How do I calculate stair rise and run?

(1) Measure total rise: deck surface to bottom-landing pad surface. (2) Pick a target riser height — 7″ for comfort, 7.75″ for minimum risers (IRC max). (3) Riser count = round(totalRise / target), then bump up if any riser exceeds 7.75″. (4) Riser height = totalRise / riserCount (equalize all). (5) Tread count = riserCount − 1. (6) Total run = treadCount × treadRunIn (11″ typical). (7) Stringer = √(rise² + run²). Example: 42″ rise, 11″ run → 6 risers @ 7.00″, 5 treads, 55″ total run, 69.2″ stringer.

What is the ideal stair rise and run for a deck?

Ideal: 7″ rise + 11″ run. This gives 2R + T = 25 (optimal Blondel value) and a 32.5° angle (mid-comfort band). For tight spaces, 7.5″ rise + 10″ run works (2R + T = 25, 36.9° angle — still optimal). Avoid 7.75″ rise + 11″ run (2R + T = 26.5 — outside ergonomic acceptable range; feels too stretched). Most contractors default to 7″/11″ unless space-constrained.

What is the maximum stair rise per IRC?

IRC 2021 R311.7.5.1: maximum riser height is 7-3/4 inches (7.75″). Additionally, every riser in a single flight must be equal within 3/8″ — variation greater than that is a code violation and an inspector tripping hazard. DeckMath enforces exact equality by dividing total rise by riser count.

What is the minimum tread depth per IRC?

IRC 2021 R311.7.5.2: 10 inches minimum tread depth (the horizontal step surface, excluding nosing). 11″ is the contractor sweet-spot — fits a 2×12 tread with a 1″ nosing and lands on the ergonomic 2R + T = 25 optimum when paired with a 7″ rise. Larger treads (12″+) waste horizontal space and don't improve comfort.

What's the 2R + T rule?

Also called the Blondel formula (Nicolas-François Blondel, 1675). 2 × riser height + tread depth should equal 24-25 inches for optimal comfort. Why: human stride length is ≈ 25″, and stairs feel natural when 2 × rise + tread = stride length. 7″ + 11″ → 25 = optimal. 8″ + 9″ → 25 = also optimal but illegal (rise > 7.75″, run < 10″). 6″ + 13″ → 25 = optimal but wastes space. 7.75″ + 10″ → 25.5 = acceptable.

How many risers should I use for a 36-inch deck?

Comfort strategy (7″ target): round(36/7) = 5 risers, but 36/5 = 7.20″ — passes. 5 risers @ 7.20″ each. Tread count = 4, total run = 44″ (at 11″ run), stringer = 56.6″ ≈ 4′-9″. Alternative — minimal-risers strategy: ceil(36/7.75) = 5 risers @ 7.20″ each (same result here since 7.20 ≤ 7.75). Pick 5 risers for a typical 36″ deck height.

How many risers should I use for a 48-inch deck?

Comfort strategy: round(48/7) = 7 risers @ 6.86″ each (well under 7.75″ max). Tread count = 6, total run = 66″ (at 11″ run), stringer = 81.6″ ≈ 6′-9.6″. Alternative — minimal-risers: ceil(48/7.75) = 7 risers (same here since 48/7 = 6.86 and 48/6 = 8.0 > 7.75 max). Always end up with 7 risers for a 48″ deck.

What's the maximum total rise for a single flight of stairs?

IRC 2021 R311.7.3: maximum 12 feet (144 inches) vertical rise per flight. Above that, an intermediate landing is required to break the stair into two flights. Most deck stairs are well under 12′ (single-story deck = 36-48″ rise; second-story deck = 96-108″ rise). The 144″ limit really applies to large multi-story decks or rooftop stairs.

How do I split a tall stair with an intermediate landing?

