How to Calculate the Volume of a Rectangular Prism

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Plus practice problems for finding a rectangular prism’s volume
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Volume is the amount of three-dimensional space taken up by an object. The computer or phone you're using right now has volume, and even you have volume! Finding the volume of a rectangular prism is actually really easy. Just multiply the length, the width, and the height of the rectangular prism or box that you want the volume of. That's all you have to do! But, this article will walk you through every step of this calculation, including what to do if you don’t know the dimensions of the prism. Calculators at the ready!

Volume of a Rectangular Prism: Formula

Calculate the volume of a rectangular prism by multiplying its width, length, and height together (in any order). Make sure all units are the same across the dimensions, then plug them into the formula Volume = W x L x H .

Section 1 of 7:

Finding the Volume of a Rectangular Prism (With Known Dimensions)

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  1. If you’ve been given a rectangular prism with stated dimensions, then it should be easy to find the length, width, and height of the box. If your box isn’t already labeled, draw a rectangular prism on a piece of paper and label the length, width, and height so they’re easier to keep track of throughout your calculations.
    • The length is the longest side of the flat surface of the rectangle on the top or bottom of the rectangular prism. [1]
    • The width is the shorter side of the flat surface of the rectangle on the top or bottom of the rectangular prism. [2]
    • The height is the part of the rectangular prism that rises up. Imagine that the height is what stretches up a flat rectangle until it becomes a three-dimensional shape.
    • For example , your box may have these dimensions: length (l) = 5 inches, width (w) = 4 inches, and height (h) = 3 inches.
  2. Multiply the three dimensions of a rectangular prism in any order to get the shape’s total volume. This calculation can also be done by plugging the dimensions into the formula for finding the volume of a rectangular prism, which is Volume = length x height x width, or V = l x h x w. [3]
    • For example , let’s say that your rectangular prism has the dimensions length (l) = 5 inches, width (w) = 4 inches, and height (h) = 3 inches.
    • To calculate this rectangular prisms volume, multiply 5 x 4 x 3 = 60 . The volume of this box is 60 .
    • These numbers can be calculated in any order. For instance, multiplying 3 x 5 x 4 would produce the same final value of 60.
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  3. 3
    Write your final answer in cubic units. Since you're calculating volume, you're working in a three-dimensional space. As a result, you must state your answer in cubic units . [4] Identify whether the original dimensions of the rectangular prism were in feet, inches, centimeters, or another unit of measurement.
    • Then, write the number value of your volume, followed by that measurement with the exponent 3 attached to it.
    • For example , the rectangular prism in our example has its dimensions stated in inches. Therefore, our final answer with units would be Volume = 60 in 3 .
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Section 2 of 7:

Finding the Volume of a Rectangular Prism (With Cube Units)

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  1. The space inside of a rectangular prism is made up of cube units, meaning that a rectangular prism can be visualized as a 3D shape with many smaller cubes fitting inside it—almost like a 3-dimensional grid inside the prism. [5] If you’ve been given a rectangular prism problem where the prism is divided up into cubes and you’re only given the side length of each cube , follow this set of steps.
    • Start by making note of the given side length of each small cube inside the rectangular prism.
    • In our example , we’ll say that each of the cubes in the prism has a side length of 1 inch .
  2. Look at the bottom layer of the rectangular prism. Count how many cubes are included in the long side of the prism. Then, count how many cubes are included on the short side.
    • For example , our rectangular prism has a 9 cubes on its long side and 2 cubes on its short side.
    • If you’re struggling to visualize this process by counting cubes on the 3-dimensional shape, imagine what it would look like if you picked up the prism and looked at the bottom. What would the dimensions of that bottom rectangle be?
    • In our example , you would see a 9 by 2 rectangle.
    • If you have MathLink Cubes or something similar on hand, it may be helpful to physically build your prism out of cubes to better visualize it and its dimensions.
  3. Now that you know how many cubes make up the long and short sides of the prism’s bottom layer, you can determine the prism’s total length and width.
    • To find the length , multiply the side length of your cubes by the number of cubes on the long side of the bottom layer.
      • For example , our rectangular prism has cubes with a side length of 1 inch, and there are 9 cubes on the long side of the rectangle. Therefore, our prism’s length = 1 inch x 9 = 9 inches .
    • To find the width , multiply the side length of your cubes by the number of cubes on the short side of the bottom layer.
      • For example , our rectangular prism has cubes with a side length of 1 inch, and there are 2 cubes on the long side of the rectangle. Therefore, our prism’s length = 1 inch x 2 = 2 inches .
  4. You now have the length and width of the bottom layer of your prism. You also know that layer’s height, which is equal to the side length of a single cube. To find the volume of that layer (just that layer—not the entire prism), multiply length by width by height. [6]
    • For example , in a rectangular prism with a bottom layer whose dimensions are 9 inches (length) by 2 inches (width) by 1 inch (height), you’d calculate Volume = 9 x 2 x 1 = 18 .
    • Since our original cube side-length was given in inches and volume is always measured in cubic units, our bottom layer’s final volume with units would be Volume = 18 inches 3
  5. You now know the volume of the bottom layer of the prism. The great news is that every layer has the same volume—so we’re almost there! Count the total number of layers in your prism, then add together your volume answer from the previous amount of steps that amount of times. [7]
    • For example , let’s say that our rectangular prism has 2 layers of cubes.
    • Since we already know that the bottom layer has a volume of 18 inches 3 , all we have to do is add that value together 2 times .
    • Therefore, the total volume of the rectangular prism is 18 inches 3 + 18 inches 3 = 36 inches 3
  6. Determine the original units of the rectangular prism (e.g, inches, centimeters, feet, etc.). Write the final volume in cubic units matching your original units. [8]
    • If your original units were in inches : in 3
    • If your original units were in centimeters : cm 3
    • If your original units were in feet : ft 3
    • In our example , the original units were given in inches, making our final answer 36 in 3 .
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Section 3 of 7:

