How to Calculate Cubic Yards: Formula and 5 Worked Examples

To calculate cubic yards, multiply length × width × depth in feet and divide by 27. A 12 ft × 10 ft area filled 3 in deep is 30 cubic feet, or 1.11 cubic yards.

When the depth is in inches, divide it by 12 first: length (ft) × width (ft) × depth (in) ÷ 12 ÷ 27.

What is a cubic yard?

A cubic yard is a unit of volume: the space inside a cube that is 3 feet long, 3 feet wide and 3 feet high. It equals exactly 27 cubic feet. Suppliers of concrete, gravel, soil, sand and mulch sell by this unit, and when they say “a yard,” they mean a cubic yard. The reason it is 27 and not 3 is covered in how many cubic feet are in a cubic yard.

How do you calculate cubic yards?

1. Measure length, width and depth. For a round area, measure the diameter instead of the width.
2. Put everything in feet. Divide any measurement in inches by 12. A depth of 4 in is 4 ÷ 12 = 0.3333 ft.
3. Find the volume in cubic feet. Multiply length × width × depth.
4. Divide by 27. The result is cubic yards.
5. Add an allowance and round up. The result is a net volume, so see the allowance section below before you order.

cubic yards = length (ft) × width (ft) × depth (ft) ÷ 27
cubic yards = length (ft) × width (ft) × depth (in) ÷ 12 ÷ 27

There is a shortcut for the common case of a known area and a depth in inches. Because 27 × 12 = 324, cubic yards = square feet × depth (in) ÷ 324. The same number tells you how far one cubic yard goes: it covers 324 sq ft at 1 in deep, a figure the University of Florida IFAS also gives for mulch.

Square feet cannot be turned into cubic yards on their own, because area has no depth. Any “sq ft to cubic yards” conversion needs a depth, and the depth is what changes the answer.

Quick reference by depth

To use the table, scale the middle column by your area. For 500 sq ft at 3 in deep, 5 × 0.9259 = 4.63 cubic yards.

Five worked examples

Example 1: a rectangle measured in feet and inches

The area is 14 ft 6 in × 9 ft 3 in and 4 in deep.

• Length: 14 + 6 ÷ 12 = 14.5 ft. Width: 9 + 3 ÷ 12 = 9.25 ft.
• Area: 14.5 × 9.25 = 134.125 sq ft
• Depth: 4 ÷ 12 = 0.3333 ft
• Volume: 134.125 × 0.3333 = 44.708 cubic feet
• Cubic yards: 44.708 ÷ 27 = 1.6559

Example 2: a circle

A round bed is 8 ft across (diameter) and 6 in deep. The radius is 4 ft.

• Area: π × 4² = 50.2655 sq ft
• Volume: 50.2655 × 0.5 = 25.1327 cubic feet
• Cubic yards: 25.1327 ÷ 27 = 0.9308

Example 3: a triangle

A triangular corner has a 12 ft base and a height of 8 ft, measured straight up from the base, and is 3 in deep.

• Area: ½ × 12 × 8 = 48 sq ft
• Volume: 48 × 0.25 = 12 cubic feet
• Cubic yards: 12 ÷ 27 = 0.4444

Example 4: square feet to cubic yards

You know the area is 500 sq ft and the layer will be 3 in deep.

• Volume: 500 × 3 ÷ 12 = 125 cubic feet
• Cubic yards: 125 ÷ 27 = 4.6296
• Shortcut check: 500 × 3 ÷ 324 = 4.6296

Example 5: several pieces and a cutout

A 20 ft × 12 ft bed has a 4 ft × 4 ft planter in it and will be filled 3 in deep. Subtract the planter from the area first.

• Area: 20 × 12 − 4 × 4 = 240 − 16 = 224 sq ft
• Volume: 224 × 0.25 = 56 cubic feet
• Cubic yards: 56 ÷ 27 = 2.0741

For an L-shaped or irregular area, split it into rectangles, triangles and circles, find each volume and add them. The square footage guide shows how to find each area.

Starting from meters

One cubic yard is 0.764554857984 cubic meters (NIST Handbook 44). Find the volume in cubic meters, then divide by that number. A 6 m × 4 m area at 0.1 m deep is 2.4 cubic meters, and 2.4 ÷ 0.764554857984 = 3.1391 cubic yards.

How much extra to order

The formula gives the net volume of a perfectly flat, perfectly measured space. Real jobs lose material to settling, compaction, spillage and uneven ground. Allowances are conventions, not standards, so treat these as starting points and adjust them for your job:

• Mulch: about 5% for settling and uneven beds.
• Concrete: about 10% for uneven subgrade and spillage.
• Gravel and crushed stone: about 15% for compaction when the material will be compacted.

For Example 4, 4.63 × 1.05 = 4.86 cubic yards of mulch. Suppliers often sell in set steps, so ask yours before you round the order. For soil, how much topsoil you need adds typical depths for lawns and raised beds.

Common mistakes

• Forgetting to convert inches. Multiplying 12 × 10 × 3 gives 360, not 30. Divide the depth in inches by 12 first.
• Dividing by 3 or 9. Those are for linear yards and square yards. Volume needs 27.
• Using the diameter as the radius. The circle area is π × radius², and the radius is half the distance across.
• Using the slanted side of a triangle. The height is measured straight up from the base.
• Skipping the allowance. An order that equals the net volume leaves you short when the material settles.
• Assuming yards mean tons. Cubic yards are volume. Weight depends on the material, as explained in how many cubic yards are in a ton.

Questions people ask