Aim for ≈ equal flights. For a 14′ total rise: each flight ≈ 84″ (7 ft) with a 36″ × 36″ landing between. Landing depth ≥ stair width per R311.7.6. For a 16′ total rise: split 96″ / 96″ (two flights of 14 risers each at 6.86″). For huge rises (20′+), consider 3 flights with 2 landings (each ≈ 80″). DeckMath flags total rise > 144″ with a warning but doesn't auto-split — that's a design decision based on your site geometry.

Does my deck stair need a handrail?

IRC 2021 R311.7.8.1: handrail required when stair has 4 or more risers. So a 24″ deck (3-4 risers depending on rise target) is on the edge; most deck stairs (36″+ rise → 5-7 risers) require a graspable handrail. Handrail height 34-38″ above the nosing line (R311.7.8.2). DeckMath returns the handrail-required flag; for the BoM see the Deck Stair Calculator or Railing Linear Feet Calculator.

stairs · pure geometry · IRC R311.7.5 + Blondel

Stair Rise & Run Calculator

Q: How many risers should I use for a 36-inch deck?

Comfort strategy (7″ target): round(36/7) = 5 risers, but 36/5 = 7.20″ — passes. 5 risers @ 7.20″ each. Tread count = 4, total run = 44″ (at 11″ run), stringer = 56.6″ ≈ 4′-9″. Alternative — minimal-risers strategy: ceil(36/7.75) = 5 risers @ 7.20″ each (same result here since 7.20 ≤ 7.75). Pick 5 risers for a typical 36″ deck height.

Q: How many risers should I use for a 48-inch deck?

Comfort strategy: round(48/7) = 7 risers @ 6.86″ each (well under 7.75″ max). Tread count = 6, total run = 66″ (at 11″ run), stringer = 81.6″ ≈ 6′-9.6″. Alternative — minimal-risers: ceil(48/7.75) = 7 risers (same here since 48/7 = 6.86 and 48/6 = 8.0 > 7.75 max). Always end up with 7 risers for a 48″ deck.

Equal-rise riser distribution, run depth, stringer hypotenuse, and stair angle for any total rise. Three strategies: comfort (7″ target), minimal-risers (max 7.75″), or custom. Every dimension cross-validated against IRC 2021 R311.7.5.1 (max rise 7-3/4″, equal within 3/8″), R311.7.5.2 (min run 10″), and the Blondel 2R + T ergonomic formula. Outputs a permit-ready geometry callout sheet + per-step layout list for the framer's framing-square stop. Pairs with deck-stair-calculator (full BoM) and stair-stringer-calculator (cut layout).

IRC R311.7.5Blondel 2R + T3 rise strategiesPermit-ready sheetPer-step layout

7.75″·IRC max rise

10″·IRC min tread

24-25″·2R + T optimum

30-38°·Comfort angle

Inputs

Total rise

Total risedeck surface to landing

Risers / treads6 / 5

Rise each7″ ✓

Total run55″

Stringer hyp69.2″

Angle37.4°

2R + T26″ (acceptable)

Rise strategy

Tread geometry

Tread runIRC ≥ 10″

Nosingoverhang

Riser style

Results

IRC R311.7.5 compliant · comfort strategy · acceptable ergonomics

Risers

@ 7″ each

Treads

@ 11″ each

Total run

hyp 69.2″

Angle

2R + T = 26″

Stair side elevation

6 risers × 7″ stringer 69.2″

Riser height 7″ ≤ IRC max 7.75″

IRC R311.7.5.1

Each of 6 risers is exactly 7″. IRC R311.7.5.1 requires every riser equal within 3/8″ — DeckMath enforces exact equality by dividing total rise by riser count.

Tread run 11″ ≥ IRC min 10″

IRC R311.7.5.2

Tread depth (excluding nosing) is 11″. IRC R311.7.5.2 requires 10″ minimum. 11″ is the contractor sweet-spot for comfort. Each tread can accept a 2×12 or 5/4×12 board.

