Volume of a Rectangular Prism — Formula & Examples

To find the volume of a rectangular prism, multiply its length, width, and height:

$$V = lwh$$

This works when $l$, $w$, and $h$ are perpendicular side lengths of the same prism and all measurements use the same unit. A rectangular prism is also called a cuboid, so both names refer to the same formula.

Why $V = lwh$ Works For A Rectangular Prism

A rectangular prism is a box-shaped solid with rectangular faces. You can picture it as identical rectangular layers stacked from bottom to top.

The area of the base is

$$l \cdot w$$

If that same base extends through height $h$, the volume is

$$V = (l \cdot w)h = lwh$$

So the main idea is simple: volume equals base area times height. For a rectangular prism, the base is a rectangle, so the base area is easy to find.

Worked Example: $8$ cm By $5$ cm By $3$ cm

Suppose a rectangular prism has length $8$ cm, width $5$ cm, and height $3$ cm. Find its volume.

Use the formula:

$$V = lwh$$

Substitute the values:

$$V = 8 \cdot 5 \cdot 3$$

Multiply:

$$V = 120$$

So the volume is

$$V = 120 \text{ cm}^3$$

The answer uses cubic centimeters, not centimeters, because volume measures three-dimensional space.

Common Mistakes With Rectangular Prism Volume

1. Mixing units. If one side is in meters and another is in centimeters, convert first before multiplying.
2. Writing square units instead of cubic units. Volume should use units such as $\text{cm}^3$ or $\text{m}^3$.
3. Confusing volume with surface area. Volume measures space inside the prism, while surface area measures the total area of the outside faces.
4. Using the formula on the wrong dimensions. The formula needs the prism's perpendicular length, width, and height.

When To Use This Formula

Use this formula when an object can be modeled as a rectangular prism, such as a shipping box, aquarium, storage bin, or room.

If the real object is only approximately box-shaped, the result is also an approximation. The formula is still useful when you need a quick capacity estimate.

Try A Similar Problem

Try a prism with length $12$ cm, width $4$ cm, and height $7$ cm. Multiply the three side lengths, then check whether your final unit is cubic.

Then change just one dimension, such as the height from $7$ cm to $14$ cm, and compare the new volume. That is a quick way to see how volume changes when one side changes and the others stay fixed.