mm3\text{mm}^{3}

cubic millimeter

VolumeSection modulusexact by definition

The cubic millimetre is 10⁻⁹ cubic metres, exactly one microlitre. It is the unit of small machined volumes and of material removal rates in cutting, and it is the classical unit of blood cell counts, where "per mm³" and "per μL" are the same denominator.

1 mm3\text{mm}^{3} (Volume)0.000001 L\text{L}
1 mm3\text{mm}^{3} (Section modulus)1 mm3\text{mm}^{3}

About the cubic millimeter

The most precisely metered volumes in engineering are written in this unit. Diesel fuel injection is calibrated in cubic millimetres per stroke: a passenger-car pilot injection is 1 to 2 mm³ per cylinder, the tiny pre-charge that stops a modern diesel knocking at idle, and injector test benches report their delivery maps in nothing else. A cubic millimetre of water weighs one milligram, so those maps are also, silently, fuel-mass maps.

This page carries a second and stranger job. The same symbol, mm³, serves section modulus on this site, the beam property in σ=M/Z\sigma = M/Z that turns a bending moment into a stress. A section modulus is not the volume of anything; it is a second moment of area divided by a distance, and its units merely happen to collapse to a length cubed. The catalog keeps the two as separate quantity types precisely so a converter never offers to express a beam property in microlitres, and a reader who arrived here from a structural steel table should follow the section modulus context rather than this one.

Blood work is the third life the definition already names: counts "per mm³" on older lab forms are identical to the modern per-μL figures, so a 1970s reference range needs no conversion at all, only relabelling.

As a unit of section modulus

The cubic millimetre is exactly 10⁻⁹ cubic metres, an exact relation. It pairs naturally with stresses in N/mm², since a moment in newton millimetres divided by a section modulus in mm³ gives a stress in N/mm², which is exactly megapascals with no conversion needed.

One cubic millimeter in every volume unit

1cubic millimeter (mm³)this unit
1microliter (μL)
0.001milliliter (mL)
0.001cubic centimeter (cm³)
0.000202884US teaspoon (tsp)
0.0001centiliter (cL)
0.000067628US tablespoon (tbsp)
0.0000610237cubic inch (in³)
0.0000351951imperial fluid ounce (imp fl oz)
0.000033814US fluid ounce (fl oz)
0.00001deciliter (dL)
0.00000422675US cup (cup)
0.00000211338US pint (pt)
0.00000175975imperial pint (imp pt)
0.00000105669US quart (qt)
0.000001liter (L)
0.000001cubic decimeter (dm³)
8.79877e-07imperial quart (imp qt)
4.23776e-07board foot (fbm)
2.64172e-07US gallon (gal)
2.19969e-07imperial gallon (imp gal)
3.53147e-08cubic foot (ft³)
2.83776e-08US bushel (bu)
1.00000e-08hectoliter (hL)
8.52168e-09US beer barrel (bbl beer)
6.28981e-09oil barrel (bbl)
1.30795e-09cubic yard (yd³)
1.00000e-09cubic meter (m³)
1.00000e-09kiloliter (kL)
3.53147e-10hundred cubic feet (CCF)
2.75896e-10cord (cord)
8.10713e-13acre-foot (ac·ft)
2.64172e-13million US gallons (MG)
1.00000e-18cubic kilometer (km³)

One cubic millimeter in every section modulus unit

1,000,000,000cubic micrometer (μm³)
1cubic millimeter (mm³)this unit
0.001cubic centimeter (cm³)
0.001thousand cubic millimeters (10³ mm³)
0.0000610237cubic inch (in³)
3.53147e-08cubic foot (ft³)
1.00000e-09cubic meter (m³)