The formula
cubic yards = (length × width × depth, all in feet) ÷ 27
Three steps, every time:
- Get every measurement into feet. This is where most mistakes happen. Depth is usually measured in inches, so divide it by 12 first.
- Multiply to get cubic feet. For a rectangle that is length × width × depth. For other shapes, find the area first (below), then multiply by depth.
- Divide by 27 to turn cubic feet into cubic yards.
If you would rather not do it by hand, the cubic yard calculator runs these steps and lets you mix units in each box.
Inches to feet for depth
| Inches | Feet | Inches | Feet |
|---|---|---|---|
| 1 | 0.083 | 6 | 0.5 |
| 2 | 0.167 | 8 | 0.667 |
| 3 | 0.25 | 9 | 0.75 |
| 4 | 0.333 | 10 | 0.833 |
| 5 | 0.417 | 12 | 1 |
Shortcut: when you have square feet and a depth in inches, skip the conversion: square feet × inches ÷ 324 = cubic yards. (324 is 12 × 27.)
Area formulas for common shapes
| Shape | Area in square feet | Example |
|---|---|---|
| Rectangle or square | length × width | 12 × 8 = 96 |
| Circle | 3.1416 × radius × radius | 10 ft across: 3.1416 × 5 × 5 = 78.5 |
| Half circle | 3.1416 × radius × radius ÷ 2 | 10 ft across: 39.3 |
| Triangle | base × height ÷ 2 | 12 base, 9 high: 54 |
| Ring (around a tree) | 3.1416 × (outer radius² − inner radius²) | 4 ft and 1 ft radius: 47.1 |
The triangle height is measured square to the base, out to the far corner, not along a sloping side.
Worked examples
1. A rectangle, depth in inches
A patio base 16 ft by 12 ft, 4 in deep.
- Depth: 4 ÷ 12 = 0.333 ft
- Volume: 16 × 12 × 0.333 = 64 cubic feet
- Cubic yards: 64 ÷ 27 = 2.37 cubic yards
Check with the shortcut: 16 × 12 = 192 sq ft; 192 × 4 ÷ 324 = 2.37. Same answer.
2. A circle
A round bed 10 ft across, filled 3 in deep.
- Radius: 5 ft. Area: 3.1416 × 5 × 5 = 78.5 sq ft
- Volume: 78.5 × 0.25 = 19.6 cubic feet
- Cubic yards: 19.6 ÷ 27 = 0.73 cubic yards
3. An L-shaped area
Split it into two rectangles that do not overlap. An L made of a 20 × 10 ft piece and a 10 × 8 ft piece, 6 in deep:
- 20 × 10 = 200 sq ft, and 10 × 8 = 80 sq ft, for 280 sq ft in total
- 280 × 0.5 = 140 cubic feet
- 140 ÷ 27 = 5.19 cubic yards
In the calculator, enter each piece as its own section and it adds them for you.
4. A curved or irregular bed
Measure the length along the middle, then measure the width at several evenly spaced points and average them. A curving border 30 ft long with widths of 3, 4, 5 and 4 ft averages 4 ft wide. At 3 in deep: 30 × 4 × 0.25 = 30 cubic feet = 1.11 cubic yards.
5. A sloped excavation
A hole 12 ft by 12 ft that is 1 ft deep at one side and 2 ft deep at the other has an average depth of 1.5 ft. 12 × 12 × 1.5 = 216 cubic feet = 8 cubic yards.
6. Several identical pieces
Eight round holes, each 1 ft across and 3 ft deep: area 3.1416 × 0.5 × 0.5 = 0.785 sq ft; × 3 ft = 2.36 cubic feet each; × 8 = 18.8 cubic feet = 0.70 cubic yards. The calculator’s “How many” box does the multiplying.
Mistakes that throw off the answer
- Leaving the depth in inches. 10 × 10 × 4 = 400, and 400 ÷ 27 = 14.8 cubic yards, which is 12 times too much. Convert inches to feet first.
- Dividing by 9 instead of 27. Nine is for square feet to square yards. Volume needs 27.
- Using the diameter as the radius. The radius is half the distance across. Using the full diameter makes a circle four times too big.
- Forgetting the waste allowance. Settling, uneven ground and spillage eat material. 5 to 10 percent extra is a common allowance.
- Not rounding up. Suppliers sell in set increments. If you need 2.37 cubic yards, you probably order 2.5.
Cubic yards from other units
| You have | Do this |
|---|---|
| Cubic feet | ÷ 27 |
| Cubic inches | ÷ 46,656 |
| Cubic meters | × 1.308 |
| Square feet and depth in inches | sq ft × inches ÷ 324 |
| Square yards and depth in inches | sq yd × inches ÷ 36 |
There is a converter for each: cubic feet, cubic inches, cubic meters and square feet.
The answer is the volume of the hole or form you measured. For loose materials that compact (soil, gravel, sand), suppliers sometimes suggest ordering a little more than the measured volume. Ask what they recommend for your material.
Questions people ask
- What is the formula for cubic yards?
- Cubic yards = length (ft) × width (ft) × depth (ft) ÷ 27. If the depth is in inches, use square feet × inches ÷ 324.
- Why divide by 27?
- A cubic yard is 3 ft × 3 ft × 3 ft, which is 27 cubic feet. Dividing cubic feet by 27 tells you how many of those cubes fit in your space.
- How do I figure cubic yards when all my measurements are in inches?
- Multiply the three measurements in inches and divide by 46,656, the number of cubic inches in a cubic yard. Or convert each to feet first by dividing by 12.
- How do I calculate cubic yards for an area with uneven depth?
- Measure the depth in several spots, average them, and use the average as the depth. For a steady slope, the average of the shallow end and the deep end is enough.
- Is a square yard the same as a cubic yard?
- No. A square yard is an area (3 ft × 3 ft = 9 sq ft). A cubic yard is a volume (27 cu ft). You need a depth to turn one into the other.