DeckMath
circular · faceted-polygon · feature deck

Round Deck Calculator

Size a circular deck — gazebo, hot-tub pad, or fire-pit surround. Framed as a 12/16/24/32-sided polygon inscribed in the circle (2× lumber cannot be bent). DeckMath returns true circle area, polygon area, per-facet rim mitre angle, chord joists, post + footing counts, and 25-28% decking waste — the highest of any deck shape.

12/16/24/32 facets5 surface optionsChord joistsPer-facet rim mitresIRC R312 / R507
π·r²·Area formula
180°/N·Mitre angle
N+1·Posts (+ center)
16″·Joist o.c.

Inputs

Circle dimensions

ft

Circle area
113 sqft
Polygon area
110 sqft
Circumference
37.7
in

Round Deck · Composite mid-tier (Trex Enhance)·Northeast
$11,139 – $14,817$98–$131 /sq ft installed
12′ Ø · 113 sqft16 facets · 11.25° mitres17 6x6 posts · 10 joists
Circle area
Polygon 110 sqft
Facet side
11.25° mitres
Materials
Low $4,517
Labor
1.22× region · ~1.45× round

Compliance · IRC + framing notes

No guardrail required — 24″ off grade < 30″

IRC R312

Under 30″ off grade, IRC R312 does not mandate a guardrail. Round decks under 30″ frequently skip the railing — the curved aesthetic stands alone.

Polygon framing — 16 facets inscribed in circle

Inscribed N-gon geometry

Polygon perimeter 37.46′ (vs circle circumference 37.7′). Each facet side 2.34′ at 11.25° rim mitres. Polygon area 110 sqft = 97% of the true circle area (113 sqft) — the 'gap' becomes decking trim.

Chord joists — 10 joists at 16″ o.c. (82 lf total)

IRC R507.6

Joists span across the diameter (12′). Each cut to chord = 2·√(r²−y²). Center joist spans full diameter; outermost joists are very short (1-3′) at the circle's edge. 2× hangers per joist (both chord ends connect to perimeter rim).

Decking waste — 23% (curved edge cuts)

Industry standard waste %

Round decks waste the most decking of any shape — every row of decking needs angled cuts at both ends to meet the circular perimeter. Composite is the lowest-waste round-deck option — slightly flexible at curved edges + capping holds finish on every mitred cut. Compare: rectangular 7-10%, octagon 15-20%, hexagon 13-18%.

Center post — recommended at 12′ Ø

IRC R507.5 + DCA-6

Above 14′ Ø, center post halves joist span. 17 posts total: 16 at facet vertices + 1 center. All 6x6 PT with ABU66Z anchors.

Bill of materials

Concrete footings — 14″ Ø to frost depth
17 footings · perimeter + center (higher load)
17 footing
$1,615
Decking — Composite mid-tier (Trex Enhance)
19 boards · 301 lf · 26 rows · 23% waste (curved edge)
19 board
$1,145
6x6 PT posts
16 facet-vertex posts + 1 center post
17 post
$884
Post anchors (ABU) + joist hangers (LUS210)
17 ABU66Z · 20 LUS210 hangers (2× per joist)
37 pc
$506
Floor joists — 2×10 PT (variable chord lengths)
10 joists · 82 lf · 16″ o.c. · each cut to circle chord
10 joist
$253
Doubled 2×10 PT perimeter beams (under rim)
16 segments doubled · 75 lf total
16 segment
$232
Perimeter rim — 16 mitred segments (2×10 PT)
16 segments at 11.25° mitres · 37 lf · facet side 2.34′
16 segment
$125
Hidden fastener clips + edge screws
113 sqft × $0.85/sqft
1,358 pc
$96
Materials subtotal
$4,856

Round deck pricing 2026-Q1. 23% decking waste baked in (curved-edge premium — highest of any deck shape). Labor 1.22× regional × ~1.45× round geometry.

Round deck framed as an N-sided polygon inscribed in the circle. 2× lumber cannot be bent — every round deck is actually a faceted polygon. Inscribed area = (N/2)·r²·sin(2π/N). Engineer review recommended above 18′ Ø.

How to use

Three steps. Permit-ready output.

  1. 01

    Set diameter

    Diameter is the distance across the circle. 12′ Ø = 113 sqft (typical hot-tub-pad size). 16′ Ø = 201 sqft. 20′ Ø = 314 sqft. Maximum 30′ Ø before structural engineering becomes mandatory.