All 6 risers equal at 7″ (within 3/8″ rule)

IRC R311.7.5.1 (3/8″ rule)

IRC R311.7.5.1 caps the maximum variation between any two risers at 3/8″. DeckMath equalizes by dividing total rise by riser count, so all risers are mathematically identical. In practice, your first riser may need to be adjusted by ≤ 3/8″ if the bottom landing isn't perfectly flush — measure carefully.

Ergonomics — 2R + T = 26″ (acceptable 23-26″)

Blondel formula

2R + T = 26″ is outside the optimal 24-25″ band but inside the 23-26″ acceptable range. Stair will be code-compliant but slightly awkward. Consider adjusting tread run by ±1″ to land in the optimal band.

Stair angle 37.4° — comfort band

IRC R311.7 comfort guidance

Angle = atan(42/55) = 37.4°. IRC comfort band is 30-38°. Below 30° wastes horizontal space; above 38° feels ladder-like.

Permit callout sheet

▸6 risers @ 7″ each (equal — IRC R311.7.5.1)
▸5 treads @ 11″ run + 1″ nosing (IRC R311.7.5.2)
▸Stringer hypotenuse 69.2″ = √(42² + 55²)
▸Stair angle 37.4° from horizontal (IRC comfort band 30-38°)

Hand this sheet to your framer or include it in your permit drawing set. Every dimension cross-validated against IRC 2021 R311.7.5 + Blondel ergonomic formula.

Per-step layout

Step	From bottom (in)	Nosing height (in)
1	7	3.5
2	14	10.5
3	21	17.5
4	28	24.5
5	35	31.5
6	42	38.5

Per-step heights from bottom landing surface. Use this list to mark your framing-square stop for cut/notched stringers.

How to use

Three steps. Permit-ready output.

Enter total rise

Total rise = top-of-deck to bottom-landing surface (the concrete pad or paver). Measure with a 4′ level + tape — don't approximate. Typical residential decks: 18-36″ for a single-story deck, 36-60″ for an elevated platform, 72-108″ for a second-story deck (most need an intermediate landing above 12′).

Pick a rise strategy

Comfort (default): targets ≈ 7″ per riser — IRC R311.7.5.1 cap is 7.75″ but ergonomic research (Blondel 1675) shows ≈ 7″ feels best. Minimal-risers: maxes out at 7.75″ each → fewest risers + steepest stair (saves horizontal space). Custom: type your own riser-height target — the calculator picks the riser count that keeps each riser ≤ your target and equal within 3/8″.

Set tread run + nosing

Tread run is the horizontal step depth — IRC R311.7.5.2 requires ≥ 10″. 11″ is the contractor sweet-spot (uses a 2×12 + 1″ nosing efficiently). Nosing projects past the riser face on closed-riser stairs (3/4″-1-1/4″ per R311.7.5.3) — typically 1″. Set nosing to 0 for open-riser stairs.

Closed vs open riser

Closed-riser: riser board behind each tread, code-default for residential stairs. Nosing is required (3/4″-1-1/4″) for safety. Open-riser: no riser board, visible from below. Allowed only if a 4-inch sphere can't pass through the opening between treads (IRC R312.1.3.1) — rare for deck stairs since most have ≤ 8″ open spacing.

Read the permit sheet

DeckMath outputs a 4-line geometry callout suitable for permit applications: riser callout, run callout, stringer callout, angle callout. Print as PDF or screenshot and submit with your permit drawings. Also generates a per-step layout list (1, 2, 3 … fromBottom inches) for the framer's framing-square stop.

How we calculate

The math, fully transparent.

The Stair Rise & Run Calculator solves the pure geometry of a deck stair: given total rise (top-of-deck to bottom-landing surface), it returns the equal-rise riser distribution, run depth, total horizontal run, stringer hypotenuse, and angle — sized to whichever strategy you pick (comfort target ≈ 7″, minimal-risers ≤ 7.75″, or a custom rise). Every dimension is cross-validated against IRC 2021 R311.7.5 + the Blondel 2R + T ergonomic check. Hand the output sheet to a framer or your AHJ as a permit-ready geometry callout. Pairs with deck-stair-calculator (full-stair BoM) and stair-stringer-calculator (cut-layout focus).

