Key takeaways
- The volume of a rectangular prism is V = l × w × h.
- Multiplying only two dimensions gives you a face's area, not the volume.
- Volume is always in cubic units, like m³ or ft³.
- Very differently shaped boxes can hold exactly the same volume.
In this guide
What is a rectangular prism?
A rectangular prism is a 3D box shape with six rectangular faces, like a shoebox or a brick. Unlike a cube, its length, width, and height can all be different.
Why does the volume of a rectangular prism matter?
Volume tells you exactly how much a shipping box, drawer, or tank can hold — and shapes that look very different can still hold the same amount.
A container that is 5 m × 4 m × 3 m holds 60 m³. A much longer, narrower container at 2 m × 3 m × 10 m holds exactly the same 60 m³, even though the two boxes look nothing alike.
The formula
| Symbol | What it means | Example |
|---|---|---|
| V | The volume you want to find | 60 m³ |
| l | The length of the box | 5 m |
| w | The width of the box | 4 m |
| h | The height of the box | 3 m |
How to find the volume step by step
- 1Measure the length. The longest horizontal edge.
- 2Measure the width. The shorter horizontal edge.
- 3Measure the height. The vertical edge.
- 4Multiply all three together.
l × w × h. - 5Add cubic units. Such as cm³ or ft³.
Now try it yourself. Change the length, width, and height in the calculator below and watch the volume update, with every step shown.
Try it yourself
Pre-filled with the example — change any value.
Common mistakes to avoid
- Mixing units. Convert all three measurements to the same unit before multiplying.
- Forgetting cubic units. Volume is always in units³, such as m³ or ft³, never plain or squared units.
- Assuming volume tells you about shape. Two boxes with the same volume can have very different dimensions and won't necessarily fit in the same space.
Tips and tricks
- To convert cubic centimeters to liters, divide by 1000, since 1 liter equals 1000 cm³.
- If all three sides are equal, you have a cube, so
s³works too.
Where you'll use it in real life
- Shipping: working out how much a moving box or crate can hold.
- Furniture: checking the capacity of a drawer or storage bin.
- Aquariums: calculating how much water a rectangular fish tank holds.
- Construction: estimating concrete needed for a rectangular slab or footing.
Quick summary
To find the volume of a rectangular prism, multiply the length, width, and height together, and label the answer in cubic units. Remember that different-shaped boxes can still hold the same volume. Use the calculator above to check your own box instantly.
Worked example
You're loading a storage container that is 5 meters long, 4 meters wide, and 3 meters tall. How much space is inside the container?
- 01V = l × w × h
- 02V = 5 × 4 × 3
- 03V = 60 m³
These numbers are pre-filled in the calculator above.
Frequently asked questions
How do I find the volume of a box if it isn't a perfect rectangle?
This formula only works for rectangular (box-shaped) prisms. For other shapes like cylinders or cones, use their own volume formulas instead.
What's the difference between a rectangular prism and a cube?
A cube is a special rectangular prism where the length, width, and height are all equal, so its volume simplifies to [s³](/calculator/volume-cube).
How do I find volume in liters instead of cubic units?
Calculate the volume in cubic centimeters (cm³) first, then divide by 1000, since 1 liter equals 1000 cm³.
Does the order I multiply length, width, and height matter?
No. Multiplication gives the same result regardless of order, so l × w × h always equals the same volume no matter which dimension you multiply first.
