How do I calculate stringer length?

Use Pythagoras: stringer length = √(rise² + run²). For a 49″ rise and 80″ run: √(2401 + 6400) = √8801 = 93.81″. Add 6″ cut allowance = 99.81″ — buy a 10ft (120″) 2×12 stringer. Calculator handles the math + recommends next-stock-up lumber length.

What size lumber for stair stringers?

2×12 is the standard for deck stairs. The 11.25″ actual depth allows 5-7 cut-outs (each cut weakens the stringer) before reaching the IRC minimum 5″ throat. 2×10 (9.25″ actual) works for 4-6 risers + short stairs. 2×8 (7.25″) is only for very low decks (3-4 risers). Pre-cut composite stringers exist too (Trex Reveal, AZEK) at 2-3× price.

How far apart should stringers be?

Standard: 16″ on-center (max per IRC R311.7.5.3 for treads under 1″ thick). Composite treads or 5/4 deck boards need 12″ OC to prevent sag. Open-style stairs (no riser boards) bump to 12″ OC regardless of tread thickness. For 36″-wide stair: 3 stringers at 16″ OC. For 48″ stair: 4 stringers at 16″ OC. Wider stairs (>48″) always 12″ OC.

What's a comfortable stair angle?

30-37° from horizontal is the residential comfort envelope. Below 30° feels excessively long (commercial-grade stair). Above 37° starts to feel steep but still legal. IRC allows up to 50° (basically ladder-like). 35° is the sweet spot — matches a 7″ rise × 10″ tread which is the most common combo. The calculator flags angles outside the comfort envelope.

How long should the cut allowance be?

6″ default for typical builds — covers waste cuts at both ends + overhang for the deck-end notch. First-time DIY: bump to 12″ for forgiveness (cuts are unforgiving). Experienced + tight cuts: 0-2″. Composite stringers need NO cut allowance — they come pre-cut to spec.

Can I use 2x10 instead of 2x12 for stringers?

Yes for short stairs (4-6 risers, run ≤ 60″). The thinner lumber leaves less material between cuts — for 7+ risers, IRC's 5″ throat requirement gets violated fast. 2×12 is always safer for stairs over 4 ft total rise. Pre-cut composite Trex Reveal stringers are 2×12 equivalents at $80-120 each.

What's the maximum stair length per stringer?

20 ft is the practical max — that's the longest stock lumber + the longest a single piece can be transported without crane. For longer stairs (>20 ft total rise/run), use intermediate landings (IRC R311.7.6 requires landings every 12 ft of vertical rise) to break up stringer length. Each landing resets the stringer math.

Does stringer length change with tread overhang?

Slightly. Tread overhang (1″ nosing) extends past the stringer face. Hypotenuse calc gives stringer centerline. For dimensional layout including the overhang, add 1″ to total run. For stock-length-to-buy, the calculator's cut allowance covers nose overhang implicitly — no separate math needed.

How do I cut stair stringers from the calculated length?

Mark the stringer with a framing square — set the square's tongue to rise + body to run. Slide the square down the stringer length, marking each step. The final mark line is the bottom-of-stair angle cut. Top mark = where stringer meets the deck rim (fasten with joist hanger or LSC connector). Always cut ONE stringer first, test fit, then use it as a template.

Stair · Pythagorean cut length

Stair Stringer Length Calculator

Pythagorean cut length for stair stringers — hypotenuse² = rise² + run². Add cut allowance + auto-recommend next-stock-up lumber length (8/10/12/14/16/20 ft). Flags angle outside the residential comfort envelope (30-37° sweet spot, IRC max 50°). 2×12 / 2×10 / 2×8 sizing with 2026-Q1 pricing per stringer. Pairs with Number of Steps + Stair Rise & Run + Stair Stringer Calculators.

Start calculating

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Pythagorean mathStock-up logicIRC R311.7.4

√·Hypotenuse math

30-37°·Comfort angle

Auto·Stock size up

$/stringer·Cost included

Inputs

Total risefinished grade → deck top

Total runhorizontal length of stair

Cut allowance6″ default · 12″ for DIY safety

Stringer lumber

Stringer · 2x12

10 ft93.8″ cut · 31.5° angle

Hypotenuse

centerline cut length

Stock to buy

2x12 lumber

Angle

comfort 30-37°

Cost/stringer

$4.85/lf

IRC compliance + sizing

Stair angle 31.49° — comfort range

Residential design literature

Within residential design comfort envelope (30-37°). 35° is sweet spot for 7″ rise × 10″ tread.

Buy 10ft 2x12 per stringer · ~$48.50 each

2026-Q1 retail

Hypotenuse 93.8″ + 6″ cut allowance = 99.8″ stock needed. Next stock size up is 10ft.

Pythagorean hypotenuse + next-up stock length. IRC R311.7.4 angle envelope. Pair with Number of Steps + Stair Rise & Run + Stair Stringer Calculators for full design.

How to use

How to use the stringer length calculator in 4 steps.

Enter total rise + run

Rise = grade-to-deck (typically 30-60″). Run = horizontal distance from stair start to deck edge (typically 60-120″).

Set cut allowance

6″ default — covers waste cuts at both ends + a touch of overhang. Bump to 12″ for first-time DIY (forgiveness for miscuts). 0″ if you're cutting tight + experienced.

Pick stringer lumber

2×12 is the standard for deck stairs (10.25″ effective depth handles 6-9 risers). 2×10 OK for 4-6 risers + short runs. 2×8 only for very low decks (3-4 risers max).

