This example problem demonstrates how to convert cubic feet to liters. The cubic foot is the U.S. and imperial unit of volume for a cube that has sides that are 1 foot in length. The liter is an SI or metric unit of volume. It is the volume of a cube that has sides that are 10 centimeters in length. The conversion between the two systems is fairly common, particularly if you're working with liquefied gases.

### Cubic Feet to Liter Conversion Problem

What is this volume of 1 cubic foot in liters?

### Solution

Many conversion factors are difficult to remember. Converting cubic feet to liters would fall into this category. The unit-canceling method is helpful in performing this kind of problem because it uses many easily remembered conversions that relate the original units to the final units, as follows:

- 1 foot = 12 inches
- 1 inch = 2.54 centimeters
- 1,000 cubic centimeters = 1 liter

Using these steps, you can express feet to centimeters as:

- Distance in cm = (distance in ft) x (12 in/1 ft) x (2.54 cm/1 in)
- Distance in cm = (distance in ft) x 30.48 cm/ft

Convert these distances into volume measurements of cm^{3} and ft^{3}:

- Cube volume = (linear measurement)
^{3}, so: - Volume in cm
^{3}= [(distance in feet) x 30.48 cm/ft]^{3} - Volume in cm
^{3}= (volume in ft^{3}) x 28316.85 cm^{3}/ft^{3}

Convert cubic centimeters to liters:

- Volume in liters = (volume in cm
^{3}) x (1 L/1,000 cm^{3})

- Volume in liters = (volume in cm
^{3})/1,000 L/cm^{3}

Insert the cubic volume from the previous step:

- Volume in liters = [(volume in ft
^{3}) x 28316.85 cm^{3}/ft^{3})]/1,000 L/cm^{3} - Volume in liters = (volume in ft
^{3}) x 28.317 L/ft^{3}

Now you have your conversion factor of cubic feet to liters. Insert 1 cubic foot into the volume in ft^{3} part of the equation:

- Volume in liters = (1 ft
^{3}) x 28.317 L/ft^{3} - Volume in liters = 28.317 L

### Answer

One cubic foot is equal to 28.317 liters of volume.

### Liter to Cubic Feet Example

The conversion factor works the other way, too. For example, convert 0.5 liter to cubic feet.

Use the conversion factor 1 cubic foot = 28.317 liters:

- Cubic feet = (0.5 liter) x (1 cubic foot / 28.317 liters)

The liters cancel out on the top and bottom, leaving you with 0.5 / 28.317, and giving an answer of 0.018 cubic feet.

### Tip for Success

The key to working the unit conversion correctly is to make certain the unwanted unit cancels out and leaves the desired unit. It's also worthwhile to keep track of significant digits (although that was not done in this example). Also, remember there are about 28 liters in a cubic foot. If you're converting from cubic feet to liters, expect to get a larger number than you started with. If you're converting from cubic feet to liters, your final answer will be a smaller number.