Mass per volume density.
Grain per Cubic inches to Carats per Cup Converter — gr/in3 to ct/cup
Convert Grain per Cubic inch (gr/in3) to Carat per Cup (ct/cup) using the exact conversion factor (1 grain per cubic inch = 4.677671316 carat per cup). See the formula, worked examples, and conversion table.
Grain per Cubic inches 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 3.954272101 / 0.8453505675.
Density uses kilograms per cubic meter as the base unit.
Reserved above the conversion cards and below the converter.
About Converting Grain per Cubic inches to Carats per Cup
Grain per Cubic inch 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 = grain per cubic inches × 4.67767131563
This factor comes from each unit's defined relationship to the category's base unit: 1 grain per cubic inch equals 3.95427210146 base units, and 1 carat per cup equals 0.845350567546 base units, so dividing one by the other gives the direct grain per cubic inch-to-carat per cup factor of 4.67767131563.
Simple example
1 gr/in3 × 4.677671316 = 4.677671316 ct/cup
1 grain per cubic inch = 4.677671316 carats per cup.
Real-world example
1,000 gr/in3 × 4.677671316 = 4,677.671316 ct/cup
1,000 grain per cubic inches = 4,677.671316 carats per cup.
Conversion table
| Grain per Cubic inch (gr/in3) | Carat per Cup (ct/cup) |
|---|---|
| 0.1 gr/in3 | 0.4677671316 ct/cup |
| 1 gr/in3 | 4.677671316 ct/cup |
| 10 gr/in3 | 46.77671316 ct/cup |
| 100 gr/in3 | 467.7671316 ct/cup |
| 1,000 gr/in3 | 4,677.671316 ct/cup |
| 10,000 gr/in3 | 46,776.71316 ct/cup |
Reverse conversion: Carat per Cup to Grain per Cubic inch
4.677671316 ct/cup × 0.2137815876 = 1 gr/in3
4.677671316 carats per cup = 1 grain per cubic inches.
grain per cubic inches = carats per cup × 0.213781587573
For a page dedicated to this direction, see Carat per Cup to Grain per Cubic inch.
Understanding the Grain per Cubic inch (gr/in3)
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 inch?
1 grain per cubic inch equals 4.677671316 carats per cup, using the exact defined conversion factor rather than an estimate.
How do I convert grain per cubic inch to carat per cup?
Multiply the grain per cubic inch value by 4.677671316. The converter above does this instantly to whatever precision you set.
How do I convert carat per cup back to grain per cubic inch?
Use the reverse factor: 1 carat per cup equals 0.2137815876 grain per cubic inches. You can also use the swap control in the converter above to flip the direction instantly.
What is a grain per cubic inch?
Grain per Cubic inch (gr/in3) 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 inch to carat per cup conversion exact?
Yes. Both grain per cubic inch and carat per cup are defined by fixed standards rather than physical artifacts, so the factor of 4.677671316 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.