Cubic Feet and Cubic Yards Converter

A cubic feet and cubic yards converter is a handy tool for anyone working with measurements in construction, landscaping, or any project that requires volume calculations. This converter makes it easy to switch between cubic feet and cubic yards, two common units of volume used in the United States. In this article, we will explain the formulas necessary to complete the calculation and provide a worked example to demonstrate the process.

Formulas

Before diving into the formulas, it’s essential to have a basic understanding of the units involved. A cubic foot (ft³) is a unit of volume equivalent to the space occupied by a cube with sides measuring one foot in length. A cubic yard (yd³) is a unit of volume equivalent to the space occupied by a cube with sides measuring one yard (3 feet) in length.

1. Conversion from cubic feet to cubic yards

To convert cubic feet to cubic yards, you need to divide the number of cubic feet by 27, as there are 27 cubic feet in a cubic yard. The formula is as follows:

cubic ~yards ~(yd^3) = \cfrac{cubic~feet~(ft^3)}{27}

2. Conversion from cubic yards to cubic feet

To convert cubic yards to cubic feet, you need to multiply the number of cubic yards by 27. The formula is as follows:

cubic ~feet ~(ft^3) \\= cubic ~yards ~(yd^3)*27

Worked Example

Let’s say you are working on a landscaping project and need to calculate the volume of soil required to fill a garden bed. The garden bed measures 10 feet long, 5 feet wide, and 2 feet deep. First, we need to calculate the volume in cubic feet, then convert it to cubic yards.

Step 1: Calculate the volume in cubic feet

To calculate the volume in cubic feet, multiply the length, width, and depth of the garden bed:

volume (ft^3) \\= length (ft)*width (ft)*depth (ft)

volume (ft^3) = 10 ft*5 ft*2 ft

volume (ft^3) = 100 ft^3

The volume of the garden bed is 100 cubic feet.

Step 2: Convert cubic feet to cubic yards

Now, we need to convert the volume from cubic feet to cubic yards using the formula mentioned earlier:

cubic ~yards (yd^3) = \cfrac{cubic ~feet (ft^3)}{27}

cubic ~yards (yd^3) = 100 ft^3 / 27

cubic ~yards (yd^3) ≈ 3.70 yd^3

The volume of the garden bed is approximately 3.70 cubic yards.

Now let’s say you have already purchased soil in cubic yards and want to know how many cubic feet you have. In this example, you have 4 cubic yards of soil.

Step 1: Convert cubic yards to cubic feet

To convert the volume from cubic yards to cubic feet, use the formula mentioned earlier:

cubic ~feet (ft^3) \\= cubic ~yards (yd^3)*27

cubic ~feet (ft^3) = 4 ~yd^3*27

cubic ~feet (ft^3) = 108 ~ft^3

You have 108 cubic feet of soil.

Conclusion

A cubic feet and cubic yards converter is a valuable tool for simplifying volume calculations in various projects. By understanding the formulas for conversion and applying them to your measurements, you can quickly determine the volume of materials needed or the volume of a specific space. The worked example provided above demonstrates the calculation process, making it easy for you to apply the same methodology to your projects.

Remember the formulas:

cubic ~yards ~(yd^3) = \cfrac{cubic~feet~(ft^3)}{27}

cubic ~feet ~(ft^3) \\= cubic ~yards ~(yd^3)*27

With these formulas and a cubic feet and cubic yards converter, you can confidently tackle any project that requires volume calculations.