| Cubic decimeters (dm³) | Teraliters (TL) |
|---|---|
| 1 Cubic decimeter | 1 × 10-12 TL |
| 2 Cubic decimeters | 2 × 10-12 TL |
| 3 Cubic decimeters | 3 × 10-12 TL |
| 4 Cubic decimeters | 4 × 10-12 TL |
| 5 Cubic decimeters | 5 × 10-12 TL |
| 10 Cubic decimeters | 1 × 10-11 TL |
| 20 Cubic decimeters | 2 × 10-11 TL |
| 25 Cubic decimeters | 2.5 × 10-11 TL |
| 50 Cubic decimeters | 5 × 10-11 TL |
| 100 Cubic decimeters | 1 × 10-10 TL |
| Reference | Cubic decimeters (dm³) | Teraliters (TL) |
|---|---|---|
| A teaspoon | 0.005 dm³ | 5 × 10-15 TL |
| A can of soft drink | 0.33 dm³ | 3.3 × 10-13 TL |
| A wine bottle | 0.75 dm³ | 7.5 × 10-13 TL |
| A bathtub | 150 dm³ | 1.5 × 10-10 TL |
| An Olympic swimming pool | 2500000 dm³ | 0.0000025 TL |
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 teralitre is a unit of volume equal to a thousand gigalitres, or 1,000,000,000,000 litres. Its symbol is TL. It is exactly one cubic kilometre, and that is how the quantity is almost always written, because at this scale what is being measured is no longer a container but a piece of the planet.
Lakes are the obvious application. Lake Baikal holds about 23,600 cubic kilometres of fresh water, more than any other lake on earth, and Lake Superior about 12,100. Those two figures alone amount to a fifth of the world's unfrozen surface fresh water, which is the kind of statement the unit exists to make.
Rivers are described by the volume they move rather than by what they hold. The Amazon discharges roughly 6600 cubic kilometres a year into the Atlantic, more than the next several rivers combined, and total human withdrawal of fresh water from all sources runs to about 4000 cubic kilometres a year. Setting those two numbers side by side in the same unit is one of the clearest ways to state the scale of water use.
Ice is measured here too, and the numbers are larger again. The Greenland ice sheet contains close to 2.9 million cubic kilometres, and in recent decades it has been losing a few hundred each year, a figure that converts directly into millimetres of sea level because the ocean's surface area is known. The Antarctic sheet is an order of magnitude larger still.
The ocean itself sets the ceiling. All the seawater on earth amounts to about 1.335 billion cubic kilometres, so a single teralitre is roughly one billionth of it. Below the ocean, the largest managed water bodies are engineered reservoirs, and even the biggest of those hold only a few tens of cubic kilometres.
In practice the name teralitre is rare and the cubic kilometre is standard. Hydrology, glaciology and climate science all use km³, and a figure given in teralitres is more likely to come from a water utility extending its own gigalitre scale upward than from a scientific source. The two are identical, so no conversion is needed, only recognition.
One teralitre equals 1,000,000,000,000 litres, 1,000,000,000 cubic metres, 1 cubic kilometre, or 1000 gigalitres.