How to Calculate Volume of a Box

PDF download Download Article
PDF download Download Article

Whether you need to mail a package or pass you next test, finding the volume of a box is easy. Volume is the measure of how big an object is in three dimensions, so the volume of a box measure how much room there is inside of the box. To find it, you need to make a few simple measurements of length, width, and height, and then multiply them.

Method 1
Method 1 of 2:

Calculating the Volume of Rectangular Boxes

PDF download Download Article
  1. If your box is a rectangular prism or a cube, the only information you need is the box's length, width, and height. You can then multiply them together to get volume. This formula is often abbreviated as V = l x w x h. [1]
    • Sample Question: "If I have a box with a length of 10cm, width of 4cm, and height of 5cm, what is the volume of the box?"
    • V = l x w x h
    • V = 10cm x 4cm x 5cm
    • V = 200cm 3
    • "Height" may be replaced with "depth." For example, "The box has a length of 10cm, width of 4cm, and is 5cm deep. " [2]
  2. If your are looking down at your box, the top appears to be a flat rectangle/The length the longest side of this rectangle. Write this number down as "length." [3]
    • Make sure you use the same measurement for each side -- if you measure one side in inches, you need to measure them all in inches.
    Advertisement
  3. The width of the box is the other edge next to the length. If you are looking one side of the box, the width is the side the forms an "L" with the length. Write down this measurement as "width." [4]
    • The width is always the shorter side.
  4. This is the last side you have not measured, and is the distance from the top of the box to the ground. Write this measurement down as "height." [5]
    • Depending on how the box is laying, which side you call "height" or "length" might be different. However, it doesn't matter what side you call the length, just that you measure 3 different sides.
  5. Remember, the equation for volume is V = length x width x height , so simply multiply all three sides together to get your volume. Be sure to include the units you used to measure with as well, so you don't forget what your numbers mean. [6]
    EXPERT TIP

    Grace Imson, MA

    Math Instructor, City College of San Francisco
    Grace Imson is a math teacher with over 40 years of teaching experience. Grace is currently a math instructor at the City College of San Francisco and was previously in the Math Department at Saint Louis University. She has taught math at the elementary, middle, high school, and college levels. She has an MA in Education, specializing in Administration and Supervision from Saint Louis University.
    Grace Imson, MA
    Math Instructor, City College of San Francisco

    Make sure all of the units are the same before multiplying. Tricky math problems will give a different unit of measurement for the length, width, and height of a box. You cannot multiply the dimensions to find the volume until all the dimensions are in the same unit.

  6. Volume is a measurement, but if you don't know what the measuring system your number will be meaningless. The correct way write out volume is with your type of measurement cubed . For example, if I measured all the sides in inches, my final answer would be in "inches 3 ." For example. [7]
    • Sample Question: "If I have a box with a length of 2 feet, width of 1 foot, and height of 4 feet what is the volume of the box?"
    • V = l x w x h
    • V = 2ft x 1ft x 4ft
    • Volume = 8ft 3
    • Advanced Note:' This is because volume tell you how many small cubes you could fit in the box. In the previous example, this means we could fit eight separate 1 foot cubes in our box.
    7. Advertisement
Method 2
Method 2 of 2:

Calculating Different Shaped Boxes

PDF download Download Article
  1. Cylinders are tubes, where the top and bottom are circles. To find volume of a cylinder, use the equation V = pi x r 2 x h. Where pi = 3.14, r is the radius of the top circle, and h is the height. [8]
    • To find the volume of a cone, or pyramid with a circle for the bottom, use the same equation time 1/3. So, Volume of a Cone = 1/3(pi x r 2 x h)
  2. Pyramids have one side, or base, and all of the other sides comes to a point. To find volume, multiply the area of the base by the height, and then multiply that by the fraction 1/3. Thus, Volume of a Pyramid = 1/3(base x height). [9]
    • Most pyramids have square or rectangular bases. The area of a base is found by multiplying the length of the base by the width.
    EXPERT TIP

    Joseph Meyer

    Math Teacher
    Joseph Meyer is a High School Math Teacher based in Pittsburgh, Pennsylvania. He is an educator at City Charter High School, where he has been teaching for over 7 years. Joseph is also the founder of Sandbox Math, an online learning community dedicated to helping students succeed in Algebra. His site is set apart by its focus on fostering genuine comprehension through step-by-step understanding (instead of just getting the correct final answer), enabling learners to identify and overcome misunderstandings and confidently take on any test they face. He received his MA in Physics from Case Western Reserve University and his BA in Physics from Baldwin Wallace University.
    Joseph Meyer
    Math Teacher

    To find a pyramid's volume, use the formula (1/3) Base Area Height. Measure a pyramid's height from its tip to the base's center. Next, find the base area using the correct formula for the base shape, whether a triangle, square, or rectangle. Finally, input these values into the formula to calculate volume.

