Mass per volume density.
Carats per Cup to Carats per Cubic Millimeter Converter — ct/cup to ct/mm3
Convert Carat per Cup (ct/cup) to Carat per Cubic Millimeter (ct/mm3) using the exact conversion factor (1 carat per cup = 0.0000042268 carat per cubic millimeter). See the formula, worked examples, and conversion table.
Carats per Cup to Carats per Cubic Millimeter converter
Converter
Density Converter
Convert thousands of mass-per-volume density combinations for science, engineering, agriculture, and fluids.
Context values
Some unit families need one extra value for a physically accurate result.
Mass per volume density.
Result = input x 0.8453505675 / 200000.
Density uses kilograms per cubic meter as the base unit.
Reserved above the conversion cards and below the converter.
About Converting Carats per Cup to Carats per Cubic Millimeter
Carat per Cup and Carat per Cubic Millimeter both measure density — mass per unit volume — a property used to identify materials, check manufacturing quality, and predict whether something floats or sinks. As a fixed reference point, water has a density of exactly 1000 kg/m³ (1 g/cm³, 1 g/mL) at its temperature of maximum density, which is why many density figures in science and engineering are quoted relative to water. Both are mass per volume density units.
Formula
carats per cubic millimeter = carats per cup × 0.00000422675283773
This factor comes from each unit's defined relationship to the category's base unit: 1 carat per cup equals 0.845350567546 base units, and 1 carat per cubic millimeter equals 200000 base units, so dividing one by the other gives the direct carat per cup-to-carat per cubic millimeter factor of 0.00000422675283773.
Simple example
1 ct/cup × 0.000004226752838 = 0.0000042268 ct/mm3
1 carat per cup = 0.0000042268 carats per cubic millimeter.
Real-world example
1,000 ct/cup × 0.000004226752838 = 0.0042267528 ct/mm3
1,000 carats per cup = 0.0042267528 carats per cubic millimeter.
Conversion table
| Carat per Cup (ct/cup) | Carat per Cubic Millimeter (ct/mm3) |
|---|---|
| 0.1 ct/cup | 4.226753e-7 ct/mm3 |
| 1 ct/cup | 0.0000042268 ct/mm3 |
| 10 ct/cup | 0.0000422675 ct/mm3 |
| 100 ct/cup | 0.0004226753 ct/mm3 |
| 1,000 ct/cup | 0.0042267528 ct/mm3 |
| 10,000 ct/cup | 0.0422675284 ct/mm3 |
Reverse conversion: Carat per Cubic Millimeter to Carat per Cup
0.0000042268 ct/mm3 × 236588.2365 = 1.000011158 ct/cup
0.0000042268 carats per cubic millimeter = 1.000011158 carats per cup.
carats per cup = carats per cubic millimeter × 236588.2365
For a page dedicated to this direction, see Carat per Cubic Millimeter to Carat per Cup.
Understanding the Carat per Cup (ct/cup)
Mass per volume density.
Understanding the Carat per Cubic Millimeter (ct/mm3)
Mass per volume density.
Reserved between the cards and the FAQ so the page stays balanced.
Frequently asked questions
How many carats per cubic millimeter are in 1 carat per cup?
1 carat per cup equals 0.0000042268 carats per cubic millimeter, using the exact defined conversion factor rather than an estimate.
How do I convert carat per cup to carat per cubic millimeter?
Multiply the carat per cup value by 0.000004226752838. The converter above does this instantly to whatever precision you set.
How do I convert carat per cubic millimeter back to carat per cup?
Use the reverse factor: 1 carat per cubic millimeter equals 236,588.2365 carats per cup. You can also use the swap control in the converter above to flip the direction instantly.
What is a carat per cup?
Carat per Cup (ct/cup) is a unit of density.
What is a carat per cubic millimeter?
Carat per Cubic Millimeter (ct/mm3) is a unit of density.
Is the carat per cup to carat per cubic millimeter conversion exact?
Yes. Both carat per cup and carat per cubic millimeter are defined by fixed standards rather than physical artifacts, so the factor of 0.000004226752838 used above is exact to as many digits as you choose to display.
What's the difference between density and mass concentration?
Density is the mass of a pure substance or material per unit volume. Mass concentration is the mass of one component — like a dissolved solute — within a mixture's total volume. The two use the same kind of units but describe different physical situations.