IRC references

IRC 2021 R311.7.5.1 — Riser height: 7-3/4″ max, every riser equal within 3/8″
IRC 2021 R311.7.5.2 — Tread depth: 10″ minimum
IRC 2021 R311.7.5.3 — Nosing: 3/4″-1-1/4″ projection on closed-riser stairs
IRC 2021 R311.7.3 — Single flight max: 12′ total rise before intermediate landing required
IRC 2021 R311.7.2 — Headroom: 80″ minimum (rarely applies to open-air deck stairs)
IRC 2021 R312.1.3.1 — Open-riser stairs: 4″ sphere can't pass through opening
Blondel formula (1675) — 2R + T = 24-25″ ergonomic optimum

IRC 2021 R311.7.5 prescriptive deck stair geometry — riser ≤ 7.75″, riser equal within 3/8″, tread ≥ 10″, nosing 3/4″-1-1/4″ on closed-riser stairs. Blondel 2R + T comfort formula from 1675 — optimal 24-25″, acceptable 23-26″. IRC R311.7.3 caps single-flight rise at 12′ (144″) before intermediate landing required. IRC R311.7.2 sets 80″ headroom minimum (rarely an issue for open-air deck stairs).

Riser count (comfort strategy)

n = max(1, round(totalRise / 7)); bump n until totalRise / n ≤ 7.75

Target 7″ per riser (ergonomic optimum). round(42 / 7) = 6 risers @ 7.00″ exactly. Always keep ≤ 7.75″ per IRC R311.7.5.1.

Riser count (minimal-risers strategy)

n = ceil(totalRise / 7.75)

Fewest risers while staying ≤ 7.75″ each. 42″ → ceil(42/7.75) = 6 risers @ 7.00″ each (lucky case — most rises give a non-integer). For 38″: ceil(38/7.75) = 5 risers @ 7.60″ each.

Equal riser height

riseEach = totalRise / n

Always equalize — never leave a 'remainder' first riser. IRC R311.7.5.1 caps variation at 3/8″, but every riser equal is best practice and what every code inspector expects.

Total horizontal run

totalRun = (n − 1) × treadRunIn

Top step is the deck edge, so treads = risers − 1. 6 risers × 11″ run = 55″ total horizontal run (excluding nosing).

Stringer hypotenuse

L = √(rise² + run²)

Right-triangle hypotenuse. 42″ rise + 55″ run → √(42² + 55²) = √(1,764 + 3,025) = √4,789 ≈ 69.2″ ≈ 5′-9.2″. Round up to next stock length (8′).

2R + T ergonomic check (Blondel)

2R + T ∈ [24, 25] = optimal; [23, 26] = acceptable

Blondel's formula from 1675 — 2 × riser + tread depth. Measures stair comfort. 7″ rise + 11″ tread → 2(7) + 11 = 25 = optimal. 7.75″ rise + 10″ tread → 25.5 = acceptable. 7.75″ + 12″ → 27.5 = too stretched. 5″ + 14″ → 24 = optimal but overdesigned.

Stair angle

θ = atan2(rise, run) × 180 / π

atan(42 / 55) = 37.4° — IRC comfort band is 30-38°. Steeper feels like a ladder, shallower wastes horizontal space.

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Stair angle + slope ratio + IRC R311.7 compliance for residential deck stairs. Dual-mode: stair geometry AND deck-drainage slope (R507.11.2) for composite + PVC + wood decking.

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Risers, treads, stringer hypotenuse, and BoM for any deck height — IRC 2021 R311.7 compliant with auto handrail + landing-pad sizing.

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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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Tread board count, total LF + waste, riser boards, fasteners — across 6 materials (PT, composite, Ipe, Cumaru, cedar). IRC R311.7.5 cross-validated.