Cubic Yard Calculation: Formula & Examples

To calculate cubic yards, multiply the length, width, and height of the space in feet, then divide by 27. Enter those three dimensions in feet into the calculator below to get the volume in cubic yards instantly.

Formula

The formula for cubic yards is straightforward:

Cubic yards = (Length × Width × Height) ÷ 27

Where:

• Length – the longest horizontal measurement, in feet (ft)
• Width – the horizontal measurement perpendicular to length, in feet (ft)
• Height (or depth) – the vertical measurement, in feet (ft)
• 27 – the number of cubic feet in one cubic yard (3 ft × 3 ft × 3 ft = 27 ft³)

All three dimensions must be in the same unit. If you measure in inches, convert to feet first by dividing by 12. If you measure in yards, you can skip the division by 27 (since length × width × height in yards already gives cubic yards).

Worked Example

Using the calculator defaults: length = 10 ft, width = 10 ft, depth = 1 ft.

1. Multiply the dimensions: 10 × 10 × 1 = 100 cubic feet
2. Divide by 27: 100 ÷ 27 = 3.7037…
3. Rounded to two decimals: 3.70 cubic yards

The calculator shows the same result: 3.70 yd³. It also displays the volume in cubic feet (100 ft³) and cubic meters (2.83 m³) for convenience.

Why 27? Understanding the Cubic Yard

A cubic yard is a cube that measures 1 yard (3 feet) on each side. Because volume is length × width × height, that cube contains 3 × 3 × 3 = 27 cubic feet. This is why the conversion factor is 27, not 3 or 9. Many people mistakenly divide by 3 (thinking of linear yards) or by 9 (thinking of square yards). Remember: for volume, you need three dimensions, so the factor is 3³ = 27.

When to Use Cubic Yards

Cubic yards are the standard unit for bulk materials in the United States, especially in construction and landscaping. You will likely need this calculation when ordering:

• Topsoil or garden soil – for raised beds or lawn leveling
• Mulch – to cover planting beds
• Concrete – for slabs, footings, or patios
• Gravel or crushed stone – for driveways or drainage
• Sand – for paver bases or sandboxes
• Fill dirt – to raise low spots or backfill

Suppliers typically sell these materials by the cubic yard, and delivery trucks are often sized in cubic yards (e.g., a standard dump truck holds about 10–14 cubic yards). Knowing the volume you need helps you order the right amount and avoid paying for excess material or making a second trip.

How to Measure for Different Shapes

The basic formula works for rectangular prisms (boxes). But real projects are rarely perfect rectangles. Here is how to handle common shapes:

• Rectangular area (e.g., garden bed): measure length, width, and depth in feet, then use the formula.
• Circular area (e.g., round planter or pond): measure the diameter in feet, divide by 2 to get the radius. Area = Ï€ × r². Multiply by depth to get cubic feet, then divide by 27.
• Triangular area (e.g., wedge-shaped border): measure base and height of the triangle in feet, area = (base × height) / 2. Multiply by depth, then divide by 27.
• Irregular shapes: break the area into rectangles, triangles, or circles. Calculate each volume in cubic feet, add them together, then divide the total by 27.

For depth, always measure the actual thickness you want, not the height of the container. For mulch or gravel, a typical depth is 2–4 inches (convert to feet: 2 in = 0.167 ft, 3 in = 0.25 ft, 4 in = 0.333 ft).

Common Mistakes and How to Avoid Them

Even experienced DIYers make errors when calculating cubic yards. Watch out for these pitfalls:

• Mixing units: Multiplying feet by inches gives nonsense. Convert everything to feet first. For example, 6 inches = 0.5 feet.
• Forgetting to divide by 27: The result in cubic feet is not the same as cubic yards. A common error is ordering 27 times too much material.
• Measuring depth incorrectly: For mulch or gravel, the depth is the loose thickness after spreading, not the depth of the bed. Compacted materials may settle, so add 10–15% to your order for compaction.
• Rounding too early: If you round each dimension to the nearest foot, you can over- or underestimate by a significant amount. Keep decimals until the final step.
• Ignoring waste: For concrete or irregular areas, add 5–10% extra to account for spillage, uneven subgrade, or variations in depth.

