| Cubic decimeters (dm³) | Liters (L) |
|---|---|
| 1 Cubic decimeter | 1 L |
| 2 Cubic decimeters | 2 L |
| 3 Cubic decimeters | 3 L |
| 4 Cubic decimeters | 4 L |
| 5 Cubic decimeters | 5 L |
| 10 Cubic decimeters | 10 L |
| 20 Cubic decimeters | 20 L |
| 25 Cubic decimeters | 25 L |
| 50 Cubic decimeters | 50 L |
| 100 Cubic decimeters | 100 L |
| Reference | Cubic decimeters (dm³) | Liters (L) |
|---|---|---|
| A teaspoon | 0.005 dm³ | 0.005 L |
| A can of soft drink | 0.33 dm³ | 0.33 L |
| A wine bottle | 0.75 dm³ | 0.75 L |
| A bathtub | 150 dm³ | 150 L |
| An Olympic swimming pool | 2500000 dm³ | 2500000 L |
The cubic decimetre is a unit of volume equal to one thousandth of a cubic metre, written dm³. It is the volume of a cube ten centimetres on each side, and since 1964 it has been the exact definition of the litre. The two are the same quantity, and the choice between them is the clearest example in the whole metric system of a name being chosen for what it does to a calculation.
Chemistry prefers the cubic decimetre for a specific reason. Concentration is written in moles per cubic decimetre, and every other quantity in the same calculation is expressed in metres, kilograms and seconds or their prefixed forms. Keeping volume as a length cubed means the units in an equation cancel by inspection, without anyone having to remember that a litre is a thousandth of a cubic metre.
That is why British and Commonwealth chemistry teaching writes mol dm⁻³ where American teaching writes molar. A one molar solution and a one mole per cubic decimetre solution are identical, but only the second form makes the dimensions visible. Students trained on it can check an answer by looking at the units, which is the most reliable error-catching habit in quantitative chemistry.
Gas volumes follow the same convention. One mole of an ideal gas occupies 22.4 cubic decimetres at zero degrees Celsius and one atmosphere, and about 24.0 cubic decimetres at room temperature, so a reaction stoichiometry converts to a measurable volume in one step. These are among the most quoted numbers in school chemistry, and they are almost always written in dm³ rather than in litres.
Elsewhere the litre wins easily. Nobody buys fuel, milk or paint in cubic decimetres, and no drink label carries the symbol, because the litre name is shorter, older and understood by everyone. The cubic decimetre survives where a formula rather than a customer is reading the number.
The relationship to its neighbours is worth keeping straight because of the cubing. A cubic decimetre holds a thousand cubic centimetres, not a hundred, and a thousand cubic decimetres make a cubic metre. Each step in length is a factor of ten and each step in volume a factor of a thousand, which is the source of most errors made with this unit.
One cubic decimetre equals 1 litre, 1000 cubic centimetres, 0.001 cubic metres, or about 61.02 cubic inches.
The litre is a unit of volume equal to one thousandth of a cubic metre, or exactly one cubic decimetre. Its symbol is L, and the lower-case l is also permitted. It is not part of the International System of Units, but it is accepted for use alongside it, and it is almost certainly the most widely used volume unit in the world.
It was created by the French metric law of 1795 as the volume of a cube one tenth of a metre on a side. In 1901 it was redefined as the volume occupied by one kilogram of pure water at its densest, which sounds equivalent but is not: the water definition made a litre 1.000028 cubic decimetres, and for sixty-three years precise volumetric work had to state which litre was meant. The 1964 General Conference on Weights and Measures restored the cubic decimetre and the discrepancy vanished.
The symbol has its own small history. The lower-case l is easily mistaken for the digit one in many typefaces, a genuine hazard on a medicine label or a laboratory record, so in 1979 the capital L was approved as an alternative. Both are correct, and usage splits by country rather than by discipline, with North America favouring L and much of Europe still writing l.
Its everyday reach is enormous. Fuel, milk, paint, soft drinks and engine displacement are all measured in litres, fuel consumption in most of the world is stated as litres per hundred kilometres, and cooking outside the United States works in litres and millilitres. Medicine uses it for blood volume, roughly five litres in an adult, and for lung capacity, around six.
One relationship makes it exceptionally useful. A litre of water has a mass very close to one kilogram, because the kilogram was originally defined that way, so volume and mass can be swapped in the head for most practical purposes. Rainfall follows the same logic: one millimetre of rain on one square metre is exactly one litre of water.
Against imperial and United States measures it converts untidily, which is why drink sizes differ so visibly between markets. One litre is 1.76 imperial pints but 2.11 United States liquid pints, and 0.22 imperial gallons but 0.264 United States gallons, so a gallon means two noticeably different quantities depending on where the label was printed.
One litre equals 1000 millilitres, 0.001 cubic metres, about 0.264 US gallons, or about 0.22 imperial gallons.