Cubic Yard Calculator - Calculator Academy

Calculate cubic yards from the length, width, and depth of the area you are filling.

Cubic Yard Formula

For a rectangle or slab, multiply the three dimensions in feet and divide by 27, since one cubic yard equals 27 cubic feet (3 ft by 3 ft by 3 ft):

CY = (L * W * D) / 27

If you measure depth in inches instead of feet, divide by 324 to convert and reduce in one step:

CY = (L * W * D_in) / 324

For a circular area, replace length and width with the area of the circle, then divide by 27:

CY = (pi * r^2 * D) / 27

When you already know the area, the volume comes straight from area times depth:

CY = (A * D) / 27

CY = volume in cubic yards
L = length in feet
W = width in feet
D = depth in feet
D_in = depth in inches
A = surface area in square feet
r = radius in feet (half the diameter)
pi = 3.14159

The calculator runs these formulas in either direction. In the standard mode it takes your measurements and returns the cubic yards needed. The depth mode rearranges the slab formula to D = (CY * 27) / A so you can see how deep a known amount of material will spread over a set area. The area mode solves A = (CY * 27) / D to show how much ground a delivered load will cover at a chosen depth. The cost mode multiplies the cubic yards by your price per unit, Cost = CY * price, and can also divide the volume into bags when you enter a bag size. Shape options for circle, triangle, trapezoid, and ring swap in the matching area formula before the divide by 27 step, so every shape ends in the same cubic yard result.

Material Depths and Weights

Depth directly scales volume. The table gives broad illustrative depth and weight ranges, not design specifications or delivery load limits. Confirm the required depth and the actual product density with your supplier; moisture and compaction can change weight substantially.

Material	Typical Depth	Approx. Weight per Cubic Yard
Mulch	2 to 3 in	400 to 800 lb
Topsoil	4 to 6 in	2,000 to 2,700 lb
Gravel	2 to 4 in	2,400 to 2,900 lb
Sand	1 to 2 in	2,600 to 3,000 lb
Concrete	4 to 6 in	3,700 to 4,000 lb

The next table converts a few common inch depths into the fraction of a foot the formula uses, so you can sanity check the depth field.

Depth in Inches	Depth in Feet
1 in	0.083 ft
2 in	0.167 ft
3 in	0.250 ft
4 in	0.333 ft
6 in	0.500 ft

Examples

Example 1: You are spreading topsoil over a rectangular bed that is 20 feet long and 10 feet wide at a depth of 6 inches. First convert the depth: 6 inches is 0.5 feet. The volume is (20 * 10 * 0.5) / 27 = 100 / 27 = 3.70 cubic yards. An order of 4 cubic yards would provide about 8% extra; choose the allowance with your supplier.

Example 2: A round patio base is 12 feet across, so the radius is 6 feet, and you want a 4-inch gravel layer, which is exactly one-third of a foot. The circle area is 3.14159 * 6^2 = 113.1 square feet. Using unrounded values, the volume is (pi * 6^2 * (4/12)) / 27 = about 1.40 cubic yards. At 40 dollars per cubic yard the estimated cost is $55.85 before any chosen allowance, delivery, or tax.

FAQ

Why divide by 27? A cubic yard is a cube measuring one yard, or 3 feet, on every side. Multiplying 3 by 3 by 3 gives 27 cubic feet in a single cubic yard. When your measurements are in feet, the length times width times depth gives cubic feet, so dividing by 27 converts that total into cubic yards.

How do I handle a depth measured in inches? Convert the depth to feet by dividing the inches by 12 before you apply the formula, or use the combined divisor of 324, which is 12 times 27. Both give the same result. The calculator does this for you when you set the depth unit to inches.

How much extra should I order? Ask the supplier for an allowance appropriate to the material, compaction and delivery increments. The calculator applies no extra material by default. For a known purchased volume, entering an allowance reserves that share relative to the usable volume: usable = purchased / (1 + allowance/100).