Volume of a Cuboid

Calculates the volume of a cuboid as depth × width × height.

Explanation

A cuboid is a solid with six rectangular faces, the shape of an ordinary box. Its three edge lengths determine the volume.

V = a b c

$V$ — the volume
$a$ — the depth
$b$ — the width
$c$ — the height

Example

With the defaults, a depth of $a = 4$ , a width of $b = 5$ and a height of $c = 6$ :

V = 4 \times 5 \times 6 = 120

The volume is 120. If the edges are in centimetres, the volume is in cubic centimetres.

Why the three edges multiply

The base is a 4 by 5 rectangle, so its area is 20. Stacking that base up through a height of 6 gives $20 \times 6 = 120$ . The same reasoning covers any prism or cylinder: volume equals base area times height, and the cuboid is simply the case where the base is a rectangle.

Watch out

All three lengths must be in the same unit; mixing centimetres and metres produces a meaningless answer. Volume scales with the cube of the length, so doubling every edge makes the volume eight times larger. When all three edges are equal the cuboid is a cube, and $V = a^3$ .