Practice Questions for Rectangular Prism Volume

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  1. 1
    Problem #1: Find the volume of a rectangular prism with these dimensions: length = 6 inches, width = 10 inches, height = 8 inches. Solution :
    • Write down the formula for the volume of a rectangular prism: Volume = length x height x width, or V = l x h x w.
    • Plug your dimensions into the formula : Volume = 6 x 8 x 10.
    • Solve the formula through multiplication: V = 480.
    • Add cubic units to match the original units (in this case, inches): V = 480 inches 3 .
    • The final volume of this rectangular prism is 480 inches 3 .
  2. 2
    Problem #2: Find the volume of a cube with a side length of 6 feet. Solution :
    • Identify the length, width, and height of the cube : Cubes have faces and sides that are all equal to each other. Therefore, the side length of the cube being 6 feet means that all of the cubes side lengths (including length, width, and height) are 6 feet.
    • Write down the formula for the volume of a rectangular prism: Volume = length x height x width, or V = l x h x w.
    • Plug your dimensions into the formula : Volume = 6 x 6 x 6.
    • Solve the formula through multiplication: V = 216.
    • Add cubic units to match the original units (in this case, feet): V = 216 feet 3 .
    • The final volume of this rectangular prism is 216 feet 3 .
  3. 3
    Problem #3: Find the volume of a rectangular prism with these dimensions: length = 4 meters, width = 2 meters, height = 50 centimeters. Solution :
    • Convert your dimensions into the same units : Note that all dimensions must be in the same unit before calculating the volume of a rectangular prism. [9] Since our height is given in centimeters (not meters), we must convert this number into meters before continuing:
    • 50 centimeters = 0.5 meters.
    • If you can’t convert units off of the top of your head, use a unit conversation calculator .
    • Write down the formula for the volume of a rectangular prism: Volume = length x height x width, or V = l x h x w.
    • Plug your adjusted dimensions into the formula : Volume = 4 x 2 x 0.5.
    • Solve the formula through multiplication: V = 4.
    • Add cubic units to match the original units (in this case, meters): V = 4 meters 3 .
    • The final volume of this rectangular prism is 4 meters 3 .
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Section 4 of 7:

Common Mistakes When Solving for Volume

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  1. Surface area and volume are two different ways to measure a rectangular prism. Surface area is the total area of the rectangular faces on the outside of the shape, while volume is the total space within the shape. [10]
  2. When writing a measurement, you must always include the units along with the number value. For volume, always use cubic units: e.g., in 3 , cm 3 , mm 3 , m 3 , etc. [11]
  3. To calculate the volume of a rectangular prism (or any shape), all of the measurements must be in the same units. For example, let’s say a prism has the dimensions 1 inch x 2 inch x 3 feet. The 3 feet must be converted into inches before volume can be calculated.
  4. If you calculate the volume of a rectangular prism with its dimensions written in centimeters, you’ll get a different number value as an answer than if you calculated the same rectangular prism’s volume with its dimensions written in meters. However, this difference doesn’t change the actual value of the prism’s volume, or the amount of space it's taking up.
    • The difference in numbers only has to do with the differing units—not because the actual volume of the prism has changed.
    • Consider if you had a cardboard box in front of you. You could use a ruler to measure that box in inches or a measuring tape to measure it in feet. You would get a different answer, but the size of the box wouldn’t actually change.
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Section 5 of 7:

What is a rectangular prism?

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  1. Also known as a box or a cuboid, a rectangular prism is a 3-dimensional shape with 8 vertices, 12 edges, and 6 faces. [12] Some real-life examples of a rectangular prism include the storage area of a truck, a chest of drawers, an aquarium, a book, and any square-shaped cardboard box.
    • A cube is also a type of rectangular prism.
Section 6 of 7:

More Formulas for Volume & Rectangular Prisms

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  1. Review or learn related math formulas and skills. Here are some handy formulas to know when calculating the surface area, volume, and other dimensions of important shapes (plus, you can see the entire step-by-step process by clicking on the links below):
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Section 7 of 7:

