Free Cuboid Surface Area Calculator

What Is a Cuboid?

A cuboid is a convex three‑dimensional shape bounded by six rectangular faces. It is also called a rectangular prism. Everyday objects such as a book, a mattress, or a brick are familiar examples. A cuboid has eight vertices, and every vertex forms a 90° angle.

Surface Area Formula (Rectangular Prism Surface Area Formula)

The total surface area of a cuboid is the sum of the areas of all six faces. The standard formula is:

$$\text{Surface Area} = 2(lw + wh + lh)$$

where $l$ is the length, $w$ is the width, and $h$ is the height of the cuboid.

How to Use the Cuboid Surface Area Calculator

This free cuboid area and diagonal calculator online also serves as a rectangular prism surface area calculator. To use it:

1. Enter the length, width, and height into the corresponding fields.
2. The tool instantly displays the total surface area.
3. You may use any consistent unit (cm, in, m, etc.) – the calculator adapts automatically.

Whether you need a quick answer or want to verify manual work, this free online cuboid surface area calculator is the simplest way to find the surface area of a cuboid.

How to Find Surface Area of a Cuboid Manually

If you prefer to calculate without the tool, follow these steps:

1. Measure the length ($l$), width ($w$), and height ($h$) of the cuboid.
2. Apply the rectangular prism surface area formula: $\text{SA} = 2(lw + wh + lh)$.
3. Multiply and add inside the parentheses, then multiply by 2.

Example: For a cuboid with $l = 10$ cm, $w = 7$ cm, and $h = 8$ cm:

$$\begin{aligned} \text{SA} &= 2[(10 \times 7) + (7 \times 8) + (10 \times 8)] \\ &= 2[70 + 56 + 80] \\ &= 2 \times 206 = 412 \text{ cm}^2 \end{aligned}$$

Reverse Calculation: Finding a Missing Dimension

If you already know the total surface area and two of the three dimensions, you can solve for the unknown side. For instance, to find the length when the surface area (SA), width ($w$), and height ($h$) are given:

$$l = \frac{\frac{SA}{2} - wh}{w + h}$$

Example: Suppose $SA = 288$ cm², $w = 6$ cm, $h = 4$ cm. Then

$$l = \frac{\frac{288}{2} - 6 \times 4}{6 + 4} = \frac{144 - 24}{10} = \frac{120}{10} = 12 \text{ cm}.$$

This capability makes the tool not only a surface area calculator but also a full cuboid area and diagonal calculator (the diagonal can be computed from the same dimensions).

Key Features

• Free to use, no registration required.
• Accepts any units – results are in squared units of the input.
• Instant results, suitable for students, designers, and professionals.