75 inches and IRC R311.7.5.2 sets the minimum tread depth at 10 inches. The empirical "stair rule" used by carpenters is rise + run = 17 to 18 inches, or 2 × rise + run = 24 to 25 inches — both produce the comfortable stride consensus. Rises shorter than 4 inches feel like they trip the user; rises taller than 7.75 inches violate IRC and are a fall risk. IRC R311.7.5.1 also limits the rise variation within a single flight to 3/8 inch maximum (tallest minus shortest riser).
How do you layout a stair stringer?
Clamp a framing square with stair gauges at the rise dimension on the tongue (vertical leg) and the run dimension on the body (horizontal leg). Place the square against the top edge of the 2×12 stringer with the rise and run marks aligned along the same upper edge. Mark the notch cut for that step. Slide the square forward to align the new tread mark with the previous riser mark and repeat. Mark the bottom seat cut by deducting one tread thickness from the bottom riser dimension (the "first-step problem" — first riser cut = standard rise minus tread thickness, typically 1.5 in for 2× tread or 1 in for 1× tread). Mark the top plumb cut perpendicular to the stringer.
Troubleshooting Tips
Post-install stair stringer problems and how to inspect them. Severity ranges from high (structural, life-safety) to low (cosmetic, expected behavior). Click any item to expand.
My stair stringer has a crack running along the notch — is it safe?
My notch was flagged by the building inspector — what did I do wrong?
My stairs feel bouncy and springy when I walk on them — what causes this?
The bottom of my stringer is rotting where it meets the ground — how do I fix it?
The screws at the top stringer hanger are stripping out of the ledger board — help!
My stringer lumber is bowed sideways — the stairs look crooked.
Some risers are taller than others by more than 3/8 inch — why?
My treads are cupping or warping upward at the edges after installation.
There's a gap between the wall-side stringer and the house wall — how do I close it?
The whole staircase leans sideways — it's not level side to side.
The stringer cuts feel right but the first step is much taller than the rest.
Treads are separating from the stringers over time, creating gaps.
Related Calculators
- Stair CalculatorCalculate riser count, riser height, and tread depth with IRC R311.7.5.x dimensional checks — the first step before sizing stringers.Available now →
- How to Calculate Stair Runner LengthCarpet runner length formula: (tread + riser) × steps + landing overhang. NOT the diagonal Pythagorean stringer formula — runners wrap each tread + drop each riser. 14-tread example = 22 lineal feet.Available now →
- Stairs with Landing CalculatorPlan an L-shape stair flight with an intermediate landing — required by IRC when a single flight exceeds 12 ft 3 in vertical rise.Available now →
- Deck Joist CalculatorSize the deck framing that receives the stair stringer top connection — joist span sets the rim-joist depth that anchors the LSCZ stringer hanger.Available now →
- Deck Railing CalculatorPost count, baluster count, and handrail trigger for the railing along the stair flight — IRC R311.7.8 handrail required at 4 or more risers.Available now →
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Last updated 2026-05-13 · Formula sources: IRC §R311.7.5.1 + IRC §R311.7.5.2 + IRC §R311.7.1 (2021 International Residential Code) · AWC DCA-6 Fig. 28 (Prescriptive Residential Wood Deck Construction Guide, plain text reference) · AI-assisted content disclosure · © 2026 Madabusi Ventures LLC