Mass per volume density.
Carats per Cubic Millimeter to Grains per Cup Converter — ct/mm3 to gr/cup
Convert Carat per Cubic Millimeter (ct/mm3) to Grain per Cup (gr/cup) using the exact conversion factor (1 carat per cubic millimeter = 730,222.8896 grain per cup). See the formula, worked examples, and conversion table.
Carats per Cubic Millimeter to Grains 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 200000 / 0.2738889767.
Density uses kilograms per cubic meter as the base unit.
Reserved above the conversion cards and below the converter.
About Converting Carats per Cubic Millimeter to Grains per Cup
Carat per Cubic Millimeter and Grain 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
grains per cup = carats per cubic millimeter × 730222.889552
This factor comes from each unit's defined relationship to the category's base unit: 1 carat per cubic millimeter equals 200000 base units, and 1 grain per cup equals 0.273888976724 base units, so dividing one by the other gives the direct carat per cubic millimeter-to-grain per cup factor of 730222.889552.
Simple example
1 ct/mm3 × 730222.8896 = 730,222.8896 gr/cup
1 carat per cubic millimeter = 730,222.8896 grains per cup.
Real-world example
1,000 ct/mm3 × 730222.8896 = 730,222,889.6 gr/cup
1,000 carats per cubic millimeter = 730,222,889.6 grains per cup.
Conversion table
| Carat per Cubic Millimeter (ct/mm3) | Grain per Cup (gr/cup) |
|---|---|
| 0.1 ct/mm3 | 73,022.28896 gr/cup |
| 1 ct/mm3 | 730,222.8896 gr/cup |
| 10 ct/mm3 | 7,302,228.896 gr/cup |
| 100 ct/mm3 | 73,022,288.96 gr/cup |
| 1,000 ct/mm3 | 730,222,889.6 gr/cup |
| 10,000 ct/mm3 | 7,302,228,896 gr/cup |
Reverse conversion: Grain per Cup to Carat per Cubic Millimeter
1 gr/cup × 0.000001369444884 = 0.0000013694 ct/mm3
1 grain per cup = 0.0000013694 carats per cubic millimeter.
carats per cubic millimeter = grains per cup × 0.00000136944488362
For a page dedicated to this direction, see Grain per Cup to Carat per Cubic Millimeter.
Understanding the Carat per Cubic Millimeter (ct/mm3)
Mass per volume density.
Understanding the Grain per Cup (gr/cup)
Mass per volume density.
Reserved between the cards and the FAQ so the page stays balanced.
Frequently asked questions
How many grains per cup are in 1 carat per cubic millimeter?
1 carat per cubic millimeter equals 730,222.8896 grains per cup, using the exact defined conversion factor rather than an estimate.
How do I convert carat per cubic millimeter to grain per cup?
Multiply the carat per cubic millimeter value by 730222.8896. The converter above does this instantly to whatever precision you set.
How do I convert grain per cup back to carat per cubic millimeter?
Use the reverse factor: 1 grain per cup equals 0.0000013694 carats per cubic millimeter. You can also use the swap control in the converter above to flip the direction instantly.
What is a carat per cubic millimeter?
Carat per Cubic Millimeter (ct/mm3) is a unit of density.
What is a grain per cup?
Grain per Cup (gr/cup) is a unit of density.
Is the carat per cubic millimeter to grain per cup conversion exact?
Yes. Both carat per cubic millimeter and grain per cup are defined by fixed standards rather than physical artifacts, so the factor of 730222.8896 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.