Volume is just how many cubes fit inside.

Meet the cubic centimetre.

To measure anything you need a unit — a standard chunk you count up. For length we use the centimetre (cm): a little line, 1 cm long. To measure volume we need a unit that takes up space, so we use a tiny cube that is 1 cm long, 1 cm wide and 1 cm tall. That little block is called a cubic centimetre, and we write it as cm³ — "centimetre, cubed."

Think of cm³ as the LEGO brick of space. Every solid shape can be imagined as a pile of these identical bricks, and the volume is simply how many of them it would take to build it. A volume of 24 cm³ means "this shape is the same size as 24 little 1 cm cubes packed together." A volume of 1000 cm³ means a thousand of them. Big shapes get bigger cubes — a swimming pool is measured in cubic metres (m³), where each brick is a cube 1 metre on every side — but the idea never changes: pick a cube, then count how many fit.

Pack a box with unit cubes.

Drag the three sliders to set the box's length, width and height — each one in centimetres. The box fills itself with 1 cm cubes and the count updates live. Hit Pack it to watch it fill layer by layer, bottom-up, so you can see the base layer repeating.

Watch what happens as you raise the height slider: the box doesn't fill randomly, it stacks one whole layer at a time. Every layer is an exact copy of the bottom one — same length, same width, same number of cubes. That bottom layer (shown in warm orange) is the key to everything that comes next.

It's one layer, stacked up.

Look closely at a single layer of the box — the flat bottom slice, one cube thick. It's a rectangle of cubes: length cubes across, width cubes deep. To count them you don't go one-by-one; you do length × width. For a box that's 3 long and 4 wide, the bottom layer holds 3 × 4 = 12 cubes. That number — the cubes in one flat layer — is the same as the area of the box's base, which is why we call it the base area.

Now stack that layer up. A box 2 cubes tall is just the base layer copied twice: 12 + 12 = 24 cubes. A box 5 tall is the base layer copied five times. So instead of adding the layers, you can multiply: base area × height. That's it — that's where the cuboid formula comes from:

Volume = length × width × height

It's three numbers multiplied because you're doing two things at once: length × width fills one layer, then × height tells you how many layers to stack. Try a quick one yourself: a box 5 cm long, 3 cm wide and 2 cm tall. The base layer is 5 × 3 = 15 cubes, and there are 2 layers, so the volume is 15 × 2 = 30 cm³. Same as writing 5 × 3 × 2 = 30 cm³ straight off. The order you multiply in doesn't matter — 5 × 3 × 2, 2 × 5 × 3 and 3 × 2 × 5 all give 30 — so you can start with whichever pair is easiest.

Base area × height works for prisms too.

Here's the lovely part. The cuboid's base happens to be a rectangle, but the "stack the base up" idea doesn't care what shape the base is. Any solid that keeps the same cross-section all the way along — like a loaf of bread, a Toblerone, or a hexagonal pencil — is called a prism. And for every prism the rule is the same: volume = base area × height, where "height" just means how far that base is stretched along.

Below is a triangular prism — a triangle stretched along its length. Set the triangle's base and height, then stretch it with the length slider. We work out the triangle's area (½ × base × height), then multiply by the length. Watch the volume climb as the triangle slides further along.

Notice the cuboid was never a special case — it's just a prism whose base is a rectangle. For a rectangle, "base area" is length × width, so base area × height becomes length × width × height, exactly the box formula. One idea, written two ways. Whenever a solid has the same shape running straight through it, find the area of that shape and multiply by how long it runs. (Cones and spheres taper or curve, so they need their own formulas — but every honest prism obeys this one.)

How much water fits in a fish tank?

Say you've got a rectangular fish tank that's 30 cm long, 20 cm wide and 25 cm tall, and you want to know how much water it holds. It's a cuboid, so reach straight for the rule.

Start with the base layer — the footprint on the table: 30 × 20 = 600 cm². That's how many 1 cm cubes cover the bottom in a single layer. Now stack that layer 25 high: 600 × 25 = 15 000 cm³. So the tank's volume is 15,000 cm³ — fifteen thousand little 1 cm cubes of water would fill it exactly.

Fifteen thousand cubes is hard to picture, which is why the next idea is so handy. A cubic centimetre of space holds exactly one millilitre (ml) of liquid — the two are the same size, just one word for space and one for liquid. So 15,000 cm³ holds 15,000 ml, and since 1000 ml make 1 litre, that's 15 litres of water. Suddenly the number means something: about fifteen large drink bottles. That bridge — 1 cm³ holds 1 ml — is how volume turns into the capacity printed on bottles and cartons.

Why the little 3? cm³ vs cm².

Those tiny raised numbers are not decoration — they tell you how many measurements got multiplied together, and getting them right is half of doing volume well.

So the exponent counts the measurements: cm² = two lengths multiplied = a flat area; cm³ = three lengths multiplied = a solid volume. If you ever write a volume as cm² you've quietly said the box is flat as paper — a dead giveaway that something went wrong. Quick rule of thumb to self-check: area answers end in ², volume answers end in ³. Match the little number to how many lengths you multiplied, and your units will always be honest.

Two mistakes almost everyone makes once.

Both traps vanish the moment you go back to the cubes. Volume is a count of little cubes, you reach that count by multiplying, and the answer is measured in cubes — cm³. Keep that picture and the mistakes have nowhere to hide.

Three quick questions.

Tap an answer to check it. Watch out for the number-that's-right-but-the-unit's-wrong, and the sneaky "added the edges" option.