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Can anyone explain why $1\ \mathrm{m}^3$ is $1000$ liters?

I just don't get it.

1 cubic meter is $1\times 1\times1$ meter. A cube. It has units $\mathrm{m}^3$.

A liter is liquid amount measurement. 1 liter of milk, 1 liter of water, etc.

Does that mean if I pump $1000$ liters of water they would take exactly $1$ cubic meter of space?

I can't wrap my head around.

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3 Answers

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1 liter is, by definition, 1 cubic decimeter, where 1 decimeter is 1/10 meter.

So $1000\,\mathrm{l} = 1000\,\mathrm{dm^3} = 1000\,(1/10\,\mathrm{m})^3 = 1000/10^3\,\mathrm{m^3} = 1\,\mathrm{m^3}$.

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Originally:

• the metre was defined as 1/10,000,000th of the distance from the North pole to the equator at sea level;
• the litre was defined as 1/1,000th of a cubic metre;
• the kilogram was defined as the mass of a litre of water at freezing point.

Nowadays we have more precise standards, which don't rely on the density of water. But these relations are still very accurate.

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Density = weight per unit volume (water density = 1 Gram per 1 Cubic centimeter)

i.e Density X 1 Centimeter cube = 1 Gram of water

 1 X 1 cc = 1 Gram 1 x 1 cc X 1000 = 1 Gram X 1000 1000 cc = 1000 Gram = 1000 Milli liter = 1 Liter 1000 cc x 1000 = 1 Liter x 1000 1 Cubic meter = 1000 Liter 

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