Mass per volume density.
Carats per Cup to Grains per Cubic Millimeter Converter — ct/cup to gr/mm3
Convert Carat per Cup (ct/cup) to Grain per Cubic Millimeter (gr/mm3) using the exact conversion factor (1 carat per cup = 0.0000130458 grain per cubic millimeter). See the formula, worked examples, and conversion table.
Carats per Cup to Grains 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 / 64798.91.
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 Grains per Cubic Millimeter
Carat per Cup and Grain 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
grains per cubic millimeter = carats per cup × 0.0000130457528922
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 grain per cubic millimeter equals 64798.91 base units, so dividing one by the other gives the direct carat per cup-to-grain per cubic millimeter factor of 0.0000130457528922.
Simple example
1 ct/cup × 0.00001304575289 = 0.0000130458 gr/mm3
1 carat per cup = 0.0000130458 grains per cubic millimeter.
Real-world example
1,000 ct/cup × 0.00001304575289 = 0.0130457529 gr/mm3
1,000 carats per cup = 0.0130457529 grains per cubic millimeter.
Conversion table
| Carat per Cup (ct/cup) | Grain per Cubic Millimeter (gr/mm3) |
|---|---|
| 0.1 ct/cup | 0.0000013046 gr/mm3 |
| 1 ct/cup | 0.0000130458 gr/mm3 |
| 10 ct/cup | 0.0001304575 gr/mm3 |
| 100 ct/cup | 0.0013045753 gr/mm3 |
| 1,000 ct/cup | 0.0130457529 gr/mm3 |
| 10,000 ct/cup | 0.1304575289 gr/mm3 |
Reverse conversion: Grain per Cubic Millimeter to Carat per Cup
0.0000130458 gr/mm3 × 76653.29922 = 1.000003611 ct/cup
0.0000130458 grains per cubic millimeter = 1.000003611 carats per cup.
carats per cup = grains per cubic millimeter × 76653.2992201
For a page dedicated to this direction, see Grain per Cubic Millimeter to Carat per Cup.
Understanding the Carat per Cup (ct/cup)
Mass per volume density.
Understanding the Grain per Cubic Millimeter (gr/mm3)
Mass per volume density.
Reserved between the cards and the FAQ so the page stays balanced.
Frequently asked questions
How many grains per cubic millimeter are in 1 carat per cup?
1 carat per cup equals 0.0000130458 grains per cubic millimeter, using the exact defined conversion factor rather than an estimate.
How do I convert carat per cup to grain per cubic millimeter?
Multiply the carat per cup value by 0.00001304575289. The converter above does this instantly to whatever precision you set.
How do I convert grain per cubic millimeter back to carat per cup?
Use the reverse factor: 1 grain per cubic millimeter equals 76,653.29922 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 grain per cubic millimeter?
Grain per Cubic Millimeter (gr/mm3) is a unit of density.
Is the carat per cup to grain per cubic millimeter conversion exact?
Yes. Both carat per cup and grain per cubic millimeter are defined by fixed standards rather than physical artifacts, so the factor of 0.00001304575289 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.