Conversion from 10 Fluid ounces to Cubic decimeters

Information about the Fluid ounce (fl oz)

The fluid ounce in the imperial system is a unit of volume equal to exactly 28.4130625 millilitres. Its symbol is fl oz. Twenty of them make an imperial pint and 160 an imperial gallon. It is the smallest unit of the imperial liquid chain in ordinary use, and its name records exactly what it was built to do.

The name is literal. The Weights and Measures Act of 1824 defined the fluid ounce as the volume occupied by one avoirdupois ounce of water, so a fluid ounce of water weighs an ounce. The modern definition is metric and the agreement is no longer exact, but it is close: a fluid ounce of water weighs 28.4 grams against the ounce's 28.35, a difference of two parts in a thousand.

The United States fluid ounce is a different quantity, and the relationship between the two is the most confusing pair of units in either system. A United States fluid ounce is 29.5735 millilitres, so it is four per cent larger than the imperial one. Yet a United States pint contains only sixteen of them where an imperial pint contains twenty, so the American pint ends up seventeen per cent smaller. The smaller unit belongs to the larger system and the larger unit to the smaller.

That reversal has practical consequences. A recipe calling for eight fluid ounces of milk means 237 millilitres in America and 227 in Britain, which is tolerable, but one calling for a pint means 473 or 568, which is not. Cosmetics, medicines and drinks all carry both figures on internationally sold packaging for exactly this reason.

British labelling now leads with millilitres. Toiletries, spirits and soft drinks are specified in metric units, with fluid ounces printed alongside for markets that expect them, and pharmacy long ago abandoned the fluid ounce and the fluid dram in favour of millilitres. What survives is culinary and conversational rather than legal.

Where an old British recipe uses it, the conversion is straightforward as long as the system is known: multiply by 28.4 for millilitres, and remember that the pint above it holds twenty and not sixteen. Getting the pint right matters more than getting the ounce right, because the error compounds with quantity.

One imperial fluid ounce equals 28.4130625 millilitres, 1/20 of an imperial pint, or about 0.961 US fluid ounces.

Information about the Cubic decimeter (dm³)

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.