Cuboid Surface Area Calculator

Created by Adena Benn
Reviewed by Aleksandra Zając, MD
Last updated: Jun 05, 2023

Are you at a loss as to how to calculate the surface area of a cuboid? Our cuboid surface area calculator will help you to sort out any questions or doubts you may have quickly and easily. Keep reading to learn:

  • The meaning of cuboid;
  • How many vertices a cuboid has;
  • How to use our surface area of a cuboid calculator;
  • The surface area of a cuboid formula; and
  • How to find the surface area of a cuboid manually.

What does the word cuboid mean?

A cuboid is a solid convex shape with each of its six faces shaped like a rectangle. It is also known as a rectangular prism. Some good real-world examples of cuboids are:

  • A book;
  • A mattress; and
  • A brick.

How many vertices does a cuboid have?

A cuboid has eight vertices. The vertices of a cuboid all form angles of 90 degrees.

How to use this surface area of a cuboid calculator

To use the surface area of a cuboid calculator, enter the following:

  • Length
  • Width; and
  • Height of the cuboid.

Our calculator will immediately return the total surface area of the solid.

Keep in mind you can use any units you wish - our tool will deal with it.

How to find the surface area of a cuboid

To find the surface area of the cuboid(s), you first need to:

  1. Know the length (l), width (w), and height (h) of the shape.
  2. Use the surface area of a cuboid formula:
s=2(l×w+w×h+l×h) sq units\small s = 2(\text{l×w} + \text{w×h} + \text{l×h})\ \text{sq units}
  1. Substitute the values for length, width and height - say 10, 7, and 8 cm, respectively. Then solve the equation
s=2((10×7)+(7×8)+(10×8)) cm2\small s = 2((10 × 7) + (7 × 8) + (10 × 8))\text{ cm}^2
  1. Then solve the equation:
s=2((10×7)+(7×8)+(10×8)) cm2=2((70)+(56)+(80)) cm2=2(206) cm2=412 cm2\small \begin{align*} s &= 2((10 × 7) + (7 × 8) + (10 × 8))\text{ cm}^2\\[.5em] &= 2((70) + (56) + (80))\text{ cm}^2\\[.5em] &= 2(206)\text{ cm}^2\\[.5em] &= 412\text{ cm}^2 \end{align*}

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How do I find the length of a cuboid from it's surface area?

Let's assume that the surface area, height, and width are 288, 4, and 6 cm, respectively. Here is what we do:

  1. Use the surface area formula:
    s = 2(l×w + w×h + l×h) sq units.
  2. Make l the subject of the formula:
    l = (s/2 - wh)/(w+h) units.
  3. Substitute the values:
    = (288/2 - 6 × 4)/(4+6) cm.
  4. Solve
    =( (144 - 24) / 10) cm.
    =120/10 cm.
    =12 cm.
Adena Benn
image of a rectangular prism, with length, height, width and diagonal marked
Length (l)
Width (w)
Height (h)
Surface area (s)
Diagonal (d)
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