How the trapezoid calculator works
Areas that widen along one side, like a tapered bed or a lot with an angled boundary, are trapezoids.
Use this cubic yard calculator for a trapezoid to get cubic yards, cubic feet, cubic meters, and a cost estimate in one step.
The calculator multiplies out the volume in cubic feet, then divides by 27, because a cubic yard is a cube that is 3 feet on each side. For this shape the formula is shown below in words and symbols.
In plain words: the average of the two parallel sides times height times depth, then divide by 27 if your answer is in cubic feet. Mixed units are fine. Pick feet, inches, yards, meters, or centimeters next to each box and the tool converts them for you.
Worked example for a trapezoid
Take a trapezoid with short side 8 ft, long side 14 ft, height 10 ft, depth 3 in. The volume works out to 27.50 cubic feet. Divide by 27 and you get 1.02 cubic yards. With 10 percent extra for waste, order about 1.12 cubic yards.
Measuring a trapezoid
Measure the two parallel sides, then the straight distance between them for the height.
Common uses for the trapezoid calculator
- Tapered garden beds
- Driveway aprons that flare out
- Lot corners and boundary fills
- Ditches with sloped sides (cross section)
Trapezoid volume at different sizes
The table scales the example above so you can see how fast volume grows. Doubling the depth doubles the volume. Doubling every length quadruples the area, and with the same depth the volume quadruples too.
| Size | Cubic feet | Cubic yards | With 10 percent extra |
|---|---|---|---|
| 4 ft by 7 ft by 5 ft by 3 in | 6.88 | 0.25 | 0.28 |
| 8 ft by 14 ft by 10 ft by 3 in | 27.50 | 1.02 | 1.12 |
| 12 ft by 21 ft by 15 ft by 3 in | 61.87 | 2.29 | 2.52 |
| 16 ft by 28 ft by 20 ft by 3 in | 110.00 | 4.07 | 4.48 |
| 24 ft by 42 ft by 30 ft by 3 in | 247.50 | 9.17 | 10.08 |
| 8 ft by 14 ft by 10 ft by 6 in | 55.00 | 2.04 | 2.24 |
| 16 ft by 28 ft by 20 ft by 6 in | 220.00 | 8.15 | 8.96 |
What the 1.02 cubic yard example weighs
Volume is only half of the story when a truck is hauling the load. The table shows planning weights for the example volume in several materials.
| Material | US tons | Pounds |
|---|---|---|
| Topsoil | 1.12 | 2,241 |
| Mulch | 0.36 | 713 |
| Gravel | 1.43 | 2,852 |
| Sand | 1.38 | 2,750 |
| Concrete | 2.06 | 4,125 |
| Compost | 0.51 | 1,019 |
These figures are planning estimates. Real material varies in moisture, size, and compaction, so confirm weights and order quantities with your supplier.
Frequently asked questions
How do I calculate cubic yards for a trapezoid?
Find the volume in cubic feet, then divide by 27. For this shape: the average of the two parallel sides times height times depth. Convert inches to feet first by dividing by 12.
How many cubic yards is the example trapezoid?
Short side 8 ft, long side 14 ft, height 10 ft, depth 3 in comes to 1.02 cubic yards, or 27.50 cubic feet.
How much extra should I order?
Most people add 5 to 10 percent for waste, and 10 to 15 percent for rough ground or loose material.
Can I use metric units?
Yes. Choose meters or centimeters next to any length. The result still shows cubic yards, and the cubic meter figure sits beside it.
Why does the answer change with the material?
The volume does not change, but weight and bag counts do, because each material has a different density.