Units of volume

A litre is a cube

A litre of milk, a litre of lemonade, a two-litre bottle. You know litres from the shop. But did you know that a litre is actually a cube?

1 litre = 1 dm³ — a cube with edge 1 decimetre (10 cm). Picture a cube that a milk carton fits into exactly. That is a litre.

And from there everything else unfolds. How many cm³ are in a litre? A cube 10 × 10 × 10 cm = 1 000 cm³. That is why a millilitre (a thousandth of a litre) = exactly 1 cm³ — a sugar cube is about a millilitre.

See the pattern? With length units jump by 10, with area by 100 (10 × 10) and with volume by 1 000 (10 × 10 × 10). A length conversion is counted three times — once for each dimension.

Today you will join two worlds: cubic units from geometry (cm³, dm³, m³) and “kitchen” units from the shop (ml, l, hl). They are one and the same volumes, just two families of names.

Filip fills a new tank. In the instructions it says: “Volume 54 litres.” Filip does not believe it: “How can they know? It is just a glass box.” “Measure it,” Tereza advises. Filip measures: 60 × 30 × 30 cm. He multiplies: 54 000 cm³. “And now divide by a thousand — a litre is a thousand cubic centimetres.” 54 comes out. “Exactly like in the instructions!” Filip carries water in a nine-litre watering can: six times and it is there. Cubic centimetres from a ruler and litres from the shop — one and the same, divided by a thousand.

Two families of units and a bridge between them

The cubic family (from geometry), jumps of 1 000:

• 1 cm³ = 1 000 mm³
• 1 dm³ = 1 000 cm³
• 1 m³ = 1 000 dm³ = 1 000 000 cm³

Why a thousand? A decimetre has 10 cm and a cube is 10 × 10 × 10 = 1 000. A length conversion three times.

The litre family (from the shop), jumps of 10 and 100:

• 1 l = 1 000 ml (milli = a thousandth)
• 1 hl (hectolitre) = 100 l (barrels, pools, water use)

The bridge between the families:

Conversion method: work out the volume in cubic units (the formula from last time), then cross the bridge: cm³ : 1 000 = litres. Or the other way: litres × 1 000 = cm³.

A sense check as always: a bath is around 150 l, a bucket 10 l, a mug a quarter of a litre (250 ml). If for a mug you get 25 litres, the point fell.

How many litres does a box 20 × 15 × 10 cm have?

Volume: V = 20 × 15 × 10 = 3 000 cm³.

Bridge: cm³ to litres is divided by 1 000: 3 000 : 1 000 = 3 litres.

A sense check: a shoebox, three milk cartons fit in — two on the bottom next to each other, one across? About right.

The whole chain in one breath: sizes → cm³ → : 1 000 → litres. You will use this chain all the time.

Convert 2.5 l to ml and to cm³

To millilitres: 1 l = 1 000 ml, so 2.5 × 1 000 = 2 500 ml. (The point three places to the right — like multiplying by a thousand from lesson five.)

To cm³: a millilitre = cm³, so straight 2 500 cm³. No more counting — ml and cm³ are twins.

Practice: a big lemonade bottle (2.5 l) fills 2 500 sugar cubes. Pour it into a measuring jug and you will see 2 500 on the ml scale.

A garden pool in m³ and hectolitres

An inflatable pool: bottom 3 × 2 m, water to a height of 0.5 m.

Volume: V = 3 × 2 × 0.5 = 3 m³.

To litres: 1 m³ = 1 000 l, so 3 × 1 000 = 3 000 litres.

To hectolitres: 3 000 : 100 = 30 hl.

For a picture: 3 000 litres is 300 buckets of ten litres, or twenty filled baths. That is why a pool is not filled with a watering can — and why water companies count use in m³.

Practice: now you do it 🎲

Now try it for real. You will see all the questions at once, like on paper. 开始 with ten. When it goes well, add more.

Practise conversions from Times-table kid — kilograms, tonnes and especially litres to millilitres. Jumps of a thousand, the same as today. The answer is a number.

Practise the questions

On paper

The best helper is a measuring jug in the kitchen — borrow it.

1. Convert: 4 l to ml, 7 000 cm³ to litres, 2 m³ to litres, 350 ml to cm³.

2. Measure (or estimate) the mug you drink tea from: how many ml does it have? Check with a measuring jug or the figure on the bottom. How many mugs is a litre?

3. A juice carton has sizes 6 × 9.5 × 19.5 cm. Work out the volume in cm³ and decide: is it a litre, or a litre and a half? (Round with sense — the walls have thickness.)

4. A bath holds 150 l. How many dm³ is that? And how many m³? How many times would you fill it with a ten-litre bucket?

Now you 💪

1. I can say by heart: 1 l = 1 dm³ = 1 000 cm³ = 1 000 ml.
2. I can convert cm³ to litres (divided by 1 000) and back.
3. I know why volume jumps by a thousand, while length jumps by ten — three dimensions.

What to take from this lesson

• A litre is a cube 10 × 10 × 10 cm: 1 l = 1 dm³ = 1 000 cm³.
• A millilitre = cm³ (a sugar cube). A hectolitre = 100 l. A cubic metre (1 m³) = 1 000 l.
• Volume units jump by 1 000 — a length conversion three times.
• The chain of calculation: sizes → volume in cm³ → : 1 000 → litres.
• Check with a picture: a mug 250 ml, a bucket 10 l, a bath 150 l, a pool thousands of litres.

© 2026 Ing. Martin Polak / AlgoRhino · 内容使用条款