Mass per volume density.
Carats per Cup to Grain per Cubic inches Converter — ct/cup to gr/in3
Convert Carat per Cup (ct/cup) to Grain per Cubic inch (gr/in3) using the exact conversion factor (1 carat per cup = 0.2137815876 grain per cubic inch). See the formula, worked examples, and conversion table.
Carats per Cup to Grain per Cubic inches 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 / 3.954272101.
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 Grain per Cubic inches
Carat per Cup and Grain per Cubic inch 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
grain per cubic inches = carats per cup × 0.213781587573
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 inch equals 3.95427210146 base units, so dividing one by the other gives the direct carat per cup-to-grain per cubic inch factor of 0.213781587573.
Simple example
1 ct/cup × 0.2137815876 = 0.2137815876 gr/in3
1 carat per cup = 0.2137815876 grain per cubic inches.
Real-world example
1,000 ct/cup × 0.2137815876 = 213.7815876 gr/in3
1,000 carats per cup = 213.7815876 grain per cubic inches.
Conversion table
| Carat per Cup (ct/cup) | Grain per Cubic inch (gr/in3) |
|---|---|
| 0.1 ct/cup | 0.0213781588 gr/in3 |
| 1 ct/cup | 0.2137815876 gr/in3 |
| 10 ct/cup | 2.137815876 gr/in3 |
| 100 ct/cup | 21.37815876 gr/in3 |
| 1,000 ct/cup | 213.7815876 gr/in3 |
| 10,000 ct/cup | 2,137.815876 gr/in3 |
Reverse conversion: Grain per Cubic inch to Carat per Cup
0.2137815876 gr/in3 × 4.677671316 = 1 ct/cup
0.2137815876 grain per cubic inches = 1 carats per cup.
carats per cup = grain per cubic inches × 4.67767131563
For a page dedicated to this direction, see Grain per Cubic inch to Carat per Cup.
Understanding the Carat per Cup (ct/cup)
Mass per volume density.
Understanding the Grain per Cubic inch (gr/in3)
Mass per volume density.
Reserved between the cards and the FAQ so the page stays balanced.
Frequently asked questions
How many grain per cubic inches are in 1 carat per cup?
1 carat per cup equals 0.2137815876 grain per cubic inches, using the exact defined conversion factor rather than an estimate.
How do I convert carat per cup to grain per cubic inch?
Multiply the carat per cup value by 0.2137815876. The converter above does this instantly to whatever precision you set.
How do I convert grain per cubic inch back to carat per cup?
Use the reverse factor: 1 grain per cubic inch equals 4.677671316 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 inch?
Grain per Cubic inch (gr/in3) is a unit of density.
Is the carat per cup to grain per cubic inch conversion exact?
Yes. Both carat per cup and grain per cubic inch are defined by fixed standards rather than physical artifacts, so the factor of 0.2137815876 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.