Mass per volume density.
Grains per Cup to Carat per Cubic inches Converter — gr/cup to ct/in3
Convert Grain per Cup (gr/cup) to Carat per Cubic inch (ct/in3) using the exact conversion factor (1 grain per cup = 0.022441181 carat per cubic inch). See the formula, worked examples, and conversion table.
Grains per Cup to Carat 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 0.2738889767 / 12.20474882.
Density uses kilograms per cubic meter as the base unit.
Reserved above the conversion cards and below the converter.
About Converting Grains per Cup to Carat per Cubic inches
Grain per Cup and Carat 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
carat per cubic inches = grains per cup × 0.0224411809524
This factor comes from each unit's defined relationship to the category's base unit: 1 grain per cup equals 0.273888976724 base units, and 1 carat per cubic inch equals 12.2047488189 base units, so dividing one by the other gives the direct grain per cup-to-carat per cubic inch factor of 0.0224411809524.
Simple example
1 gr/cup × 0.02244118095 = 0.022441181 ct/in3
1 grain per cup = 0.022441181 carat per cubic inches.
Real-world example
1,000 gr/cup × 0.02244118095 = 22.44118095 ct/in3
1,000 grains per cup = 22.44118095 carat per cubic inches.
Conversion table
| Grain per Cup (gr/cup) | Carat per Cubic inch (ct/in3) |
|---|---|
| 0.1 gr/cup | 0.0022441181 ct/in3 |
| 1 gr/cup | 0.022441181 ct/in3 |
| 10 gr/cup | 0.2244118095 ct/in3 |
| 100 gr/cup | 2.244118095 ct/in3 |
| 1,000 gr/cup | 22.44118095 ct/in3 |
| 10,000 gr/cup | 224.4118095 ct/in3 |
Reverse conversion: Carat per Cubic inch to Grain per Cup
0.022441181 ct/in3 × 44.56093474 = 1.000000002 gr/cup
0.022441181 carat per cubic inches = 1.000000002 grains per cup.
grains per cup = carat per cubic inches × 44.5609347441
For a page dedicated to this direction, see Carat per Cubic inch to Grain per Cup.
Understanding the Grain per Cup (gr/cup)
Mass per volume density.
Understanding the Carat per Cubic inch (ct/in3)
Mass per volume density.
Reserved between the cards and the FAQ so the page stays balanced.
Frequently asked questions
How many carat per cubic inches are in 1 grain per cup?
1 grain per cup equals 0.022441181 carat per cubic inches, using the exact defined conversion factor rather than an estimate.
How do I convert grain per cup to carat per cubic inch?
Multiply the grain per cup value by 0.02244118095. The converter above does this instantly to whatever precision you set.
How do I convert carat per cubic inch back to grain per cup?
Use the reverse factor: 1 carat per cubic inch equals 44.56093474 grains per cup. You can also use the swap control in the converter above to flip the direction instantly.
What is a grain per cup?
Grain per Cup (gr/cup) is a unit of density.
What is a carat per cubic inch?
Carat per Cubic inch (ct/in3) is a unit of density.
Is the grain per cup to carat per cubic inch conversion exact?
Yes. Both grain per cup and carat per cubic inch are defined by fixed standards rather than physical artifacts, so the factor of 0.02244118095 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.