Leo+DadMade for Leo
Choosing & Converting Units
Rung 3 of 3 · The traps

One Metre Cube Is a million Little Cubes

The conversion that catches almost everyone: 1 m³ is not 100 cm³, and not 10 000 either. When you cube the length, you cube the factor.


ExploreTap the factor you think is right, then hit “show why it's a million”.
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You know 1 m = 100 cm. So it's tempting to write 1 m³ = 100 cm³. It feels right, and it's wildly wrong — out by a factor of ten thousand. Here's why the brain trips, and how to never trip again.

Why It's a Million, Not a Hundred

A cube has three directions. To go from a metre-cube to centimetre-cubes you swap the unit on every edge: 100 cm across, 100 cm deep, 100 cm tall. So the count is 100 × 100 × 100 = 1 000 000. The length factor (100) got cubed along with the shape. That's why 1 m³ = 1 000 000 cm³.

Say it plainly: cube the length → cube the factor. (× 100)³ = × 1 000 000. The little ³ tells you to multiply the factor by itself three times.

The Same Trap, Smaller, with Area

It bites in 2-D too. 1 m² = 10 000 cm² (that's 100², not 100). So three factors live side by side: length × 100, area × 100² = 10 000, volume × 100³ = 1 000 000. In the toy, tap each one — only the cubed factor is right for a volume. Count the little number on the unit (², ³) and let it tell you the power.

Volume Is Not Capacity

One more wording trap. Volume is how much space a solid takes up, in cm³ or m³. Capacity is how much a container can hold, in mL, L or kL. They're joined by 1 cm³ = 1 mL and 1 m³ = 1000 L, so the same box has both — but a question asking for "capacity" wants litres, and one asking for "volume" usually wants cubic units. Read which word they used.

Us, Thinking Out Loud

Why does cubing the shape mean you cube the conversion factor too?

Give me a question where they ask for capacity and one where they ask for volume — what changes?