Read stock length to buy

Calculator finds the smallest stock lumber length that covers the hypotenuse + cut allowance. Lumber yards stock 8/10/12/14/16/20 ft — anything over 20 ft is custom-order.

How we calculate

How DeckMath calculates this — IRC 2021 sources.

The Stringer Length Calculator computes the cut length of stair stringers using Pythagoras: hypotenuse² = rise² + run². Inputs: total rise (grade → deck) + total run (horizontal stair length) + cut allowance + stringer lumber (2×12 standard, 2×10/2×8 for short runs). Output: hypotenuse + stock length to buy + stair angle. Auto-recommends next stock lumber size up. Flags shallow stairs (<30° comfort minimum) and steep stairs (>37° comfort max, >50° ladder territory).

IRC references

IRC R311.7.4 — Stair geometry standards
IRC R311.7.5.2 — Tread depth min 10″
ANSI A14 — max-safe-stair angle 50°

IRC 2021 R311.7.4 stair geometry. ANSI A14 ladder code for max-safe-angle reference.

Hypotenuse (stringer centerline)

hyp = √(rise² + run²)

Pythagorean theorem — exact cut length for the stringer. 49″ rise + 80″ run = √(2401 + 6400) = √8801 = 93.81″ stringer centerline.

Stock length

stock = hyp + cut_allowance

Hypotenuse + waste allowance. 93.81″ + 6″ = 99.81″ → buy a 10ft (120″) stringer. Lumber yard stock sizes only — round up to next available.

Stair angle

angle = atan(rise / run) × 180 / π

Angle from horizontal. IRC allows 50° max but comfortable range is 30-37°. Outside that envelope, stairs feel either steep (>37°) or excessively long (<30°).

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Stringer length questions, answered.

Use Pythagoras: stringer length = √(rise² + run²). For a 49″ rise and 80″ run: √(2401 + 6400) = √8801 = 93.81″. Add 6″ cut allowance = 99.81″ — buy a 10ft (120″) 2×12 stringer. Calculator handles the math + recommends next-stock-up lumber length.
2×12 is the standard for deck stairs. The 11.25″ actual depth allows 5-7 cut-outs (each cut weakens the stringer) before reaching the IRC minimum 5″ throat. 2×10 (9.25″ actual) works for 4-6 risers + short stairs. 2×8 (7.25″) is only for very low decks (3-4 risers). Pre-cut composite stringers exist too (Trex Reveal, AZEK) at 2-3× price.
Standard: 16″ on-center (max per IRC R311.7.5.3 for treads under 1″ thick). Composite treads or 5/4 deck boards need 12″ OC to prevent sag. Open-style stairs (no riser boards) bump to 12″ OC regardless of tread thickness. For 36″-wide stair: 3 stringers at 16″ OC. For 48″ stair: 4 stringers at 16″ OC. Wider stairs (>48″) always 12″ OC.
30-37° from horizontal is the residential comfort envelope. Below 30° feels excessively long (commercial-grade stair). Above 37° starts to feel steep but still legal. IRC allows up to 50° (basically ladder-like). 35° is the sweet spot — matches a 7″ rise × 10″ tread which is the most common combo. The calculator flags angles outside the comfort envelope.
6″ default for typical builds — covers waste cuts at both ends + overhang for the deck-end notch. First-time DIY: bump to 12″ for forgiveness (cuts are unforgiving). Experienced + tight cuts: 0-2″. Composite stringers need NO cut allowance — they come pre-cut to spec.
Yes for short stairs (4-6 risers, run ≤ 60″). The thinner lumber leaves less material between cuts — for 7+ risers, IRC's 5″ throat requirement gets violated fast. 2×12 is always safer for stairs over 4 ft total rise. Pre-cut composite Trex Reveal stringers are 2×12 equivalents at $80-120 each.
20 ft is the practical max — that's the longest stock lumber + the longest a single piece can be transported without crane. For longer stairs (>20 ft total rise/run), use intermediate landings (IRC R311.7.6 requires landings every 12 ft of vertical rise) to break up stringer length. Each landing resets the stringer math.
Slightly. Tread overhang (1″ nosing) extends past the stringer face. Hypotenuse calc gives stringer centerline. For dimensional layout including the overhang, add 1″ to total run. For stock-length-to-buy, the calculator's cut allowance covers nose overhang implicitly — no separate math needed.
Mark the stringer with a framing square — set the square's tongue to rise + body to run. Slide the square down the stringer length, marking each step. The final mark line is the bottom-of-stair angle cut. Top mark = where stringer meets the deck rim (fasten with joist hanger or LSC connector). Always cut ONE stringer first, test fit, then use it as a template.

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Stair Stringer Calculator

Stringer hypotenuse, notch depth, throat (DCA-6 ≥ 5″), stringer count, stock-length pick, brackets + fasteners. IRC R311.7 + AWC DCA-6 cross-validated.

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IRC-compliant step count from total rise + ideal step height. Auto-enforces IRC R311.7.5.1 max riser 7.75″ + uniformity ±3/8″. Pair with Stringer Length + Rise & Run calcs.

Stair Rise and Run Calculator

Equal-rise riser distribution, run depth, stringer hypotenuse, and angle for any deck height. IRC R311.7.5 + Blondel 2R + T ergonomic check. Permit-ready callout sheet.