Mass per volume density.
Carats per Cup to Grains per Cubic Centimeter Converter — ct/cup to gr/cm3
Convert Carat per Cup (ct/cup) to Grain per Cubic Centimeter (gr/cm3) using the exact conversion factor (1 carat per cup = 0.0130457529 grain per cubic centimeter). See the formula, worked examples, and conversion table.
Carats per Cup to Grains per Cubic Centimeter 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 / 64.79891.
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 Centimeter
Carat per Cup and Grain per Cubic Centimeter 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 centimeter = carats per cup × 0.0130457528922
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 centimeter equals 64.79891 base units, so dividing one by the other gives the direct carat per cup-to-grain per cubic centimeter factor of 0.0130457528922.
Simple example
1 ct/cup × 0.01304575289 = 0.0130457529 gr/cm3
1 carat per cup = 0.0130457529 grains per cubic centimeter.
Real-world example
1,000 ct/cup × 0.01304575289 = 13.04575289 gr/cm3
1,000 carats per cup = 13.04575289 grains per cubic centimeter.
Conversion table
| Carat per Cup (ct/cup) | Grain per Cubic Centimeter (gr/cm3) |
|---|---|
| 0.1 ct/cup | 0.0013045753 gr/cm3 |
| 1 ct/cup | 0.0130457529 gr/cm3 |
| 10 ct/cup | 0.1304575289 gr/cm3 |
| 100 ct/cup | 1.304575289 gr/cm3 |
| 1,000 ct/cup | 13.04575289 gr/cm3 |
| 10,000 ct/cup | 130.4575289 gr/cm3 |
Reverse conversion: Grain per Cubic Centimeter to Carat per Cup
0.0130457529 gr/cm3 × 76.65329922 = 1.000000001 ct/cup
0.0130457529 grains per cubic centimeter = 1.000000001 carats per cup.
carats per cup = grains per cubic centimeter × 76.6532992201
For a page dedicated to this direction, see Grain per Cubic Centimeter to Carat per Cup.
Understanding the Carat per Cup (ct/cup)
Mass per volume density.
Understanding the Grain per Cubic Centimeter (gr/cm3)
Mass per volume density.
Reserved between the cards and the FAQ so the page stays balanced.
Frequently asked questions
How many grains per cubic centimeter are in 1 carat per cup?
1 carat per cup equals 0.0130457529 grains per cubic centimeter, using the exact defined conversion factor rather than an estimate.
How do I convert carat per cup to grain per cubic centimeter?
Multiply the carat per cup value by 0.01304575289. The converter above does this instantly to whatever precision you set.
How do I convert grain per cubic centimeter back to carat per cup?
Use the reverse factor: 1 grain per cubic centimeter equals 76.65329922 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 centimeter?
Grain per Cubic Centimeter (gr/cm3) is a unit of density.
Is the carat per cup to grain per cubic centimeter conversion exact?
Yes. Both carat per cup and grain per cubic centimeter are defined by fixed standards rather than physical artifacts, so the factor of 0.01304575289 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.