Mass per volume density.
Grains per Cubic Millimeter to Carats per Cup Converter — gr/mm3 to ct/cup
Convert Grain per Cubic Millimeter (gr/mm3) to Carat per Cup (ct/cup) using the exact conversion factor (1 grain per cubic millimeter = 76,653.29922 carat per cup). See the formula, worked examples, and conversion table.
Grains per Cubic Millimeter to Carats per Cup 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 64798.91 / 0.8453505675.
Density uses kilograms per cubic meter as the base unit.
Reserved above the conversion cards and below the converter.
About Converting Grains per Cubic Millimeter to Carats per Cup
Grain per Cubic Millimeter and Carat per Cup 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 cup = grains per cubic millimeter × 76653.2992201
This factor comes from each unit's defined relationship to the category's base unit: 1 grain per cubic millimeter equals 64798.91 base units, and 1 carat per cup equals 0.845350567546 base units, so dividing one by the other gives the direct grain per cubic millimeter-to-carat per cup factor of 76653.2992201.
Simple example
1 gr/mm3 × 76653.29922 = 76,653.29922 ct/cup
1 grain per cubic millimeter = 76,653.29922 carats per cup.
Real-world example
1,000 gr/mm3 × 76653.29922 = 76,653,299.22 ct/cup
1,000 grains per cubic millimeter = 76,653,299.22 carats per cup.
Conversion table
| Grain per Cubic Millimeter (gr/mm3) | Carat per Cup (ct/cup) |
|---|---|
| 0.1 gr/mm3 | 7,665.329922 ct/cup |
| 1 gr/mm3 | 76,653.29922 ct/cup |
| 10 gr/mm3 | 766,532.9922 ct/cup |
| 100 gr/mm3 | 7,665,329.922 ct/cup |
| 1,000 gr/mm3 | 76,653,299.22 ct/cup |
| 10,000 gr/mm3 | 766,532,992.2 ct/cup |
Reverse conversion: Carat per Cup to Grain per Cubic Millimeter
1 ct/cup × 0.00001304575289 = 0.0000130458 gr/mm3
1 carat per cup = 0.0000130458 grains per cubic millimeter.
grains per cubic millimeter = carats per cup × 0.0000130457528922
For a page dedicated to this direction, see Carat per Cup to Grain per Cubic Millimeter.
Understanding the Grain per Cubic Millimeter (gr/mm3)
Mass per volume density.
Understanding the Carat per Cup (ct/cup)
Mass per volume density.
Reserved between the cards and the FAQ so the page stays balanced.
Frequently asked questions
How many carats per cup are in 1 grain per cubic millimeter?
1 grain per cubic millimeter equals 76,653.29922 carats per cup, using the exact defined conversion factor rather than an estimate.
How do I convert grain per cubic millimeter to carat per cup?
Multiply the grain per cubic millimeter value by 76653.29922. The converter above does this instantly to whatever precision you set.
How do I convert carat per cup back to grain per cubic millimeter?
Use the reverse factor: 1 carat per cup equals 0.0000130458 grains per cubic millimeter. You can also use the swap control in the converter above to flip the direction instantly.
What is a grain per cubic millimeter?
Grain per Cubic Millimeter (gr/mm3) is a unit of density.
What is a carat per cup?
Carat per Cup (ct/cup) is a unit of density.
Is the grain per cubic millimeter to carat per cup conversion exact?
Yes. Both grain per cubic millimeter and carat per cup are defined by fixed standards rather than physical artifacts, so the factor of 76653.29922 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.