Why is 1 cubic meter 1000 liters?

Question

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.

Liters measure volume, just like cubic meters do. And yes, 1000 liters would take up the same volume as 1 cubic meter. — Regret, Mar 07 '15 at 13:10
so is unit of measurement for liters [m^3]? 1 liter is 1/1000 of a cubic meter? — bodacydo, Mar 07 '15 at 13:11
The liter is itself a unit of measurement, and $1000~ \mathrm l = 1~\mathrm m^3$. — Regret, Mar 07 '15 at 13:13
But who invented that 1000l = 1m^3? Is it arbitrary definition? Where does this definition come from? — bodacydo, Mar 07 '15 at 13:14
$1$ m is a reasonable standard of length, compared to the size of a man. $1>{\rm m}^3$ is much more than a man can drink, therefore one had to invent a more handy unit for everyday use, but still coupled to the metric system. $1$ Liter serves this purpose well. — Christian Blatter, Mar 07 '15 at 13:46
Seems to me that the Wikipedia article touches far too lightly on the history. The point is, roughly, that the revolutionaries, in a desire to make a completely reasonable system, based everything on the meter, which was to be (I think) $10^{-7}$ of the distance from the pole to the equator. From that all was to follow. Litre is, as many have said, a cubic decimeter, so the relation between litres and meters follows directly from that. — Lubin, Mar 07 '15 at 14:40

score 4 · Accepted Answer · answered Mar 07 '15 at 13:14

4

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

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

answered Mar 07 '15 at 13:14

celtschk

43,384

Thanks. Do you know how people came to define this? – bodacydo Mar 07 '15 at 13:15
Because it's convenient? – celtschk Mar 07 '15 at 13:15
1

What came first? Liter or cubic decimeter? – bodacydo Mar 07 '15 at 13:15
@bodacydo: You should check out this link: http://en.wikipedia.org/wiki/Litre#Definition – Regret Mar 07 '15 at 13:16
Another way to look at it is 1 meter = 10 liters, so $1\times 1\times 1$ (cubic meter) is equal to $10 \times 10\times 10 = 1000$ cubic liters. – amWhy Mar 07 '15 at 13:18
5

1 meter can't be 10 liters because units don't match. 1 meter is [m], 10 liters is [m^3] – bodacydo Mar 07 '15 at 13:18

score 1 · Answer 2 · answered Mar 07 '15 at 14:49

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.

score 0 · Answer 3 · edited Jan 12 '18 at 01:47

0

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

edited Jan 12 '18 at 01:47

Shailesh

3,789

answered Dec 28 '17 at 14:59

C V V Kumar

1

Why is 1 cubic meter 1000 liters?

3 Answers3