Frequently Asked Questions About Volume & Rectangular Prisms

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  1. 1
    When can the formula for finding the volume of a rectangular prism be used in real life? The formula for the volume of a rectangular prism can be used for any real-life scenario where you need to know how much space is inside of or taken up by a 3D rectangular shape or box.
    • For instance, say you bought a box-shaped fish tank. If you want to know how much water you need to fill that tank, use the rectangular prism volume formula.
    • In another example, you may want to construct a raised garden bed and fill it with potting soil. To know how much potting soil you’ll need, plug the dimensions of your bed into the rectangular prism volume formula.
    • Or, maybe you’re going on a dream vacation and need to choose between two suitcases. If you want to know which suitcase would fit more inside it, calculate the volume of each one and see which number value is largest.
  2. 2
    How do I find the height of a rectangular prism when given its volume? If you are given the volume of the rectangular prism but not its height, you can use this formula to solve for height: Volume (V) = base area (B) x height (h).
    • For example, if you know that the volume of a prism is 200 cubic units and the base area is 20 square units, then plug those values into the equation.
    • Then, you’ll have the formula 200 = 20 x h .
    • To solve for h , divide both sides of the equation by 20 to be left with 10 = h .
    • Therefore, the height of the rectangular prism is 10 units !
  3. 3
    What happens to the volume of a rectangular prism if its length, width, and height are doubled? If the length, width, and height of a rectangular prism are all doubled, then its volume will be eight times its original value. [13]
    • To explain this result, consider the original formula for the volume of a rectangular prism: V = length x width x height.
    • If all of the dimensions are doubled, the volume will then be (2l) x (2w) x (2h) = 8lwh = 8 x V.
    • As a result, the volume will be 8 x V, or 8 times its original value.
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Volume of a Rectangular Prism Practice Worksheets

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  • Question
    If l=45, w=15, h=x, how do I find the volume?
    Donagan
    Top Answerer
    You have to know the height. Otherwise, you'd have to say the volume is 675x cubic units.
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  • Question
    Can you give me another example? I still don't get it.
    Community Answer
    Remember that length x width x height. A rectangular prism that is five inches high, ten inches long, and two inches deep will have a volume of 100 square in. 5x10x2=100.
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  • Question
    How can I calculate the dimension when I know the volume?
    Community Answer
    The rectangle's area, times the prism's height vertical to the rectangle, gives the volume; various combinations of dimensions give the same volume, so if you know the volume, and want the dimensions, you will find many sets of dimensions. For example volume 24 could give the length, width, and height of 2, 2, and 6; or 2, 3, 4; or 1, 1, 24; and so on.
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      • In the United States public school system, calculating the volume of a rectangular prism is typically first taught as a math skill in the 5th grade (according to Common Core State Standards). Then, it’s reinforced and expanded upon in 6th grade. [14]
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      • If you’re teaching a student how to calculate the volume of a rectangular prism, try to focus on activities that show the cube units within a rectangular prism so that the student can really understand why volume is calculated the way it is. Be sure to also teach real-life applications for this problem to students.
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      References

      1. ↑ http://www.softschools.com/math/geometry/topics/volume_of_a_rectangular_prism/
      2. ↑ https://www.khanacademy.org/math/cc-fifth-grade-math/5th-volume/volume-word-problems/a/volume-of-rectangular-prisms-review
      3. ↑ https://collected.jcu.edu/cgi/viewcontent.cgi?referer=&httpsredir=1&article=1032&context=mastersessays
      4. ↑ https://flexbooks.ck12.org/cbook/ck-12-interactive-middle-school-math-7-for-ccss/section/6.9/primary/lesson/volume-of-cubes-and-rectangular-prisms-4424741-msm7-ccss/
      5. ↑ https://flexbooks.ck12.org/cbook/ck-12-interactive-middle-school-math-7-for-ccss/section/6.9/primary/lesson/volume-of-cubes-and-rectangular-prisms-4424741-msm7-ccss/
      6. ↑ https://flexbooks.ck12.org/cbook/ck-12-interactive-middle-school-math-7-for-ccss/section/6.9/primary/lesson/volume-of-cubes-and-rectangular-prisms-4424741-msm7-ccss/
      7. ↑ https://flexbooks.ck12.org/cbook/ck-12-interactive-middle-school-math-7-for-ccss/section/6.9/primary/lesson/volume-of-cubes-and-rectangular-prisms-4424741-msm7-ccss/
      8. ↑ https://www.avc.edu/sites/default/files/studentservices/lc/math/volumes.pdf
      9. ↑ https://www.ohlone.edu/mathmods/mathmod8
      1. ↑ https://byjus.com/maths/surface-areas-volumes/
      2. ↑ https://www.ohlone.edu/mathmods/mathmod8
      3. ↑ https://amsi.org.au/ESA_middle_years/Year6/Year6_2cT/Year6_2cT_R1_pg2.html
      4. ↑ https://www.geeksforgeeks.org/how-to-calculate-the-volume-of-a-rectangular-prism/
      5. ↑ https://www.thecorestandards.org/Math/Content/5/MD/

      About This Article

      Article Summary X

      1. Find the length, width, and height of the rectangular prism.
      2. Multiply the length, width, and height to get the volume.
      3. Write the answer in cubic units.

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