Volume is the heart of every concrete estimate. Once you know the volume of the space you’re filling, everything else — bags, weight, cost — falls out of it. The only trick is that each shape has its own formula, and thickness is almost always measured in a different unit than length and width. This guide gives you the exact formula for every common shape, with a worked example for each.
The universal starting point
For any pour, the idea is the same:
Volume = Area of the base × Depth (thickness)
The base area is what changes between shapes. Get the area right, multiply by a consistent depth, and convert. Remember the three conversions that cover almost every job:
| Conversion | Value |
|---|---|
| 1 cubic yard | 27 cubic feet |
| 1 cubic yard | 0.7646 cubic meters |
| 1 cubic meter | 1,000 litres |
| 1 inch | 0.0833 feet |
Rectangle and slab
Volume = Length × Width × Thickness
This is the workhorse formula for slabs, footings, sidewalks and pads. Convert thickness from inches to feet first (divide by 12).
Example: A 10 ft × 10 ft slab at 4 inches thick → 10 × 10 × 0.333 = 33.3 ft³ ÷ 27 = 1.23 cubic yards (≈ 0.94 m³). Run your own numbers through the slab calculator or the general concrete calculator.
Circle and round slab
Volume = π × radius² × Thickness
Measure the diameter (the full distance across), halve it for the radius, then square it.
Example: A 10 ft diameter round pad at 4 inches → π × 5² × 0.333 = 26.2 ft³ ≈ 0.97 cubic yards. A round slab uses about 78.5% of the concrete of the square that contains it.
Cylinder, column and sonotube
Volume = π × radius² × Height
The same circle-area formula, extended vertically instead of into a thin slab.
Example: A 12-inch diameter sonotube 4 feet tall → π × 0.5² × 4 = 3.14 ft³ per tube. Filling six of them means about 18.8 ft³, or roughly 0.70 yd³.
Trench and duct bank
Volume = Length × Width × Depth
A trench is just a long, deep rectangle.
Example: A 30 ft trench, 18 inches wide and 18 inches deep → 30 × 1.5 × 1.5 = 67.5 ft³ = 2.5 cubic yards. Trenches over-break, so add 10–15% here rather than the usual 5%.
Triangle
Volume = ½ × Base × Height × Thickness
Use the perpendicular height — the straight-line distance from the base to the opposite corner, not a slanted side.
Example: A triangle with a 10 ft base and 8 ft height at 4 inches → 0.5 × 10 × 8 × 0.333 = 13.3 ft³ ≈ 0.49 cubic yards.
Stairs
Solid concrete steps stack, so the volume grows faster than you’d expect:
Volume = Width × Run × Rise × [n(n+1) / 2] for n steps
Example: 4 steps at 7-inch rise, 11-inch run, 4 ft wide → 4 × 0.917 × 0.583 × (4 × 5 / 2) = 21.4 ft³ ≈ 0.79 cubic yards. Doubling the number of steps roughly quadruples the concrete.
From volume to everything else
Once you have volume, the rest is quick:
- Bags: divide cubic feet by the bag yield — 0.60 ft³ per 80 lb bag (45 per yard), 0.45 ft³ per 60 lb bag. The bag calculator compares sizes.
- Weight: multiply cubic yards by ≈ 4,050 lb (normal concrete). See the weight calculator.
- Cost: multiply cubic yards by your local price ($120–$180 typical) with the cost calculator.
Always add waste
No sub-base is perfectly flat, and a grade off by half an inch across a 10 × 10 slab quietly eats an extra 4 ft³. Add 5–10% for formed pours and up to 15% against rough ground. Then round up to your supplier’s increment. For any shape you’d rather not compute by hand, the volume calculator does all of the above instantly in both unit systems.