  2. 02

    Pick facet count

    12 facets = chunky polygon look (30° rim mitres), 16 = visually round at typical viewing distance (11.25° mitres — the sweet spot for DIY), 24 = nearly perfectly round (7.5° mitres, double the labor), 32 = circle-perfect but very high labor (5.625° mitres, pro-only). More facets = more posts, more footings, more rim segments.

  3. 03

    Pick height + railing

    Above 30″ off grade triggers IRC R312 — 36″ guardrail required around full polygon perimeter. Round-deck rails use angled corner connectors matched to your facet count (every cap-rail system sells generic 15°, 22.5°, 30°, 45° connectors — pick facet count that matches available connectors).

  4. 04

    Pick surface material

    Composite mid (Trex Enhance, $3.80/lf) is the typical pick — 23% waste on curved edges. PT pine cheapest but wastes 25%. Ipe / cedar waste 28% from mitre splintering. Composite premium (Transcend, $5.40/lf) holds finish best on hundreds of mitred edges.

  5. 05

    Read your round deck cost

    Project total, $/sqft, true circle area, polygon area, facet side length, mitre angle, post count, joist + footing counts, BoM, share link, PDF/CSV export.

How we calculate

The math, fully transparent.

The Round Deck Calculator sizes a circular deck — gazebo, hot-tub pad, or fire-pit surround — using a faceted-polygon framing model. Real-world circular decks are framed as 12, 16, 24, or 32-sided polygons inscribed in the circle, because 2× lumber can't be bent — the rim is built from short straight mitred segments. Pick diameter, facet count (more facets = smoother circle), height, surface, post size, and state. DeckMath returns true circle area (π·r²), polygon inscribed area, chord joists, per-facet rim segments with exact mitre angle (180°/N), 25-28% decking waste (highest of any deck shape), and a 36″ railing line item when height exceeds 30″ (IRC R312). Round decks carry the largest labor premium of any geometry (+35-60% over rectangular) — every single rim segment is a custom mitre.

IRC references

  • IRC 2021 R507.6 — Joist span (chord joists size to longest chord = full diameter)
  • IRC 2021 R507.5 — Beam span (perimeter beam is N segments at facet-side length)
  • IRC 2021 R507.3 — Footings at each facet vertex + center (if >14′ Ø)
  • IRC 2021 R312 — 36″ guardrail required ≥ 30″ off grade
  • AWC DCA-6 — Faceted-polygon framing is non-standard; engineer review recommended above 18′ Ø

Round deck pricing 2026-Q1. Decking waste 22-28% (curved-edge premium — highest of any deck shape). Labor 1.35-1.60× rectangular deck. Faceted-polygon model: 2× lumber cannot bend — every round deck is a polygon inscribed in the circle.

Circle area
A = π·r²

True circle area used for material and labor coefficients. 12′ Ø → 113 sqft, 16′ Ø → 201 sqft, 20′ Ø → 314 sqft.

Polygon inscribed area
A_poly = (1/2)·N·r²·sin(2π/N)

Area of the regular N-sided polygon inscribed in the circle. With N=16, recovers 97.4% of the circle area. With N=24, 99.4%. The 'gap' between polygon and circle is the trim/cut-off waste at each facet.

Facet side length
s = 2·r·sin(π/N)

Length of each chord (one polygon side). With N=16 and r=6′: s = 2·6·sin(11.25°) = 2.34′. This is the length of each 2× rim segment.

Rim mitre angle
θ = 180°/N

Each rim joint is cut at this angle from the lumber face. N=16 → 11.25° mitres (each end). Compound saw set to 11.25°, every cut. Two cuts × N segments × 2 ends = 4N total mitres for the rim band.

Joist count
n = floor(d·12 / 16) + 1

Joists span across diameter at 16″ o.c. Each cut to its circle chord at position y: chord = 2·√(r²−y²). Center joist spans full diameter; outermost joists are very short (1-3′) at the circle's edge.

Decking waste
22-28% — highest of any deck shape

Curved-edge decking is the worst-case for cut-off waste. Composite 22-23% (clean cuts hold finish). PT pine 25%. Cedar / Ipe 28% (premium hardwood mitre splintering). Compare: rectangular 7-10%, octagon 15-20%.

Labor premium
1.35× to 1.60× rectangular labor

PT 1.35× (chord joists + N mitred rim segments). Composite 1.45× (hidden fastener at every angled cut). Ipe 1.60× (predrill every fastener at angled cuts). DIY: add 50% above pro labor — round decks are the LEAST DIY-friendly geometry.

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