Free Cuboid Calculator

This cuboid calculator offers a straightforward way to obtain three essential properties of a rectangular prism: volume, surface area, and space diagonal. Often referred to as a cuboid volume calculator, box volume calculator, or rectangular prism calculator, it streamlines geometry tasks by reducing manual calculation overhead.

What Is a Cuboid?

A cuboid is a 3D geometric solid bounded by six rectangular faces. Each adjacent pair of faces meets at a right angle, and the three dimensions—length, width, and height—are usually distinct from one another. The shape has eight vertices and twelve edges.

How to Use the Calculator

To use this cuboid surface area and volume tool, input the values for length ($l$), width ($w$), and height ($h$). The tool then instantly computes the volume, total surface area, and the length of the space diagonal, presenting all results in real time.

Volume Calculation

The volume of a cuboid is the product of its three dimensions:

$$\text{Volume} = l \times w \times h$$

For instance, with $l = 12\,\text{cm}$, $w = 9\,\text{cm}$, and $h = 10\,\text{cm}$,

$$\text{Volume} = 12 \times 9 \times 10 = 1080\,\text{cm}^{3}$$

Surface Area Calculation

The total surface area equals the sum of the areas of all six faces. The formula is:

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

As an example, take a cuboid with $l = 8\,\text{cm}$, $w = 7\,\text{cm}$, and $h = 6\,\text{cm}$:

$$\begin{aligned} \text{Surface Area} &= 2(8 \times 7 + 7 \times 6 + 8 \times 6) \\ &= 2(56 + 42 + 48) \\ &= 2 \times 146 = 292\,\text{cm}^{2} \end{aligned}$$

Diagonal Length

The space diagonal (the longest line connecting opposite vertices) is obtained from the 3D version of the Pythagorean theorem:

$$\text{Diagonal} = \sqrt{l^{2} + w^{2} + h^{2}}$$

This value is also displayed by the cuboid diagonal calculator feature of the tool.

Whether you need a box volume calculator for shipping dimensions or a scale model project, this tool delivers quick and accurate figures.