Concrete Calculator: Irregular Polygon Slab Volume
Estimate the volume of an irregular polygon concrete slab using vertices. Enter the slab thickness, a waste allowance, and your polygon points in order around the boundary. The tool returns area and volume in multiple units, plus approximate bag counts. Formulas, notes, and FAQs are included for clarity.
Results
Net area
0.000 m²
Net volume
0.000 m³
0.000 yd³
0.00 ft³
With waste
0.000 m³
0.000 yd³
0.00 ft³
Approximate bag counts
US bag sizes (QUIKRETE® yield)
Yields per bag from QUIKRETE data sheet. Actual yield varies by placement and compaction. Source
Metric bag sizes
Default yields are common published figures. Edit to match your local product.
How to use this concrete calculator
- Select metric or US units.
- Enter slab thickness and waste allowance.
- Set the number of vertices, then enter X and Y for each vertex in order around the slab. Coordinates can be local offsets from a corner.
- Optionally subtract one rectangular opening.
- Read the area and volume, then review bag counts. Round up when ordering.
Formulas and assumptions
- Polygon area uses the shoelace formula. For vertices \((x_i, y_i)\) listed around the boundary:
Area = 0.5 × |Σ(x_i y_{i+1} − x_{i+1} y_i)|, with the last point wrapping to the first. - Volume:
V = Area × Thickness. Inputs are converted to meters internally soVis in m³. - Opening: Net area = polygon area minus opening rectangle area.
- Waste:
Vwaste = V × (1 + waste%). - Bag counts: bags =
Required volume ÷ bag yield. US yields use ft³ per bag. Metric yields are editable in m³ per bag. - Vertex order: Enter points in order around the perimeter. Self-intersecting polygons are not supported.
References
- Shoelace formula for polygon area (Wikipedia)
- Waste allowance 4% to 10%: NRMCA Concrete In Practice (CIP 8, CIP 31)
- US bag yields: QUIKRETE® Concrete Mix 1101 (data sheet)
FAQs
Do coordinates need to be global site coordinates?
No. You can use a simple local grid in meters or feet. Pick any convenient origin and list points around the slab in order.
What if my slab has an L shape or multiple recesses?
Enter every corner of the outer boundary in order around the edge. For an internal recess that does not go to the edge, use the optional rectangular opening, or split the shape into separate polygons and add the volumes.
How many vertices can I enter?
Between 3 and 12 in this version. If you need more, let me know and I will raise the limit.
What thickness should I use?
Follow your engineer and local code. Many residential slabs on ground are about 4 inches, but requirements vary by load and soil.