Mass per volume density.
Grains per Cup to Carats per Cubic foot Converter — gr/cup to ct/ft3
Convert Grain per Cup (gr/cup) to Carat per Cubic foot (ct/ft3) using the exact conversion factor (1 grain per cup = 38.77836069 carat per cubic foot). See the formula, worked examples, and conversion table.
Grains per Cup to Carats per Cubic foot 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 / 0.007062933344.
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 Carats per Cubic foot
Grain per Cup and Carat per Cubic foot 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 cubic foot = grains per cup × 38.7783606857
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 foot equals 0.0070629333443 base units, so dividing one by the other gives the direct grain per cup-to-carat per cubic foot factor of 38.7783606857.
Simple example
1 gr/cup × 38.77836069 = 38.77836069 ct/ft3
1 grain per cup = 38.77836069 carats per cubic foot.
Real-world example
1,000 gr/cup × 38.77836069 = 38,778.36069 ct/ft3
1,000 grains per cup = 38,778.36069 carats per cubic foot.
Conversion table
| Grain per Cup (gr/cup) | Carat per Cubic foot (ct/ft3) |
|---|---|
| 0.1 gr/cup | 3.877836069 ct/ft3 |
| 1 gr/cup | 38.77836069 ct/ft3 |
| 10 gr/cup | 387.7836069 ct/ft3 |
| 100 gr/cup | 3,877.836069 ct/ft3 |
| 1,000 gr/cup | 38,778.36069 ct/ft3 |
| 10,000 gr/cup | 387,783.6069 ct/ft3 |
Reverse conversion: Carat per Cubic foot to Grain per Cup
38.77836069 ct/ft3 × 0.02578757798 = 1 gr/cup
38.77836069 carats per cubic foot = 1 grains per cup.
grains per cup = carats per cubic foot × 0.0257875779769
For a page dedicated to this direction, see Carat per Cubic foot to Grain per Cup.
Understanding the Grain per Cup (gr/cup)
Mass per volume density.
Understanding the Carat per Cubic foot (ct/ft3)
Mass per volume density.
Reserved between the cards and the FAQ so the page stays balanced.
Frequently asked questions
How many carats per cubic foot are in 1 grain per cup?
1 grain per cup equals 38.77836069 carats per cubic foot, using the exact defined conversion factor rather than an estimate.
How do I convert grain per cup to carat per cubic foot?
Multiply the grain per cup value by 38.77836069. The converter above does this instantly to whatever precision you set.
How do I convert carat per cubic foot back to grain per cup?
Use the reverse factor: 1 carat per cubic foot equals 0.025787578 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 foot?
Carat per Cubic foot (ct/ft3) is a unit of density.
Is the grain per cup to carat per cubic foot conversion exact?
Yes. Both grain per cup and carat per cubic foot are defined by fixed standards rather than physical artifacts, so the factor of 38.77836069 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.