| Cubic millimeters (mm³) | Cubic inches (in³) |
|---|---|
| 1 Cubic millimeter | 0.0000610237440947 in³ |
| 2 Cubic millimeters | 0.000122047488189 in³ |
| 3 Cubic millimeters | 0.000183071232284 in³ |
| 4 Cubic millimeters | 0.000244094976379 in³ |
| 5 Cubic millimeters | 0.000305118720474 in³ |
| 10 Cubic millimeters | 0.000610237440947 in³ |
| 20 Cubic millimeters | 0.00122047488189 in³ |
| 25 Cubic millimeters | 0.00152559360237 in³ |
| 50 Cubic millimeters | 0.00305118720474 in³ |
| 100 Cubic millimeters | 0.00610237440947 in³ |
| Reference | Cubic millimeters (mm³) | Cubic inches (in³) |
|---|---|---|
| A teaspoon | 5000 mm³ | 0.305119 in³ |
| A can of soft drink | 330000 mm³ | 20.1378 in³ |
| A wine bottle | 750000 mm³ | 45.7678 in³ |
| A bathtub | 150000000 mm³ | 9153.56 in³ |
| An Olympic swimming pool | 2.5 × 1012 mm³ | 152559360 in³ |
The cubic millimetre is a unit of volume equal to one thousandth of a cubic centimetre, written mm³. It is the volume of a cube one millimetre on each side, and it is exactly one microlitre. Which of the two names is used depends on whether the thing being measured is a solid or a liquid, and the distinction is entirely a matter of professional habit.
Machining measures productivity in it. The material removal rate of a milling cutter or a grinding wheel is quoted in cubic millimetres per minute, and that single figure captures what a machine and a tool can achieve better than spindle speed or feed rate can on their own. Comparing two cutting strategies, two tool coatings or two machines means comparing how many cubic millimetres of metal each turns into swarf per unit time.
Additive manufacturing inverts the same measurement. A fused-filament printer deposits ten to twenty cubic millimetres a second, a laser powder-bed machine rather less, and build time follows directly from the part volume divided by that rate. Because the volume of a component is known exactly from its model, the estimate is unusually reliable.
Wear and durability testing uses the unit to describe loss. A specific wear rate is stated in cubic millimetres removed per newton of load and metre of sliding, which allows materials of very different hardness to be compared on one scale. Bearing life, brake pad testing and coating evaluation all reduce to counting cubic millimetres that are no longer there.
Medical imaging works at the same magnitude. Micro-computed tomography of bone reports trabecular volume and porosity in cubic millimetres, tumour volumes in early imaging are given the same way, and voxel sizes in high-resolution scans are quoted as fractions of one. In each case the unit is small enough to describe structure rather than merely size.
Its identity with the microlitre is worth remembering when moving between fields. An engineer discussing a cubic millimetre of material and a biologist discussing a microlitre of solution are talking about the same quantity, and any calculation that mixes the two needs no conversion factor at all.
One cubic millimetre equals 1 microlitre, 0.001 cubic centimetres, 0.000000001 cubic metres, or about 0.000061 cubic inches.
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.