How the cubic yard calculator works
Mulch, topsoil, gravel, sand, and concrete are all sold by the cubic yard, and almost nobody measures a garden bed in yards. So there is a translation to do: measure the area in feet or inches, measure how deep the layer should be, and turn the two into a volume. This calculator does it for a rectangle, a circle, or a triangle, gives the answer in cubic yards, cubic feet, and cubic meters, and rounds the yards up, because running out with one corner bare is worse than a little left over. Pick a material and it adds the weight and the number of bags that would make the same volume.
It also checks your work for the two mistakes that account for most bad orders. You will find both in the steps under every answer, priced on your own numbers.
The formula
depth (ft) = depth (in) ÷ 12
circle area = π × (diameter ÷ 2)² triangle area = ½ × base × height
cubic meters = cubic yards × 0.764554857984
Everything goes into feet first: divide inches by 12. Length times width is the area in square feet; times the depth in feet is cubic feet; and a cubic yard is 3 feet by 3 feet by 3 feet, which is 27 cubic feet. For a circle, use the diameter straight across the middle. For a triangle, the height is measured square to the side you called the base, out to the far corner. The metric factor is exact, because the yard has been defined as exactly 0.9144 meters since 1959.
Worked example
A 12 by 20 foot bed with 3 inches of mulch. The area is 240 square feet. Three inches is 0.25 of a foot, so the volume is 240 × 0.25 = 60 cubic feet, and 60 ÷ 27 = 2.2222 cubic yards, which rounds up to about 2.23 cubic yards of mulch: 30 bags of 2 cubic feet. That is 1.7 cubic meters, and at 473 pounds a yard for damp mulch, about 1,051 pounds.
An 8 foot circle of mulch around a tree, 3 inches deep. The area is 50.27 square feet, the volume 12.57 cubic feet, which is 0.4654 cubic yards, rounded up to 0.47: seven bags of 2 cubic feet.
A triangular corner bed, 10 feet along the fence and 8 feet out, 4 inches of topsoil. Half of 10 times 8 is 40 square feet; times a third of a foot is 13.33 cubic feet, which is 0.4938 cubic yards, rounded up to 0.50. In bags of 1.5 cubic feet that is 9 of them, about 1,037 pounds of soil. Measured in inches instead (120 by 96), the calculator converts first and lands in the same place.
The two mistakes that order twelve times too much
Square yards are not cubic yards. A square yard measures a flat area; a cubic yard measures a volume. The 12 by 20 foot bed is 26.67 square yards of ground, but at 3 inches deep it needs only 2.22 cubic yards of mulch. Write "26.67 yards" on the order and twelve times too much arrives on a truck. The gap depends on the depth, because a square yard would only equal a cubic yard if the layer were a full yard deep:
| Depth | Square yards of area for each cubic yard of material |
|---|---|
| 2 inches | 18 |
| 3 inches | 12 |
| 4 inches | 9 |
| 6 inches | 6 |
| 12 inches | 3 |
| 36 inches | 1 |
Inches in the feet box. Three inches is 0.25 of a foot. Type 3 into a box that expects feet and you have asked for a layer 3 feet deep, twelve times too much, every time, at any depth. On the 12 by 20 foot bed that is 26.67 cubic yards instead of 2.22.
Here is the curious part: at 3 inches, the two mistakes produce exactly the same wrong number, 26.67. That is not a coincidence of this bed. Square yards are the area divided by 9, and a 3 foot layer is the area times 3 divided by 27, which is also the area divided by 9. So at the single most common depth for mulch, both slips land on the same figure, and if two people make different mistakes on the same order, they will agree with each other, which makes the error harder to spot. The steps under every answer show both checks for your numbers.
What a cubic yard weighs, and how many bags make one
| Material | One cubic yard weighs | Bags per cubic yard |
|---|---|---|
| Mulch | 243 to 473 pounds, dry to damp | 13.5 bags of 2 cubic feet |
| Topsoil | about 2,100 pounds (2,000 to 2,700, dry to wet) | 18 bags of 1.5 cubic feet |
| Gravel (#57 crushed stone) | about 2,800 pounds (2,376 to 2,996) | 54 half-cubic-foot bags |
| Sand | about 2,600 pounds (2,565 to 2,782) | 54 half-cubic-foot bags |
| Concrete | about 4,050 pounds (3,780 to 4,050) | 45 bags of 80-pound mix |
The mulch figures are EPA's for wood chips, dry and green. Topsoil uses the same 2,100 pounds as our soil calculator, gravel and sand the same figures as our gravel calculator (which explains where they come from), and concrete the 150 pounds a cubic foot our dumpster size calculator uses for a slab. Quikrete's data sheet puts its own bagged mix nearer 140 pounds a cubic foot, 3,780 a yard, so we show that as the light end and plan on the heavier figure. An 80 pound bag makes about 0.6 cubic feet, the same yield our concrete calculator counts.
The weights are why a cubic yard of mulch rides home easily in a pickup while a cubic yard of gravel does not: at 2,800 pounds, it is more than the best payload rating of any version of the Ford F-150, Ram 1500, or Chevrolet Silverado 1500. The gravel calculator works out the trips.
Cubic yards and cubic meters
A cubic yard is 0.764554857984 cubic meters, exactly, because the yard is exactly 0.9144 meters and a cube multiplies it by itself three times. Going the other way, a cubic meter is about 1.308 cubic yards, a little under one and a third. If your supplier quotes in cubic meters, divide the cubic yards shown above by 1.308 for a quick check, or read the cubic meters straight off the result table.