Cubic Yards Formula: Calculate Volume

This calculator works out the volume of a rectangular space in cubic yards. You enter the length, width, and depth (in feet or inches), and it returns the volume in cubic yards, plus the equivalent in cubic feet and cubic meters. The formula is: Volume (yd³) = (Length × Width × Depth) / 27, where all measurements are in feet.

Formula

The cubic yards formula is a straightforward volume calculation. In words: multiply the length, width, and depth (all in feet) to get cubic feet, then divide by 27 to get cubic yards. The number 27 comes from the fact that one yard equals three feet, so one cubic yard (3 ft × 3 ft × 3 ft) equals 27 cubic feet.

In symbols: V = (L × W × D) / 27

• V = volume in cubic yards (yd³)
• L = length in feet (ft)
• W = width in feet (ft)
• D = depth in feet (ft)

If you measure in inches, first convert to feet by dividing each dimension by 12. If you measure in meters, multiply the result by 1.30795 to get cubic yards.

Worked Example

Using the default values from the calculator: length = 10 ft, width = 5 ft, depth = 0.5 ft.

1. Multiply length × width × depth: 10 × 5 × 0.5 = 25 cubic feet.
2. Divide by 27: 25 / 27 = 0.9259… cubic yards.
3. Rounded to two decimals: 0.93 cubic yards.

The calculator shows the same result: 0.93 yd³. It also shows 25.0 ft³ and 0.71 m³ as equivalents.

When to Use Cubic Yards

Cubic yards are the standard unit for ordering bulk materials in the US and Canada. You will use this formula when you need to:

• Order topsoil, compost, or mulch for a garden bed.
• Estimate concrete for a slab, footing, or driveway.
• Calculate gravel or sand for a patio base or trench.
• Estimate the volume of a dumpster or debris pile.

For example, a 10 ft × 10 ft garden bed that needs 4 inches of soil: 4 inches = 0.333 ft, so volume = 10 × 10 × 0.333 = 33.3 ft³, which is 1.23 yd³. Most soil suppliers sell in whole or half yards, so you would order 1.5 yd³.

How to Measure Correctly

Accuracy depends on your measurements. Here are the key points:

• Use feet for length and width, and feet for depth (convert inches to feet by dividing by 12).
• For irregular areas, break the space into rectangles, calculate each, then add the volumes.
• For sloped ground, measure depth at several points and use the average.
• For circular areas (e.g., a round planter), use the formula: Ï€ × radius² × depth, then divide by 27.

When ordering material, add 5–10% extra to account for compaction, settling, or uneven ground. For example, if your calculation gives 2.0 yd³, order 2.2 yd³.

Common Mistakes and How to Avoid Them

The most frequent error is mixing units. If you measure length and width in feet but depth in inches, you must convert the inches to feet first. For instance, 6 inches = 0.5 ft, not 6 ft. Another common mistake is forgetting to divide by 27 – that leaves you with cubic feet, not cubic yards. Also, be careful with decimal places: 0.3 ft is not the same as 3 inches (0.25 ft).

Rounding too early can also cause errors. If you round each dimension to the nearest foot, a 10.4 ft × 5.2 ft area becomes 10 × 5 = 50 ft², but the true area is 54.08 ft² – a difference of 8%. Always keep full precision until the final step.

Limits of the Formula

This formula works perfectly for rectangular prisms with flat, parallel sides. It does not apply to:

• Conical piles (use â…“ × Ï€ × radius² × height).
• Spheres (use 4/3 × Ï€ × radius³).
• Irregular shapes – you must approximate with rectangles or use water displacement.

Also, the formula gives the theoretical volume. Real materials settle, compact, or have air gaps. For example, a yard of loose topsoil may compact to less than a yard once spread. This is why adding a small surplus is common practice.

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 × 3 × 3 = 27 cubic feet.

How do I convert square feet to cubic yards?

You cannot convert directly because square feet measure area and cubic yards measure volume. You need the depth as well. Multiply the area (in square feet) by the depth (in feet) to get cubic feet, then divide by 27 to get cubic yards.

How many cubic yards do I need for a 10×10 area?

It depends on the depth. For a 10 ft × 10 ft area: at 1 inch deep, you need about 0.31 yd³; at 4 inches, about 1.23 yd³; at 6 inches, about 1.85 yd³. Use the formula: (10 × 10 × depth in ft) / 27.

What does 1 cubic yard of topsoil weigh?

Dry topsoil typically weighs about 2,000–2,700 pounds per cubic yard, but this varies with moisture and composition. Wet soil can weigh significantly more. For concrete, a cubic yard weighs about 4,000 pounds. Always check with your supplier for the specific material.

Can I use the formula for a circular area?

Yes, but you need a different formula. For a circle, use: (π × radius² × depth) / 27. For example, a circular bed with a 5 ft radius and 0.5 ft depth: (3.1416 × 25 × 0.5) / 27 = 1.45 yd³.

Is the formula the same for concrete and soil?

Yes, the volume formula is identical. The difference is in weight and cost. Concrete is usually ordered by the cubic yard, and soil by the cubic yard or ton. Always confirm the unit your supplier uses.

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in length | Length | ft | 10 | 0
in width | Width | ft | 5 | 0
in depth | Depth | ft | 0.5 | 0
out cubic_yards | Cubic yards | yd³ | (length * width * depth) / 27 | 2
out cubic_feet | Cubic feet | ft³ | length * width * depth | 1
out cubic_meters | Cubic meters | m³ | (length * width * depth) * 0.0283168 | 2