  3. For example, if I need to find the volume of an "L" shaped box, there are more than three sides to measure. If you view the box as two smaller boxes, however, you can find the volume of each smaller box and add them together to get the final volume. With our "L" shaped box, for example, we can view the vertical line as a rectangular box and the bottom horizontal line as a square box. [10]
    4. Advertisement

Calculator, Practice Problems, and Answers

Community Q&A

Search
Add New Question
  • Question
    How do I tell how many bottles I can put on a tray?
    Donagan
    Top Answerer
    Assuming identical, cylindrical bottles and a square or rectangular tray: Divide the diameter of a bottle into the length of the tray. That's how many bottles you can fit in one direction. Divide the diameter into the width of the tray. That's how many bottles you can fit in the other direction. Multiply the two numbers together to get the total number of bottles that will fit.
    Thanks! We're glad this was helpful.
    Thank you for your feedback.
    If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission. Support wikiHow
    Yes No
    Not Helpful 7 Helpful 17
  • Question
    Is it possible to find the volume of a rectangular prism without the depth?
    Donagan
    Top Answerer
    No. The volume is calculated by multiplying the depth (height) by the area of the base.
    Thanks! We're glad this was helpful.
    Thank you for your feedback.
    If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission. Support wikiHow
    Yes No
    Not Helpful 6 Helpful 12
  • Question
    How do I convert cubic centimeters into liters?
    Donagan
    Top Answerer
    There are 1,000 cubic centimeters in one liter. To convert cubic centimeters to liters, divide the number of cubic centimeters by 1,000.
    Thanks! We're glad this was helpful.
    Thank you for your feedback.
    If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission. Support wikiHow
    Yes No
    Not Helpful 5 Helpful 19
See more answers
Ask a Question
200 characters left
Include your email address to get a message when this question is answered.
Submit
      Advertisement

      Video

      Tips

      Submit a Tip
      All tip submissions are carefully reviewed before being published
      Name
      Please provide your name and last initial
      Submit
      Thanks for submitting a tip for review!

      You Might Also Like

      How to
      Calculate the Volume of a Sphere
      How to
      Find the Volume of a Cone
      How to
      Calculate the Volume of a Prism
      How to
      Calculate the Volume of an Irregular Object
      How to
      Calculate the Volume of a Cylinder
      How to
      Calculate the Volume of a Triangular Prism: Formulas & Examples
      How to
      Find the Volume of Basic Shapes
      How to
      Find the Volume of a Cube from a Side, Surface Area, or Diagonals
      How to
      Calculate the Volume of a Rectangular Prism
      How to
      Calculate CBM
      How to
      Calculate the Volume of a Pyramid
      How to
      Find Density
      Advertisement

      References

      1. ↑ https://www.khanacademy.org/math/basic-geo/basic-geo-volume-sa/volume-rect-prism/a/volume-of-rectangular-prisms-review
      2. ↑ https://elementarymath.edc.org/resources/measurement-length-width-height-depth/
      3. ↑ https://www.omnicalculator.com/math/volume
      4. ↑ https://www.omnicalculator.com/math/volume
      5. ↑ https://www.omnicalculator.com/math/volume
      6. ↑ https://sciencing.com/calculate-area-perimeter-volume-8465825.html
      7. ↑ https://www.mathopenref.com/cubevolume.html
      8. ↑ https://www.mathopenref.com/cylindervolume.html
      9. ↑ https://www.mathopenref.com/pyramidvolume.html
      1. ↑ https://math.libretexts.org/Bookshelves/Applied_Mathematics/Math_For_Liberal_Art_Students_2e_(Diaz)/06%3A_Geometry/6.03%3A_Volume_of_Geometric_Solids

      About This Article

      Article Summary X

      To calculate the volume of a rectangular box, first measure its length, width, and height. Be sure to use the same units, like inches or centimeters, for all 3 measurements! Then, simply multiply the 3 measurements together using the formula Volume = Length × Width × Height. Finally, add the units cubed. For more on calculating the volume of a box, including a box that’s not rectangular, read on!

      Did this summary help you?
      In other languages
      Thanks to all authors for creating a page that has been read 629,476 times.

      Reader Success Stories

      • Jerry Tasker

        Dec 10, 2017

        "This article helped me tremendously with building a speaker cabinet. I have the woofer and other items that I ..." more
      More reader stories Hide reader stories
      Share your story

      Did this article help you?

      Advertisement