Mass per volume density.
Carats per Cubic Millimeter to Grain per Cubic inches Converter — ct/mm3 to gr/in3
Convert Carat per Cubic Millimeter (ct/mm3) to Grain per Cubic inch (gr/in3) using the exact conversion factor (1 carat per cubic millimeter = 50,578.2088 grain per cubic inch). See the formula, worked examples, and conversion table.
Carats per Cubic Millimeter to Grain 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 200000 / 3.954272101.
Density uses kilograms per cubic meter as the base unit.
Reserved above the conversion cards and below the converter.
About Converting Carats per Cubic Millimeter to Grain per Cubic inches
Carat per Cubic Millimeter and Grain 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
grain per cubic inches = carats per cubic millimeter × 50578.2088001
This factor comes from each unit's defined relationship to the category's base unit: 1 carat per cubic millimeter equals 200000 base units, and 1 grain per cubic inch equals 3.95427210146 base units, so dividing one by the other gives the direct carat per cubic millimeter-to-grain per cubic inch factor of 50578.2088001.
Simple example
1 ct/mm3 × 50578.2088 = 50,578.2088 gr/in3
1 carat per cubic millimeter = 50,578.2088 grain per cubic inches.
Real-world example
1,000 ct/mm3 × 50578.2088 = 50,578,208.8 gr/in3
1,000 carats per cubic millimeter = 50,578,208.8 grain per cubic inches.
Conversion table
| Carat per Cubic Millimeter (ct/mm3) | Grain per Cubic inch (gr/in3) |
|---|---|
| 0.1 ct/mm3 | 5,057.82088 gr/in3 |
| 1 ct/mm3 | 50,578.2088 gr/in3 |
| 10 ct/mm3 | 505,782.088 gr/in3 |
| 100 ct/mm3 | 5,057,820.88 gr/in3 |
| 1,000 ct/mm3 | 50,578,208.8 gr/in3 |
| 10,000 ct/mm3 | 505,782,088 gr/in3 |
Reverse conversion: Grain per Cubic inch to Carat per Cubic Millimeter
1 gr/in3 × 0.00001977136051 = 0.0000197714 ct/mm3
1 grain per cubic inch = 0.0000197714 carats per cubic millimeter.
carats per cubic millimeter = grain per cubic inches × 0.0000197713605073
For a page dedicated to this direction, see Grain per Cubic inch to Carat per Cubic Millimeter.
Understanding the Carat per Cubic Millimeter (ct/mm3)
Mass per volume density.
Understanding the Grain per Cubic inch (gr/in3)
Mass per volume density.
Reserved between the cards and the FAQ so the page stays balanced.
Frequently asked questions
How many grain per cubic inches are in 1 carat per cubic millimeter?
1 carat per cubic millimeter equals 50,578.2088 grain per cubic inches, using the exact defined conversion factor rather than an estimate.
How do I convert carat per cubic millimeter to grain per cubic inch?
Multiply the carat per cubic millimeter value by 50578.2088. The converter above does this instantly to whatever precision you set.
How do I convert grain per cubic inch back to carat per cubic millimeter?
Use the reverse factor: 1 grain per cubic inch equals 0.0000197714 carats per cubic millimeter. You can also use the swap control in the converter above to flip the direction instantly.
What is a carat per cubic millimeter?
Carat per Cubic Millimeter (ct/mm3) is a unit of density.
What is a grain per cubic inch?
Grain per Cubic inch (gr/in3) is a unit of density.
Is the carat per cubic millimeter to grain per cubic inch conversion exact?
Yes. Both carat per cubic millimeter and grain per cubic inch are defined by fixed standards rather than physical artifacts, so the factor of 50578.2088 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.