Cuboid Calculator

Created by Adena Benn
Reviewed by Aleksandra Zając, MD
Last updated: Nov 03, 2022

Are you struggling with cuboid calculations? Our cuboid calculator is just the tool you need to help solve those math problems. Keep reading to learn:

  • What is a cuboid;
  • How to use our cuboid calculator;
  • The surface area and volume of a cuboid formula; and
  • How to manually calculate the surface area and volume of a cuboid.

What is a cuboid?

A cuboid is a three-dimensional shape that has six rectangular faces. A cuboid's length, width, and height are of different measurements. The corners of these faces form right angles. Cuboids have eight vertices and twelve edges.

How to use our cuboid calculator

Our cuboid calculator calculates the surface area of a cuboid as well as the volume. To calculate either of these two unknowns, you simply need to enter the length (l), width (w), and height (h) of the shape, and the result will be generated in real-time.

As a bonus, you will also be able to see the diagonal of the shape.

How to calculate the volume of a cuboid

To calculate the volume of a cuboid, we use the following formula:

volume=(l×w×h) cubic units\small \text {volume} = (l × w × h)\ \text{cubic units}

So if we have the following problem:
Find the volume of a cuboid whose length is 12 cm, width is 9 cm, and height is 10 cm.

Using the above formula, we can then say:

volume=(12×9×10) cm3\small \text{volume} = (12 × 9 × 10)\ \text{cm}^3
volume=1080 cm3\small \text{volume} = 1080\ \text{cm}^3

How to calculate the surface area of a cuboid

We calculate the surface area of a cuboid by finding the sum of the area of its six faces. To calculate the surface area of a cuboid (SAC), we use the following formula:

SAC=2(lw+wh+lh) sq units\small SAC = 2(lw + wh + lh)\ \text{sq units}

So if we need to find the total surface area of a cuboid whose length is 8 cm, width is 7 cm, and height is 6 cm, using the above, we begin by substituting the values:

SAC=2((8×7)+(7×6)+(8×6)) cm2=2(56+42+48) cm2=2(146) cm2=292 cm2\small \begin{align*} SAC &= 2((8 × 7 )+ (7 × 6) + (8 × 6))\ \text{cm}^2\\[.5em] &= 2(56+ 42 + 48)\ \text{cm}^2\\[.5em] &= 2(146)\ \text{cm}^2\\[.5em] &= 292\ \text{cm}^2\\[.5em] \end{align*}

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FAQ

What is the difference between a cube and a cuboid?

The main difference between a cube and a cuboid is that the length, width, and height of a cube are of equal measurements. On the other hand, a cuboid has length, width, and height that are of different sizes.

How do I calculate the volume of a cuboid?

To calculate the volume of a cuboid you need to:

  1. Get the length, width, and height.
  2. Put the dimensions into the formula:
    volume = (l × w × h) cubic unit.
  3. Do the calculation to find the answer.
Adena Benn
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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