Mass per volume density.
Carats per Cup to Grains per Cubic Meter Converter — ct/cup to gr/m3
Convert Carat per Cup (ct/cup) to Grain per Cubic Meter (gr/m3) using the exact conversion factor (1 carat per cup = 13,045.75289 grain per cubic meter). See the formula, worked examples, and conversion table.
Carats per Cup to Grains per Cubic Meter 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 / 6.479891e-5.
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 Cubic Meter
Carat per Cup and Grain per Cubic Meter 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 cubic meter = carats per cup × 13045.7528922
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 cubic meter equals 0.00006479891 base units, so dividing one by the other gives the direct carat per cup-to-grain per cubic meter factor of 13045.7528922.
Simple example
1 ct/cup × 13045.75289 = 13,045.75289 gr/m3
1 carat per cup = 13,045.75289 grains per cubic meter.
Real-world example
1,000 ct/cup × 13045.75289 = 13,045,752.89 gr/m3
1,000 carats per cup = 13,045,752.89 grains per cubic meter.
Conversion table
| Carat per Cup (ct/cup) | Grain per Cubic Meter (gr/m3) |
|---|---|
| 0.1 ct/cup | 1,304.575289 gr/m3 |
| 1 ct/cup | 13,045.75289 gr/m3 |
| 10 ct/cup | 130,457.5289 gr/m3 |
| 100 ct/cup | 1,304,575.289 gr/m3 |
| 1,000 ct/cup | 13,045,752.89 gr/m3 |
| 10,000 ct/cup | 130,457,528.9 gr/m3 |
Reverse conversion: Grain per Cubic Meter to Carat per Cup
1 gr/m3 × 0.00007665329922 = 0.0000766533 ct/cup
1 grain per cubic meter = 0.0000766533 carats per cup.
carats per cup = grains per cubic meter × 0.0000766532992201
For a page dedicated to this direction, see Grain per Cubic Meter to Carat per Cup.
Understanding the Carat per Cup (ct/cup)
Mass per volume density.
Understanding the Grain per Cubic Meter (gr/m3)
Mass per volume density.
Reserved between the cards and the FAQ so the page stays balanced.
Frequently asked questions
How many grains per cubic meter are in 1 carat per cup?
1 carat per cup equals 13,045.75289 grains per cubic meter, using the exact defined conversion factor rather than an estimate.
How do I convert carat per cup to grain per cubic meter?
Multiply the carat per cup value by 13045.75289. The converter above does this instantly to whatever precision you set.
How do I convert grain per cubic meter back to carat per cup?
Use the reverse factor: 1 grain per cubic meter equals 0.0000766533 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 cubic meter?
Grain per Cubic Meter (gr/m3) is a unit of density.
Is the carat per cup to grain per cubic meter conversion exact?
Yes. Both carat per cup and grain per cubic meter are defined by fixed standards rather than physical artifacts, so the factor of 13045.75289 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.