Cubic inch (in³)

The cubic inch is a unit of volume equal to 16.387064 cubic centimetres exactly. Its symbol is cu in, sometimes written in³. It is the volume of a cube one inch on each side, and 1728 of them make a cubic foot. Its most consequential role is legal rather than descriptive: the United States gallon is defined as exactly 231 cubic inches.

That definition is the reason American liquid measure is the shape it is. The figure of 231 comes from the English wine gallon standardised under Queen Anne in 1707, which the United States kept when Britain replaced its own gallons with a single imperial gallon in 1824. Every American fluid ounce, pint and quart descends from that one number, and it is why the two gallons differ by a fifth.

Engines made the unit famous. American car engines were quoted in cubic inches until the 1980s, and the numbers became names in their own right: a 350 is 5.7 litres, a 426 is 7.0, and a 302 is 4.9. Motorcycles still carry both figures, and the conversion is worth knowing, since 61 cubic inches make a litre.

Machinery uses it for swept volume. Pump and compressor displacement per revolution, hydraulic cylinder volume and metering pump strokes are all specified in cubic inches in American engineering, because the bores and strokes that produce them are already in inches and squaring or cubing an inch keeps the calculation in one system.

Freight pricing uses it in an unexpected way. American parcel carriers calculate a dimensional weight by dividing the package volume in cubic inches by a fixed divisor, commonly 139, to obtain a chargeable weight in pounds. A light bulky parcel is therefore priced by its cubic inches rather than by what it weighs, which changes how goods are packed.

The conversion to metric is exact but unhelpful. Because the inch is defined as exactly 2.54 centimetres, a cubic inch is exactly 16.387064 cubic centimetres, and no rounding is involved. That precision does not make the number easier to use, and it is the main reason engineering drawings outside the United States moved to millimetres.

One cubic inch equals 16.387 cubic centimetres, about 0.0164 litres, about 0.554 US fluid ounces, or 1/1728 of a cubic foot.

Cubic inch conversion table