Cubic Yard Formulas for Every Shape and Material

The complete reference for cubic yard math: the master formula, equations for four common shapes, unit conversions, and material formulas for concrete, gravel, mulch, and soil. Every formula comes with a worked example.

The Master Formula

The cubic yard formula multiplies length, width, and depth in feet, then divides by 27. There are 27 cubic feet in one cubic yard, because a cubic yard measures 3 feet on every side.

Cubic Yards = ( Length ft x Width ft x Depth ft ) / 27

Why You Divide by 27

This single step trips up more people than any other part of the calculation. The logic is simple once you see it.

Multiplying length by width by depth gives you a result in cubic feet, not cubic yards. To convert, you need to know how many cubic feet fit inside one cubic yard. Since a yard is 3 feet, a cube one yard on each side is 3 ft by 3 ft by 3 ft, which equals 27 cubic feet. Dividing your cubic feet total by 27 gives the answer in cubic yards.

The relationship in one line

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

Formulas for Different Shapes

Most projects are rectangles, but circles, triangles, and trapezoids come up often in landscaping and corner sections. Each formula assumes feet, with depth converted from inches by dividing by 12.

Rectangle

Patios, driveways, slabs, and garden beds.

CY = ( L x W x D ) / 27

Example: 10 ft x 8 ft, 4 in deepDepth: 4 / 12 = 0.333 ft
10 x 8 x 0.333 = 26.67 cu ft
26.67 / 27 = 0.99 CY

Circle

Round planters, fire pit pads, and circular beds.

CY = ( pi x r squared x D ) / 27

Example: 5 ft radius, 4 in deepDepth: 4 / 12 = 0.333 ft
3.1416 x 5 squared x 0.333 = 26.15 cu ft
26.15 / 27 = 0.97 CY

Triangle

Triangular plots and corner sections.

CY = ( 0.5 x B x H x D ) / 27

Example: base 6 ft, height 8 ft, 3 in deepDepth: 3 / 12 = 0.25 ft
0.5 x 6 x 8 x 0.25 = 6 cu ft
6 / 27 = 0.22 CY

Trapezoid

Sloped areas and tapered retaining wall fills.

CY = ( 0.5 x (B1 + B2) x W x D ) / 27

Example: bases 4 ft and 6 ft, width 10 ft, 6 in deepDepth: 6 / 12 = 0.5 ft
0.5 x (4 + 6) x 10 x 0.5 = 25 cu ft
25 / 27 = 0.93 CY

Key: L = length, W = width, D = depth, r = radius, B = base, H = triangle height, and B1 and B2 = the two parallel sides of the trapezoid. All values are in feet.

Unit Conversion Formulas

When your measurements are not already in cubic feet, use these direct conversions to reach cubic yards.

Starting unit	Conversion to cubic yards
Cubic feet	cubic feet / 27
Cubic inches	cubic inches / 46,656
Cubic meters	cubic meters x 1.308
Mixed units	convert all to feet first, then apply the master formula

Note: 46,656 is simply 36 inches cubed, since one yard is 36 inches.

Material Formulas: Bags and Tonnage

Once you know your cubic yards, these formulas turn that figure into the number of bags or tons you need to order, plus the extra to add for waste or settling.

How many concrete bags per cubic yard

Bag count depends on bag size, because larger bags yield more cubic feet. Use this table for accuracy:

Bag size	Approx. yield per bag	Bags per cubic yard
40 lb	0.30 cu ft	90
50 lb	0.375 cu ft	72
60 lb	0.45 cu ft	60
80 lb	0.60 cu ft	45

Formula: bags = cubic yards x bags-per-yard from the table above. Add 10 percent for waste and spillage.

Tonnage and bag formulas by material

Material	Quick formula	Extra to add
Gravel and stone	tons = CY x 1.4	15 to 20% compaction
Mulch, 2 cu ft bags	bags = CY x 13.5	none
Topsoil, dry	tons = CY x 1.1	10 to 15% settling
Concrete, poured	tons = CY x 2.0	10% waste

Note: tonnage multipliers are averages. Gravel ranges from about 1.3 to 1.5 tons per cubic yard depending on stone type and moisture, so confirm with your supplier for large orders.

Irregular Shapes: Split and Add

There is no single formula for a complex shape. The reliable method is to break it down.

Divide any irregular area into simple shapes like rectangles, triangles, and circles. Calculate the cubic yards for each piece using its own formula, then add the totals. This approach handles L-shaped patios, curved borders, and split-level beds with full accuracy.

Formula FAQs

What is the cubic yard formula?

The cubic yard formula is length times width times depth, divided by 27, with all measurements in feet. Multiplying the three dimensions gives cubic feet, and dividing by 27 converts cubic feet to cubic yards.

Why do you divide by 27 to get cubic yards?

You divide by 27 because one cubic yard equals 3 feet by 3 feet by 3 feet, and 3 times 3 times 3 equals 27 cubic feet. Dividing total cubic feet by 27 converts the volume into cubic yards.

How do I calculate cubic yards for a circle?

Use pi times the radius squared times the depth, all in feet, then divide by 27. The radius is half the diameter, so a circle measuring 10 feet across has a 5 foot radius.

How do I calculate cubic yards for an irregular shape?

Break the irregular shape into simpler shapes such as rectangles, triangles, and circles. Calculate the cubic yards for each part, then add the results together.

How do I convert cubic meters to cubic yards?

Multiply cubic meters by 1.308 to get cubic yards. One cubic meter equals about 1.308 cubic yards.

How many bags of concrete are in a cubic yard?

It depends on bag size. One cubic yard takes about 45 of the 80 pound bags, 60 of the 60 pound bags, or 90 of the 40 pound bags, because larger bags yield more cubic feet each.

Should I always add a waste factor?

Yes. A 10 percent waste factor is standard for concrete, while loose materials that compact, such as gravel and soil, often need 15 to 20 percent extra.

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