Have you ever needed to convert cubic feet to liters or ft3 to L?A cubic foot is an imperial volume measurement equal to a cube with sides equal to one foot in length. The unit often appears in industrial applications involving liquids and gases. Converting this unit to SI units does not come up all that often, so the conversion factor is not really worth memorizing unless you are in the industry. Converting cubic feet to liters is a good example of using smaller known conversion factors chained together in the Ladder conversion method.
Convert Cubic Feet to Liters Example Problem
Question: Natural gas companies charge you by the cubic foot of gas which goes through their meter outside your house. If you receive a bill for 50 cubic feet, how many liters of natural gas was delivered?
Solution:
First, let’s figure out how many liters are in one cubic foot.
Here are a few common conversion factors everyone should know.
1 foot = 12 inches
1 inch = 2.54 centimeters
1000 cubic centimeters = 1 liter
Let’s convert feet to centimeters.
1 foot = 30.48 cm
1 cubic foot (CFT) = 1 foot ⋅ 1 foot ⋅ 1 foot = (1 foot)3
Plug our value for 1 foot in centimeters into this equation
1 CFT = (30.48 cm)3
1 CFT = 28,316.85 cm3
Next, use the centimeters to liters conversion to find the number of liters
1 CFT = 28.316 liters
Now we know how many liters in one cubic foot, we can quickly figure out how many liters in 50 cubic feet.
1 CFT = 28.316 liters
50 ⋅ 1 CFT = 50 ⋅ 28.316 liters
50 CFT = 1415.8 liters
Answer: 1415.8 liters of natural gas was delivered to your house.
The actual conversion factor between cubic feet and liters is 1 cubic foot = 28.316846592 liters. Most applications involving cubic feet don’t need all those significant figures, so the method outlined above works out remarkably well.
The typical concern for this type of problem is making sure your unwanted units cancel out and leave only the units you need. If you include the units in your math steps, you can usually avoid easily avoided mistakes.