Cubic Yard Calculator: Formula, Steps & Examples

A cubic yard calculator works out the volume of a rectangular space in cubic yards (yd³) when you enter its length, width, and depth. You input the three dimensions in feet, inches, yards, or meters, and the calculator returns the volume in cubic yards, plus often the equivalent in cubic feet and cubic meters. This is the number you need when ordering concrete, topsoil, mulch, gravel, or sand for a project.

Formula

The formula for cubic yards is straightforward: multiply the three dimensions (length, width, depth) in feet, then divide by 27. Since one yard equals 3 feet, one cubic yard equals 3 × 3 × 3 = 27 cubic feet.

Cubic yards = (Length in ft × Width in ft × Depth in ft) ÷ 27

If you measure in inches, convert depth to feet first by dividing by 12. If you measure in meters, multiply the result in cubic meters by 1.30795 to get cubic yards (since 1 m³ = 1.30795 yd³).

Worked Example

Using the default values from the calculator above: length = 10 ft, width = 5 ft, depth = 4 in.

1. Convert depth to feet: 4 in ÷ 12 = 0.3333 ft
2. Calculate volume in cubic feet: 10 × 5 × 0.3333 = 16.6665 ft³
3. Convert to cubic yards: 16.6665 ÷ 27 = 0.6173 yd³

The calculator rounds to 0.62 cubic yards (two decimals). This is the amount of material you would need to fill a space 10 ft long, 5 ft wide, and 4 inches deep.

Why Use Cubic Yards Instead of Cubic Feet?

Suppliers of bulk materials—concrete, soil, mulch, gravel—typically sell by the cubic yard. A cubic yard is a large unit, roughly the size of a washing machine (3 ft × 3 ft × 3 ft). Ordering in cubic yards keeps the numbers manageable: a small patio might need 2 yd³, not 54 ft³. Knowing the cubic yardage also helps you compare prices from different suppliers who may quote per cubic yard or per ton.

For reference, one cubic yard of material covers:

• 324 square feet at 1 inch deep
• 162 square feet at 2 inches deep
• 108 square feet at 3 inches deep
• 81 square feet at 4 inches deep

This coverage table is handy when you know the area but not the volume.

How to Measure for the Calculator

Accurate measurements are the key to a correct estimate. Here is a practical approach:

1. Length and width: Use a tape measure to get the longest and widest points of the area. For irregular shapes, break them into rectangles and calculate each separately, then add the volumes.
2. Depth: For a new bed or fill, decide how deep you want the material. For mulch, 2–3 inches is common; for gravel under a patio, 4–6 inches; for concrete, 4 inches for a walkway.
3. Units: Keep all measurements in the same unit. If you measure length in feet, use feet for width and depth (convert inches to feet). Mixing feet and inches without conversion is the most common error.

Common Mistakes and How to Avoid Them

Even with a calculator, errors happen. Watch for these pitfalls:

• Mixing units: Always convert inches to feet (divide by 12) before multiplying. A depth of 6 inches is 0.5 ft, not 6 ft.
• Forgetting to divide by 27: The result in cubic feet is not the same as cubic yards. One cubic yard = 27 cubic feet, so always divide.
• Rounding too early: Round only at the final answer. If you round the depth to 0.3 ft instead of 0.333, your volume will be off.
• Ordering too little: For loose materials like mulch or gravel, add 5–10% extra to account for compaction, settling, or uneven ground. For concrete, order exactly what you need or slightly more (but check with the supplier about overage).

Limits of the Formula

The cubic yard formula assumes a perfect rectangular prism with flat, parallel sides. Real-world projects often have irregularities:

• Sloped ground: If the depth varies, measure at several points and use the average depth.
• Curved edges: For circles, use the formula for cylinder volume (Ï€ × r² × depth) and then convert to cubic yards. For irregular shapes, divide into smaller rectangles and sum the volumes.
• Compaction: Loose materials like soil or gravel compact when tamped. The volume you order is the loose volume; after compaction it will be less. If you are filling a hole that needs to be compacted, order extra (often 10–20%).

The calculator gives a theoretical volume. Always confirm with your supplier, as they may have specific guidelines for their material.

Frequently Asked Questions

How many cubic feet are in a cubic yard?

Exactly 27 cubic feet. Since a yard is 3 feet, a cubic yard is 3 ft × 3 ft × 3 ft = 27 ft³. This is the conversion factor used in the calculator.

How do I convert cubic yards to tons?

You need the material’s density (weight per cubic yard). For example, dry topsoil weighs about 1.2 tons per cubic yard, while gravel can weigh 1.4–1.7 tons per cubic yard. Multiply the cubic yards by the density in tons/yd³ to get tons. The calculator gives volume, not weight, because density varies by material and moisture content.

Can I use the calculator for a circular area?

Yes, but you need to adjust the formula. For a circle, measure the radius (half the diameter) in feet. The volume in cubic feet is π × r² × depth (in feet). Then divide by 27 to get cubic yards. This calculator is for rectangular areas; for circles, do the calculation separately.

What is the difference between cubic yards and square yards?

Cubic yards measure volume (3D space), while square yards measure area (2D surface). A cubic yard has three dimensions; a square yard has only two. For example, 1 cubic yard of mulch spread 1 inch deep covers 324 square feet, but it is still 1 cubic yard in volume.

How much material do I need for a 10×10 area with 6 inches of gravel?

Use the formula: 10 ft × 10 ft × 0.5 ft = 50 ft³. Divide by 27 = 1.85 cubic yards. Round up to 2 cubic yards to account for settling and waste. This is a common patio base size.

Should I round up when ordering?

Yes, for most bulk materials. Add 5–10% for compaction, spillage, or uneven surfaces. For concrete, you may order slightly more (some suppliers charge for a full yard even if you use less), but check with your supplier. For mulch and soil, rounding up to the nearest half yard is typical.

Related

• Cubic Foot Calculator with Inches
• Excavation Calculator per Cubic Yard
• Elevation to Feet Calculator: Convert Elevation

in l | Length | ft | 10 | 0
in w | Width | ft | 5 | 0
in d | Depth | in | 4 | 0
out cy | Cubic yards | yd³ | (l * w * (d / 12)) / 27 | 2
out cf | Cubic feet | ft³ | l * w * (d / 12) | 2
out cm | Cubic meters | m³ | (l * w * (d / 12)) * 0.0283168 | 2