Volume Of Box Calculator

What this calculator does

A box is a rectangular container, and its volume is how much it holds. This works it out from the three measurements that describe the box: its length, its width, and its height.

Type the three in, pick a unit, and you have the space inside: a shipping carton, a storage bin, a drawer, a fish tank.

Using the calculator

1. Type the length, the width, and the height.
2. Pick the unit they are measured in.
3. Press Calculate.

All three values have to be positive. They share one unit here, and the volume comes back in cubic units of that unit.

The formula | volume = length × width × height

The volume of a box is:

volume = length × width × height

Multiply the three dimensions together. A nice way to picture it: work out the floor of the box first, its length × width, then stack that floor up layer by layer to the full height. Filling the bottom and raising it to the top is what the three numbers multiplied are really doing.

What it is good for

This is the everyday capacity question. How much a shipping box holds, whether a parcel comes in under a courier's size limit, how much compost fills a planter, how much water a tank takes. The answer is the space inside, in cubic units, and from there you can turn it into litres or gallons if you need a capacity you can pour.

Cubic units, litres, and keeping units matched

Because you multiply three lengths, the volume comes out in cubic units, matched to the unit you picked: a box measured in centimetres gives a volume in cubic centimetres, cm³. The one rule to respect is that all three measurements must be in the same unit before multiplying, which the single unit setting here keeps true for you.

For capacity, the handy bridge is that 1 litre is 1,000 cm³ (a cube 10 cm on each side). So a volume in cubic centimetres divided by 1,000 gives litres.

A worked example | a 30 by 20 by 15 cm box

Say the box is 30 cm long, 20 cm wide and 15 cm tall.

1. Floor area first: 30 × 20 = 600.
2. Raise it to the height: 600 × 15 = 9,000.

So the volume is 9,000 cm³. Divide by 1,000 and that is 9 litres of space inside.

A box is a rectangular prism

"Box" is the everyday word for the shape geometry calls a rectangular prism, or a cuboid. They are the same thing, so the formula is identical. If all the sides happen to be equal, it is a cube. For the more formal treatment of the shape, see the rectangular prism calculator, and for the equal-sided case, the volume of a cube calculator.

Questions people ask

What is the volume of a 30 by 20 by 15 box?

It is 9,000 cm³, which is 9 litres. Multiply length, width and height: 30 × 20 × 15.

How do I turn the volume into litres?

If the volume is in cubic centimetres, divide by 1,000, since 1 litre is 1,000 cm³.

Do the three measurements have to be in the same unit?

Yes. They all need to be in one unit before multiplying. The single unit setting here keeps them matched.

What if it is a cube?

Then all three sides are equal, and the volume is edge × edge × edge. The volume of a cube calculator does that from one number.

Is a box the same as a rectangular prism?

Yes. "Box", "rectangular prism" and "cuboid" all describe the same shape, with the same length × width × height volume.

References

A note on the capacity side of this. The link between volume and the litre is fixed by definition: one litre is exactly one cubic decimetre, the volume of a cube 10 cm on each side, which is 1,000 cubic centimetres. That is what lets a box measured in centimetres be read off as litres. For further reading, see Cuboid.

1. The litre, defined as one cubic decimetre, equal to 1,000 cubic centimetres, the volume of a cube 10 cm on each side.