It's time to buy your first pet: a goldfish! But in order to ensure that your goldfish is happy and healthy, you will need to purchase a tank that is large enough for the goldfish. To determine how much water fits into a tank, you'll need calculate the volume of the container.

## Volume of a Container

The volume of a container is the amount of space it encloses; or how much space is inside of it. For a box, the volume is determined simply by this formula: A box with height *H*, width *W* and length *L*, has volume V = L × W × H. There are many units that can be used, but due to the way in which this formula is written, the volume would have dimensions of length to the third power. For example, if the dimensions of the container are given in meters, the volume of the box is in meters cubed, or m^{3}.

For a cylindrical container, such as a glass or a vase for flowers, the formula for volume is different. Therefore, the formula for the volume of a cup with height *h*, and a circular base of radius *r* is V = π × r^{2} × h. Just like for a rectangular container, this volume will have dimensions of length cubed.

However, we do not often use units of meters cubed to describe liquid volumes. Therefore a liquid volume calculator would not only calculate the volume of a container, but convert that volume into units such as liters, cups or gallons.

## What Is a Liquid Volume Calculator?

A liquid volume calculator can calculate the volume of a container and convert it to units that are commonly used for measuring liquids. Essentially, the calculator just needs to know the conversion factor between either metric or imperial length units when cubed, to the necessary volume unit.

Often, in the United States, the volume of a liquid is measured in gallons, such as milk. The conversion factor for cubic meters to U.S. gallons is: 1 m^{3} = 264.172 gallons. From cubic feet, 1 ft^{3} = 7.48052 gallons.

Therefore, a liquid volume calculator would simply multiply the number of cubic meters or cubic feet that a container holds, by the appropriate conversion factor, to represent the volume in U.S. gallons.

## Volume-of-a-Cup Calculator

It turns out that, although the formula for calculating the volume of a cup is quite different than the volume of a rectangular container, a volume-of-a-cup calculator would essentially be the same as a rectangular-tank volume calculator.

Once the calculator determines the volume of the cup in units of length cubed by using the formula above, it could apply any conversion factor to represent the answer in a liquid volume unit.

## Dimensions of a Fish Tank

For your new pet goldfish, you need to purchase a tank that can hold enough water for the fish to be able to swim in to stay healthy. At the store, there are usually several shapes and styles of tanks, so picking the correct one can be challenging.

To save you time, most stores label fish tanks by the amount of water they hold in gallons; but not always the dimensions of the tank itself. Knowing the relationship between volume and dimensions of a container, one can determine an unknown dimension.

The tank you want holds 25 gallons of liquid and has square sides. You noticed that the depth and height of the tank are the same as the shelf it sits on, which is 12 inches. Knowing this information, you need to determine the length of the tank.

Using the conversion factor of 1 gallon = 231 cubic inches, the volume in cubic inches is simply:

V = 25 × 231 in^{3} = 5775 in^{3}

If V = L × W × H, and W × H = 12 in × 12 in, then V / 144 in^{2} = L. Therefore, the unknown length is about 40.1 inches.

References

About the Author

Lipi Gupta is currently pursuing her Ph. D. in physics at the University of Chicago. She earned her Bachelor of Arts in physics with a minor in mathematics at Cornell University in 2015, where she was a tutor for engineering students, and was a resident advisor in a first-year dorm for three years. With this experience, when not working on her Ph. D. research, Gupta participates in STEM outreach activities to promote young women and minorities to pursue science careers.