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Thanks to our rectangular prism calculator, you can easily find the cuboid volume, surface area, and rectangular prism diagonal. Whether you are wondering how much water your fish tank holds or trying to find out how much paper you need to wrap a gift, give this rectangular prism calculator a go! If you are still unsure how it works, keep scrolling to learn about rectangular prism formulas.

What is a rectangular prism?

A right rectangular prism is a box-shaped object, that is, a 3-dimensional solid with six rectangular faces.

Rectangular prisms can also be oblique - leaning to one side - but in this instance, the side faces are parallelograms, not rectangles. When this happens, they are called oblique rectangular prism.

A right rectangular prism is also called a cuboid, box, or rectangular hexahedron. Moreover, the names "rectangular prism" and "right rectangular prisms" are often used interchangeably.

The most common math problems related to this solid are of the type right rectangular prism calc find V or find A, where the letters stand for the Volume and Area, respectively. Let's see the necessary rectangular prism formula and learn how to solve t these problems quickly and easily.

How do I find the volume of a rectangular prism?

We calculate the volume of a rectangular prism with the following formula:

volume = h × w × l,

where h is the height of the prism, w is its width, and l is its length. To calculate the volume of a cardboard box:

  1. Find the length of the box, say 18 in.
  2. Determine its width - 12 in.
  3. Find out the height of the rectangular prism - 15 in.
  4. Calculate the volume of the cuboid. Using the rectangular prism volume formula, we get:
    volume = (18 × 12 × 15) in³
    volume = 3240 in³.

How do I find the area of a rectangular prism?

The surface area of the cuboid consists of 6 faces - three pairs of parallel rectangles. To find the rectangular prism surface area, add the areas of all faces:

surface_area = 2 × (h × w) + 2 × (h × l) + 2 × (l × w) = 2 × (h × w + h × l + l × w),

where h is prism height, w is its width, and l is its length.

Let's see an example of how to solve the right rectangular prism calc - find A problem. We'll come back to our example with the box and calculate its surface area:

  1. Calculate the rectangular prism surface area. First rectangle area is 15in × 12in = 180in², second 15in × 18in = 270in² and third one 18in × 12in = 216in². Add all three rectangles' areas - it's equal to 666 in² (what a number!) - and finally multiply by 2. The surface area of our cardboard box is 1332in².
  2. Or save yourself some time and use our rectangular prism calculator.

Finally, let's attack the right rectangular prism calc find d (that is, the diagonal) type of problem.

How do I calculate the diagonal of a rectangular prism?

To determine the diagonal of a rectangular prism, follow these steps:

  1. Apply the formula:

    diagonal = √(l² + h² + w²)

    where h is the height of the prism, w is its width, and l is its length.

  2. Substitute the values.

  3. Calculate.

Do you have the feeling that you saw the formula before? Yes, that's possible because this equation resembles the famous one from the Pythagorean theorem.

How to calculate volumes of the other solids?

That rectangular prism was a piece of cake! If you are amazed at how easily you can calculate the volume with our tool, try out the other volume calculators:

Be sure to check out the volume calculator - the volume of basic 3D solids, all in one place!

FAQ

How many edges does a rectangular prism have?

The answer is twelve edges. A rectangular prism has:

  • Six faces;
  • Eight vertices (or corners); and
  • Twelve edges.

If you are not sure about the result, you can try to draw a rectangular prism and count its faces, vertices, and edges.

How do I calculate the volume of a rectangular prism with only its length?

You cannot calculate the volume of a rectangular prism, knowing only its length. You need to know its length, width, and height to calculate it. Once you have these parameters, you can use the equation:

volume = h × w × l.

What is the volume of a box with all sides equal?

Assuming that all sides are equal to 20 in, the volume is 8,000 in³. We arrive at this answer by following these steps:

  1. Get the length, width, and height of the box.
  2. Using the rectangular prism volume formula, we get:
    volume = (20 × 20 × 20) in³
    volume = 8,000 in³.

How do I find the perimeter of a rectangular prism?

In a 3D solid, you find the surface area of the solid instead of the perimeter. For the rectangular prism, you can find its surface area using the formula:

surface_area = 2 × (h × w) + 2 × (h × l) + 2 × (l × w) = 2 × (h × w + h × l + l × w),

where h is the height of the prism, w is its width, and l is its length.

Hanna Pamuła, PhD
image of a rectangular prism, with length, height, width and diagonal marked
Length (l)
in
Width (w)
in
Height (h)
in
Surface area
in²
Volume
cu in
Diagonal (d)
in
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