Mass per volume density.
Carat per Cubic inches to Grains per Cup Converter — ct/in3 to gr/cup
Convert Carat per Cubic inch (ct/in3) to Grain per Cup (gr/cup) using the exact conversion factor (1 carat per cubic inch = 44.56093474 grain per cup). See the formula, worked examples, and conversion table.
Carat per Cubic inches 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 12.20474882 / 0.2738889767.
Density uses kilograms per cubic meter as the base unit.
Reserved above the conversion cards and below the converter.
About Converting Carat per Cubic inches to Grains per Cup
Carat per Cubic inch 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 = carat per cubic inches × 44.5609347441
This factor comes from each unit's defined relationship to the category's base unit: 1 carat per cubic inch equals 12.2047488189 base units, and 1 grain per cup equals 0.273888976724 base units, so dividing one by the other gives the direct carat per cubic inch-to-grain per cup factor of 44.5609347441.
Simple example
1 ct/in3 × 44.56093474 = 44.56093474 gr/cup
1 carat per cubic inch = 44.56093474 grains per cup.
Real-world example
1,000 ct/in3 × 44.56093474 = 44,560.93474 gr/cup
1,000 carat per cubic inches = 44,560.93474 grains per cup.
Conversion table
| Carat per Cubic inch (ct/in3) | Grain per Cup (gr/cup) |
|---|---|
| 0.1 ct/in3 | 4.456093474 gr/cup |
| 1 ct/in3 | 44.56093474 gr/cup |
| 10 ct/in3 | 445.6093474 gr/cup |
| 100 ct/in3 | 4,456.093474 gr/cup |
| 1,000 ct/in3 | 44,560.93474 gr/cup |
| 10,000 ct/in3 | 445,609.3474 gr/cup |
Reverse conversion: Grain per Cup to Carat per Cubic inch
44.56093474 gr/cup × 0.02244118095 = 0.9999999999 ct/in3
44.56093474 grains per cup = 0.9999999999 carat per cubic inches.
carat per cubic inches = grains per cup × 0.0224411809524
For a page dedicated to this direction, see Grain per Cup to Carat per Cubic inch.
Understanding the Carat per Cubic inch (ct/in3)
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 inch?
1 carat per cubic inch equals 44.56093474 grains per cup, using the exact defined conversion factor rather than an estimate.
How do I convert carat per cubic inch to grain per cup?
Multiply the carat per cubic inch value by 44.56093474. The converter above does this instantly to whatever precision you set.
How do I convert grain per cup back to carat per cubic inch?
Use the reverse factor: 1 grain per cup equals 0.022441181 carat per cubic inches. You can also use the swap control in the converter above to flip the direction instantly.
What is a carat per cubic inch?
Carat per Cubic inch (ct/in3) 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 inch to grain per cup conversion exact?
Yes. Both carat per cubic inch and grain per cup are defined by fixed standards rather than physical artifacts, so the factor of 44.56093474 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.