Every concrete job, from a single fence post to a full driveway, is worked out with the same small set of sums. Learn the concrete calculator formula once and you can price a slab on the back of an envelope, check a supplier’s quote, or spot a measuring mistake before the truck leaves the plant. This page gathers every formula in one place, explains why each conversion works, and runs a worked example for every common shape. If you would rather let a tool do the arithmetic, our concrete calculator applies exactly these formulas to your own dimensions.
The master formula
Start with the volume of the space you are filling: Volume = Length × Width × Depth. Measure all three in feet and the answer is in cubic feet. Depth is the one that catches people out, because it is usually chosen in inches, so divide the inches by 12 before you multiply: 4 inches becomes 0.333 ft, and 6 inches becomes 0.5 ft.
From cubic feet, the conversions are simple. Cubic yards = cubic feet ÷ 27. The 27 is not a fudge factor: a cubic yard is a cube that measures 3 ft by 3 ft by 3 ft, and 3 × 3 × 3 = 27, so there are exactly 27 cubic feet in every cubic yard. Working in metric is even simpler, because length × width × depth measured in metres gives the answer directly in cubic metres, with no conversion step at all. Finish every calculation by adding 5 to 10 percent for waste, then round up to a deliverable quantity.
Formulas by shape, with worked examples
Rectangular slab
Formula: length × width × thickness, all in feet. Example: a slab 10 ft long, 10 ft wide and 4 in thick. The thickness is 4 ÷ 12 = 0.333 ft, so the volume is 10 × 10 × 0.333 = 33.3 cubic feet. Divide by 27 and you get 1.23 cubic yards. This is the shape behind almost every patio, shed base and garage floor, and it is the calculation our guide to how much concrete do i need uses for its quick-answer table.
Round slab
Formula: π × radius² × thickness. The radius is half the diameter, and π is about 3.1416. Example: a round slab 10 ft across and 4 in thick has a radius of 5 ft, so the sum is 3.1416 × 25 × 0.333 = 26.2 cubic feet, which is 0.97 cubic yards. The most common slip here is squaring the diameter instead of the radius, which inflates the answer four times over.
Strip footing
Formula: length × width × depth of the trench, exactly like a slab. Example: a footing trench 20 ft long, 1 ft wide and 1 ft deep holds 20 × 1 × 1 = 20 cubic feet, which is 0.74 cubic yards. Because a trench is long, small errors in width or depth repeat along the whole run, so measure the dug trench in a few places and use the averages.
Post hole
Formula: π × radius² × depth, the cylinder formula. Example: a hole 12 in in diameter is 1 ft wide, so the radius is 0.5 ft, and at 36 in, or 3 ft, deep the volume is 3.1416 × 0.25 × 3 = 2.36 cubic feet. That is the volume of the empty hole; the buried part of the post displaces some of it, which is why bag counts for posts are always a little lower than the raw hole volume suggests.
Stairs
Stairs look complicated but need no new formula. Treat each step as a rectangular box, work out its volume with the slab formula, and add the boxes together. A flight is really a stack of slabs of increasing length, so the patient, step-by-step approach is also the accurate one.
From volume to bags
Bagged concrete is sold by weight, but what fills your forms is volume, so each bag size has a yield: the cubic feet of placed concrete one bag makes when mixed. Divide your volume in cubic feet by the yield to get the bag count, and always round up to the next whole bag.
| Bag size | Yield per bag | Bags in one cubic yard |
|---|---|---|
| 80 lb | 0.60 cu ft | 45 |
| 60 lb | 0.45 cu ft | 60 |
| 40 lb | 0.30 cu ft | 90 |
The yard figures are just the same division done once: 27 cubic feet divided by 0.60 is 45, by 0.45 is 60, and by 0.30 is 90. For full job-by-job bag counts, including a fence-post example with the post displacement taken out, see our guide on how many bags of concrete do i need.
Every formula at a glance
| Shape or conversion | Formula |
|---|---|
| Rectangular slab | Length × Width × Thickness (feet) |
| Round slab | π × Radius² × Thickness |
| Strip footing | Length × Width × Depth of trench |
| Post hole | π × Radius² × Depth |
| Cubic yards | Cubic feet ÷ 27 |
| Cubic metres | Length × Width × Depth (metres) |
| Bags needed | Cubic feet ÷ yield per bag, rounded up |
| Waste allowance | Net volume × 1.05 to 1.10 |
Common formula mistakes
- Mixing inches and feet. Multiplying 10 × 10 × 4 without converting the 4 inches into feet gives an answer twelve times too big. Convert the depth first, every time: inches ÷ 12 = feet.
- Forgetting the waste allowance. The formula gives the neat geometric volume of a perfect box. Real ground dips, forms bow and some concrete stays in the barrow, so an order with no allowance is an order that runs short.
- Using diameter where the formula wants radius. Circle formulas need the radius, half the diameter. Squaring the diameter instead multiplies the result by four, which turns a modest round slab into a very expensive surprise.
- Rounding down. Concrete is ordered and bagged in whole units. A result of 1.23 yards or 55.5 bags always rounds up, never down.
Put the formulas to work
Worked through by hand once, these sums stop being mysterious, and checking any quote or calculator result becomes a two-minute job. For your own pour, run the same numbers through the concrete calculator and compare: the tool uses the identical formulas, including the waste allowance you choose. If the two answers disagree, one of the mistakes above is hiding in the hand calculation. Readers planning a specific job may also find our step-by-step guide to how much concrete do i need helpful, because it applies these formulas to slabs, footings and post holes in turn, and our concrete estimating calculator will then turn the volume into bags and an estimated weight.
Frequently asked questions
What is the formula for concrete in cubic yards?
Multiply length by width by depth in feet to get cubic feet, then divide by 27. A 10 × 10 ft slab at 4 in thick is 10 × 10 × 0.333 = 33.3 cubic feet, and 33.3 ÷ 27 = 1.23 cubic yards before waste.
How do I calculate concrete in m³?
Measure length, width and depth in metres and multiply them together; the answer is already in cubic metres. To convert an imperial answer instead, divide cubic feet by 35.31 to get cubic metres.
How many bags make a cubic yard?
It depends on the bag size: 45 bags at 80 lb, 60 bags at 60 lb, or 90 bags at 40 lb. Each figure comes from dividing 27 cubic feet by the yield of one bag, which is 0.60, 0.45 and 0.30 cubic feet respectively.
Why do calculators add 10%?
Because the neat formula assumes a perfect box on perfectly level ground. Waste, spillage, forms that bow under pressure and an uneven subgrade all consume extra concrete, so a 10 percent allowance protects the pour from running short at the end.