Mass per volume density.
Carats per Cup to Grains per Cup Converter — ct/cup to gr/cup
Convert Carat per Cup (ct/cup) to Grain per Cup (gr/cup) using the exact conversion factor (1 carat per cup = 3.086471671 grain per cup). See the formula, worked examples, and conversion table.
Carats per Cup 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 0.8453505675 / 0.2738889767.
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 Cup
Carat per Cup 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 = carats per cup × 3.08647167059
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 cup equals 0.273888976724 base units, so dividing one by the other gives the direct carat per cup-to-grain per cup factor of 3.08647167059.
Simple example
1 ct/cup × 3.086471671 = 3.086471671 gr/cup
1 carat per cup = 3.086471671 grains per cup.
Real-world example
1,000 ct/cup × 3.086471671 = 3,086.471671 gr/cup
1,000 carats per cup = 3,086.471671 grains per cup.
Conversion table
| Carat per Cup (ct/cup) | Grain per Cup (gr/cup) |
|---|---|
| 0.1 ct/cup | 0.3086471671 gr/cup |
| 1 ct/cup | 3.086471671 gr/cup |
| 10 ct/cup | 30.86471671 gr/cup |
| 100 ct/cup | 308.6471671 gr/cup |
| 1,000 ct/cup | 3,086.471671 gr/cup |
| 10,000 ct/cup | 30,864.71671 gr/cup |
Reverse conversion: Grain per Cup to Carat per Cup
3.086471671 gr/cup × 0.32399455 = 1 ct/cup
3.086471671 grains per cup = 1 carats per cup.
carats per cup = grains per cup × 0.32399455
For a page dedicated to this direction, see Grain per Cup to Carat per Cup.
Understanding the Carat per Cup (ct/cup)
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 cup?
1 carat per cup equals 3.086471671 grains per cup, using the exact defined conversion factor rather than an estimate.
How do I convert carat per cup to grain per cup?
Multiply the carat per cup value by 3.086471671. The converter above does this instantly to whatever precision you set.
How do I convert grain per cup back to carat per cup?
Use the reverse factor: 1 grain per cup equals 0.32399455 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 cup?
Grain per Cup (gr/cup) is a unit of density.
Is the carat per cup to grain per cup conversion exact?
Yes. Both carat per cup and grain per cup are defined by fixed standards rather than physical artifacts, so the factor of 3.086471671 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.