Density Calculator

One formula, three arrangements

Density is ρ = m / V. Rearranged, mass is density times volume and volume is mass divided by density. The only thing that makes it fiddly in practice is units: grams per cubic centimeter, kilograms per cubic meter and pounds per cubic foot are all in common use, and they differ by factors of 1000 and 16.02 respectively. One gram per cubic centimeter is exactly 1000 kilograms per cubic meter, because a cubic meter holds a million cubic centimeters and a kilogram is a thousand grams.

Specific gravity and floating

Specific gravity is density expressed relative to water, which has a density very close to 1.000 g/cm³ at 4 °C. It is dimensionless, which is why it appears on hydrometers and in brewing, where the reading is compared against water rather than against an absolute standard. Anything with a specific gravity below 1 floats in water and anything above it sinks — ice at 0.917 floats, which is unusual, because most substances are denser as solids than as liquids. That one anomaly is why lakes freeze from the top down and why aquatic life survives winter.

Why hollow objects confuse the issue

A steel ship floats even though steel has a density around 7.85 g/cm³. The relevant figure is the average density of the whole object including any air it encloses, not the density of the material it is made from. Naval architecture is largely the business of keeping that average below 1. The same logic explains why a solid block of pumice floats and a pebble does not despite both being rock.

Density is not constant

Both mass and volume can change with conditions, and volume changes far more. Nearly all materials expand when heated, so density falls with temperature — which is what drives convection currents in air and water. Gases are the extreme case: their density depends on pressure and temperature so strongly that quoting a gas density without stating both is meaningless. Air at sea level is about 1.225 kg/m³ at 15 °C, and roughly a third of that at cruising altitude. Values for solids and liquids in tables are usually quoted at 20 or 25 °C for this reason.

Measuring volume honestly

Mass is easy to measure; volume is where errors creep in. For a regular solid, calculate it from dimensions. For an irregular one, displacement is the classical method — submerge it and measure the water pushed aside, which is exactly what Archimedes is supposed to have worked out in the bath. For powders and granular material, distinguish bulk density, which includes the air gaps between particles, from true density, which does not; the two can differ by a factor of two and quoting the wrong one is a common mistake.

Frequently Asked Questions