Concrete Calculator: Slab on Grade (Polygon / Irregular) — Volume & Bags

Estimate concrete for irregular slabs by entering polygon vertices (X,Y). The tool computes area via the shoelace formula, perimeter, optional rectangular openings, and an optional perimeter thickening “ring” (approx). Get base, thickening, and total volumes in m³, yd³, and ft³ plus approximate bag counts. Notes, formulas, and FAQs included.

Units Metric (m, mm) US Customary (ft, in)

Number of vertices

3–20

Enter vertices in order around the perimeter. The last point closes back to the first.

Slab thickness

Waste allowance

Covers spillage and dimensional variation (common 4–10%).

Polygon vertices (X,Y)

#	X m	Y m

Use a consistent coordinate system. Units change with the toggle above.

Subtract rectangular openings (optional)

Enter up to 5 openings (length × width). Their area is subtracted before volume is computed.

#	Length m	Width m
1
2
3
4
5

Add perimeter thickening (approximate) — optional

Ring model

Approximate band area using perimeter P and band width E. Rounded adds corner rounding.

Band width E

Total edge thickness

Only the extra depth beyond the base slab is added.

Helpers (optional)

Create rectangle (quick fill)

m m

Fills vertices as (0,0), (L,0), (L,W), (0,W).

Results

Geometry

Area (net): 0.000 m²

Perimeter:

Openings subtracted from area only.

Base slab volume

0.000 m³

0.000 yd³

0.00 ft³

Thickening volume (approx)

0.000 m³

0.000 yd³

0.00 ft³

Total with waste

0.000 m³

0.000 yd³

0.00 ft³

Approximate bag counts (total with waste)

US bag sizes (QUIKRETE® yield)

40 lb bag00.30 ft³ per bag

50 lb bag00.375 ft³ per bag

60 lb bag00.45 ft³ per bag

80 lb bag00.60 ft³ per bag

90 lb bag00.675 ft³ per bag

Yields per bag from QUIKRETE data sheet. Actual yield varies with placement and compaction. Source

Metric bag sizes

Edit yields to match your local supplier data.

20 kg bag yield m³ 25 kg bag yield m³ 40 kg bag yield m³

20 kg bag0

25 kg bag0

40 kg bag0

How to use this polygon slab calculator

Select metric or US units.
Set the number of vertices and enter X,Y coordinates in order around the slab. The last point closes to the first.
Enter slab thickness and (optional) waste percentage.
Optional: add rectangular openings to subtract.
Optional: add a perimeter thickening band using the simple or rounded approximation.
Read geometry, volumes, and bag counts. Round up for ordering.

Formulas and assumptions

Polygon area (shoelace): A = ½ |Σ(xᵢyᵢ₊₁ − xᵢ₊₁yᵢ)|, indices wrap (i = 1…n).
Perimeter: P = Σ √[(xᵢ₊₁ − xᵢ)² + (yᵢ₊₁ − yᵢ)²].
Openings: A_open = Σ (L × W) (rectangles). Net area A_net = max(A − A_open, 0).
Base volume: V_base = A_net × T (T converted to meters).
Thickening band (approx):
- Simple: band area A_band ≈ P × E
- Rounded-corner: A_band ≈ P × E + πE²
Extra depth Δ = max(T_edge − T, 0); ring volume V_ring = A_band × Δ. These are approximations for quick estimating.
Total with waste: V_tot,w = (V_base + V_ring) × (1 + waste%).
Scope: Volume only—does not size reinforcement, joints, subbase, or vapor control. Follow your engineer and local code.

References

Shoelace formula for polygon area: see standard texts (e.g., overview).
Concrete waste allowance ~4–10%: NRMCA Concrete In Practice CIP 8, CIP 31.
Slab-on-ground practice: ACI 302.1R / ACI 360R (see ACI resources: ACI Slab-on-Ground).
US bag yields: QUIKRETE® Concrete Mix 1101 data sheet.

FAQs

How accurate is the perimeter thickening option?

It’s a practical approximation. The simple model uses P×E; the “rounded” model adds πE² to mimic rounded corners. For exact band area on complex shapes, use CAD and enter the extra volume directly.

Do I have to repeat the first vertex at the end?

No. Enter each vertex once in order; the calculator automatically closes the polygon back to the first point.

Can I enter bearings and distances instead of X,Y?

This version uses X,Y for reliability. Use the rectangle helper for simple shapes, or ask for a “bearings & runs” variant and I’ll add it.