Calculating Cubic Yards: Formula and Examples

Searching calculating cubic yards usually means you need to estimate material for concrete, mulch, gravel, topsoil, sand, or fill dirt. Cubic yards measure volume — a three-dimensional quantity — so you need all three dimensions: length, width, and depth. Getting this right saves you from ordering too little (running short mid-project) or too much (wasting money and materials).

Why Cubic Yards?

A cubic yard is the standard unit for bulk materials in the United States. It equals a cube that is 3 feet on every side:

1 cubic yard = 3 ft × 3 ft × 3 ft = 27 cubic feet

Most suppliers price gravel, mulch, concrete, and topsoil by the cubic yard.

Cubic Yards Formula

Cubic yards = (Length × Width × Depth in feet) / 27

All three measurements must be in feet before you multiply them.

Example 1: Garden Bed

A raised garden bed is:

• Length: 12 ft
• Width: 6 ft
• Depth: 0.5 ft (6 inches of soil)

Volume in cubic feet: 12 × 6 × 0.5 = 36 cubic feet

Convert to cubic yards: 36 / 27 = 1.33 cubic yards

Order 1.5 cubic yards to account for settling.

Example 2: Concrete Slab

A patio slab:

• Length: 20 ft
• Width: 16 ft
• Depth: 0.33 ft (4 inches of concrete)

Volume: 20 × 16 × 0.33 = 105.6 cubic feet

Cubic yards: 105.6 / 27 = 3.91 cubic yards

Order 4.5 cubic yards to cover waste and overflow during the pour.

Example 3: Gravel Driveway

A gravel driveway:

• Length: 40 ft
• Width: 12 ft
• Depth: 0.5 ft (6 inches of gravel)

Volume: 40 × 12 × 0.5 = 240 cubic feet

Cubic yards: 240 / 27 = 8.89 cubic yards

Order 10 cubic yards for the standard 10–15% overage.

Converting Inches to Feet

Depth is often measured in inches. Convert to feet by dividing by 12:

Inches	Feet
2	0.167
3	0.25
4	0.333
6	0.5
8	0.667
12	1.0

So if your depth is 4 inches, use 0.333 feet in the formula.

How Much to Order: Waste Factors

Always order extra to account for:

• Settling (soil and mulch compress over time)
• Spillage during delivery or placement
• Uneven ground needing more fill in low spots
• Cuts and trimming waste (for concrete forms)

Material	Recommended Overage
Mulch	10%
Topsoil	10–15%
Gravel	10%
Concrete	5–10%
Sand	10%

For concrete especially, running short mid-pour causes structural problems. It is better to over-order slightly than to run out.

Circular Areas

If you are filling a circular area (like a round planting bed), use this formula:

Volume = π × Radius² × Depth

Then divide by 27 to get cubic yards.

Example: A circular bed 8 feet in diameter (radius = 4 ft), filled 0.5 ft deep:

Volume = 3.14159 × 4² × 0.5 = 3.14159 × 16 × 0.5 = 25.13 cubic feet

Cubic yards: 25.13 / 27 = 0.93 cubic yards

Irregular Shapes

For irregular areas, break the space into rectangles and calculate each separately:

1. Divide the area into recognizable shapes
2. Calculate cubic feet for each section
3. Add all sections together
4. Divide total by 27

Quick Reference: Common Material Depths

Use	Typical Depth
Mulch (garden bed)	3–4 inches
Topsoil (lawn repair)	4–6 inches
Gravel (driveway base)	4–6 inches
Concrete (patio/slab)	4 inches
Sand (play area)	6–12 inches
Concrete (driveway)	6 inches

Cubic Yards to Tons Conversion

Many suppliers sell gravel and stone by weight (tons), not cubic yards. A rough conversion:

• 1 cubic yard of gravel ≈ 1.35 tons
• 1 cubic yard of sand ≈ 1.35 tons
• 1 cubic yard of topsoil ≈ 0.9 tons

These vary with moisture content and material density. Ask your supplier for the specific weight of the material you are ordering.

Common Mistakes

Forgetting to convert inches to feet is the most common error. If depth is 6 inches and you enter 6 instead of 0.5, you will calculate 12 times too much material.

Not adding overage — the exact cubic yardage for the space is never enough in practice due to settling and waste.

Using different units across dimensions — mixing meters, inches, and feet gives a useless result. Standardize everything to feet first.

The Bottom Line

To calculate cubic yards, multiply length, width, and depth in feet, then divide by 27. Add a waste buffer of 10–15% when ordering materials. For concrete, always check with a professional if you are unsure about structural requirements.

Use our Scientific Calculator to run the multiplication and division steps quickly without manual errors.

How to Calculate: Step-by-Step Guide

1

Measure the space

Record the length, width, and depth of the area you want to fill.

2

Convert to feet

Use feet for all measurements before calculating volume.

3

Divide cubic feet by 27

One cubic yard equals 27 cubic feet, so divide by 27 to convert.