Conversion from 3 Cubic feet to Cubic decimeters

Information about the Cubic foot (ft³)

The cubic foot is a unit of volume equal to 1728 cubic inches, or 28.3168 litres. Its symbol is cu ft, sometimes written ft³. It is the volume of a cube one foot on each side, and it is the unit in which the United States measures natural gas, appliance capacity and air flow, three fields with almost nothing else in common.

Natural gas is its largest use by far. American gas meters record consumption in hundreds of cubic feet, bills are issued in thousands, and national reserves are quoted in trillions. Because the energy in a given volume of gas depends on its composition, utilities also publish a heating value per cubic foot, and the bill is the product of the two.

Appliances are sized in it. Refrigerator and freezer capacity in the United States is quoted in cubic feet, so a family refrigerator is about twenty and a chest freezer perhaps seven, and the same convention covers microwave ovens, washing machines and truck cargo boxes. Shoppers compare products by a number that describes usable space rather than external dimensions, which is genuinely more useful.

Air movement uses it per unit time. Fans, extractors, air conditioners and compressors are rated in cubic feet per minute, a figure abbreviated to CFM in every American catalogue. Ventilation standards are written as required air changes, which convert to cubic feet per minute once the room volume is known, so the unit sits on both sides of the calculation.

Materials and freight follow the same scale. Concrete, gravel, mulch and topsoil are sold by the cubic foot in smaller quantities and by the cubic yard in larger ones, twenty-seven cubic feet making one cubic yard. A cubic foot of fresh water weighs 62.4 pounds and holds about 7.48 United States gallons, which are the two figures most often needed alongside it.

Its metric equivalent is not memorable, at 28.3168 litres or 0.0283 cubic metres, and neither is its relationship to the cubic inch, at 1728. Those factors are why engineering outside the United States moved to metric volumes early even where lengths stayed imperial for longer.

One cubic foot equals 1728 cubic inches, about 28.317 litres, about 7.48 US gallons, or about 0.0283 cubic metres.

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.