Mass per volume density.
Grains per Cubic Meter to Carats per Cup Converter — gr/m3 to ct/cup
Convert Grain per Cubic Meter (gr/m3) to Carat per Cup (ct/cup) using the exact conversion factor (1 grain per cubic meter = 0.0000766533 carat per cup). See the formula, worked examples, and conversion table.
Grains per Cubic Meter to Carats 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 6.479891e-5 / 0.8453505675.
Density uses kilograms per cubic meter as the base unit.
Reserved above the conversion cards and below the converter.
About Converting Grains per Cubic Meter to Carats per Cup
Grain per Cubic Meter and Carat 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
carats per cup = grains per cubic meter × 0.0000766532992201
This factor comes from each unit's defined relationship to the category's base unit: 1 grain per cubic meter equals 0.00006479891 base units, and 1 carat per cup equals 0.845350567546 base units, so dividing one by the other gives the direct grain per cubic meter-to-carat per cup factor of 0.0000766532992201.
Simple example
1 gr/m3 × 0.00007665329922 = 0.0000766533 ct/cup
1 grain per cubic meter = 0.0000766533 carats per cup.
Real-world example
1,000 gr/m3 × 0.00007665329922 = 0.0766532992 ct/cup
1,000 grains per cubic meter = 0.0766532992 carats per cup.
Conversion table
| Grain per Cubic Meter (gr/m3) | Carat per Cup (ct/cup) |
|---|---|
| 0.1 gr/m3 | 0.0000076653 ct/cup |
| 1 gr/m3 | 0.0000766533 ct/cup |
| 10 gr/m3 | 0.000766533 ct/cup |
| 100 gr/m3 | 0.0076653299 ct/cup |
| 1,000 gr/m3 | 0.0766532992 ct/cup |
| 10,000 gr/m3 | 0.7665329922 ct/cup |
Reverse conversion: Carat per Cup to Grain per Cubic Meter
0.0000766533 ct/cup × 13045.75289 = 1.00000001 gr/m3
0.0000766533 carats per cup = 1.00000001 grains per cubic meter.
grains per cubic meter = carats per cup × 13045.7528922
For a page dedicated to this direction, see Carat per Cup to Grain per Cubic Meter.
Understanding the Grain per Cubic Meter (gr/m3)
Mass per volume density.
Understanding the Carat per Cup (ct/cup)
Mass per volume density.
Reserved between the cards and the FAQ so the page stays balanced.
Frequently asked questions
How many carats per cup are in 1 grain per cubic meter?
1 grain per cubic meter equals 0.0000766533 carats per cup, using the exact defined conversion factor rather than an estimate.
How do I convert grain per cubic meter to carat per cup?
Multiply the grain per cubic meter value by 0.00007665329922. The converter above does this instantly to whatever precision you set.
How do I convert carat per cup back to grain per cubic meter?
Use the reverse factor: 1 carat per cup equals 13,045.75289 grains per cubic meter. You can also use the swap control in the converter above to flip the direction instantly.
What is a grain per cubic meter?
Grain per Cubic Meter (gr/m3) is a unit of density.
What is a carat per cup?
Carat per Cup (ct/cup) is a unit of density.
Is the grain per cubic meter to carat per cup conversion exact?
Yes. Both grain per cubic meter and carat per cup are defined by fixed standards rather than physical artifacts, so the factor of 0.00007665329922 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.