Limits of the Calculation

This formula assumes a perfect rectangular prism with straight sides and a uniform depth. Real-world conditions differ:

• Sloped ground: If the area is not level, the depth varies. Measure at several points and use the average depth.
• Compaction: Materials like fill dirt or gravel compact when rolled or tamped. The volume you order (loose volume) will shrink by 10–20% after compaction. Check with your supplier for the compaction factor.
• Material settling: Mulch and soil settle over time. You may need to top up after a season.
• Shape irregularities: For curved or non-uniform shapes, the calculation is an approximation. Break the area into smaller sections and sum the volumes.

For concrete, note that it is usually ordered by the cubic yard, but ready-mix trucks have minimum loads (often 1–2 cubic yards) and you may pay for the full minimum even if you need less. For small projects, bagged concrete (measured in cubic feet) might be more practical.

Converting to Other Units

Sometimes you need the volume in different units. Here are the key conversions:

• 1 cubic yard = 27 cubic feet
• 1 cubic yard = 46,656 cubic inches (since 1 ft = 12 in, so 27 × 12³)
• 1 cubic yard ≈ 0.7646 cubic meters
• 1 cubic yard ≈ 764.6 liters
• 1 cubic yard ≈ 202 US gallons (for water, but not for dry materials)

To convert from cubic yards to cubic meters, multiply by 0.7646. To convert from cubic meters to cubic yards, divide by 0.7646. The calculator above provides the cubic meters result for the default example.

Frequently Asked Questions

How many cubic feet are in a cubic yard?
There are 27 cubic feet in one cubic yard. This is because a yard is 3 feet long, so a cubic yard is 3 ft × 3 ft × 3 ft = 27 ft³. To convert cubic feet to cubic yards, divide by 27.

How do I calculate cubic yards from inches?
Convert all inch measurements to feet first by dividing by 12. For example, a depth of 6 inches becomes 0.5 feet. Then multiply length × width × depth in feet and divide by 27. Alternatively, multiply length × width × depth in inches and divide by 46,656 (the number of cubic inches in a cubic yard).

How much area does a cubic yard cover?
It depends on depth. At 1 inch deep, one cubic yard covers 324 square feet (since 1 yd³ = 27 ft³, and 27 ft³ / (1/12 ft) = 324 ft²). At 2 inches deep, it covers 162 ft². At 3 inches deep, it covers 108 ft². At 4 inches deep, it covers 81 ft². Divide 324 by the depth in inches to get the coverage.

How many cubic yards do I need for a 10×10 slab that is 4 inches thick?
First convert 4 inches to feet: 4/12 = 0.333 ft. Then volume = 10 × 10 × 0.333 = 33.3 ft³. Divide by 27: 33.3 / 27 = 1.23 cubic yards. For concrete, order about 1.35 cubic yards to account for waste and uneven subgrade.

What is the difference between a cubic yard and a square yard?
A square yard measures area (2 dimensions) and equals 9 square feet. A cubic yard measures volume (3 dimensions) and equals 27 cubic feet. You cannot directly convert between them because they measure different things. To get cubic yards from square yards, you need a depth.

How much does a cubic yard of topsoil weigh?
It varies by moisture and composition. Dry topsoil typically weighs about 1,000–1,200 pounds per cubic yard, while moist topsoil can weigh 1,300–1,500 pounds. Gravel is heavier, around 2,800–3,000 pounds per cubic yard. Always check with your supplier, especially if you are concerned about weight limits for delivery or structural loads.

Related

• Square Feet to Square Yards: Formula and Examples
• Feet to Meters: Conversion Formula and Examples
• Cubic Yards to Tons: Formula and Material Examples

in length | Length | ft | 10 | 0
in width | Width | ft | 10 | 0
in depth | Depth | ft | 1 | 0
out cubic_yards | Cubic yards | yd³ | (length * width * depth) / 27 | 2
out cubic_feet | Cubic feet | ft³ | length * width * depth | 2
out cubic_meters | Cubic meters | m³ | (length * width * depth) * 0.0283168 | 2