| Cubic decimeters (dm³) | Gallons (gal) |
|---|---|
| 1 Cubic decimeter | 0.219969248299 gal |
| 2 Cubic decimeters | 0.439938496598 gal |
| 3 Cubic decimeters | 0.659907744897 gal |
| 4 Cubic decimeters | 0.879876993196 gal |
| 5 Cubic decimeters | 1.0998462415 gal |
| 10 Cubic decimeters | 2.19969248299 gal |
| 20 Cubic decimeters | 4.39938496598 gal |
| 25 Cubic decimeters | 5.49923120748 gal |
| 50 Cubic decimeters | 10.998462415 gal |
| 100 Cubic decimeters | 21.9969248299 gal |
| Reference | Cubic decimeters (dm³) | Gallons (gal) |
|---|---|---|
| A teaspoon | 0.005 dm³ | 0.00109985 gal |
| A can of soft drink | 0.33 dm³ | 0.0725899 gal |
| A wine bottle | 0.75 dm³ | 0.164977 gal |
| A bathtub | 150 dm³ | 32.9954 gal |
| An Olympic swimming pool | 2500000 dm³ | 549923 gal |
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 gallon in the imperial system is a unit of volume equal to exactly 4.54609 litres. Its symbol is gal. It contains four quarts, eight pints and 160 imperial fluid ounces, and it is about a fifth larger than the United States gallon, a difference that causes more confusion than any other single discrepancy between the two systems.
Its original definition was elegant. The Weights and Measures Act of 1824 fixed the imperial gallon as the volume occupied by ten pounds of distilled water at sixty-two degrees Fahrenheit under a barometric pressure of thirty inches of mercury. That tied liquid measure directly to the avoirdupois pound, so a gallon of water weighed ten pounds and a pint weighed a pound and a quarter. In 1985 the definition was replaced by the exact metric figure, but the old relationship still holds to within a fraction of a per cent.
Fuel economy keeps it in daily use. British and Irish drivers describe consumption in miles per gallon even though fuel has been sold in litres since the 1990s, and the figure is an imperial one. The same car scores about twenty per cent higher in British miles per gallon than in American, purely because the gallon is larger, which is why cross-Atlantic comparisons of efficiency are meaningless unless the gallon is specified.
Legal use in Britain is now narrow but real. Draught beer and cider must be sold in pints, half pints or third pints, and milk in returnable containers may be sold in pints, which keeps the whole imperial chain alive by keeping its smallest working member alive. Several Caribbean territories still sell motor fuel by the imperial gallon.
The difference from the American gallon is worth stating plainly. One imperial gallon is 4.546 litres and one United States gallon is 3.785, so an imperial gallon is 1.2 United States gallons. Recipes, fuel figures, tank capacities and chemical dilutions all break if the wrong one is assumed, and the error is large enough to matter but small enough to look plausible.
Below it the chain runs quart, pint, gill and fluid ounce, each a quarter or a fifth of the one above rather than a decimal step. That structure was designed for dividing a container by halving it repeatedly, which is a practical merit when pouring and a serious nuisance when calculating.
One imperial gallon equals 4.54609 litres, 8 imperial pints, 160 imperial fluid ounces, or about 1.201 US gallons.