Density Calculator Guide: Mass Volume and Density Relationships

Density is mass divided by volume, written as the formula p = m / V, and it is one of the few physical quantities you can use to identify a material without knowing anything else about the sample. Gold has a density of 19.3 g/cm3 regardless of whether you are holding a coin or a bar, which is exactly why jewelers and pawn shops still use density tests to catch fakes.

The Formula and Its Two Rearrangements

Density equals mass divided by volume: p = m / V. Rearranged, mass equals density times volume (m = p x V), and volume equals mass divided by density (V = m / p). If you know any two of the three values, you can find the third. For example, a block of aluminum with a volume of 50 cm3 and a known density of 2.7 g/cm3 has a mass of 50 x 2.7 = 135 grams. If instead you weighed an unknown metal block at 135 grams and measured its volume at 50 cm3, dividing gives you 2.7 g/cm3, close enough to aluminum's known density to identify the metal.

Common Material Densities Worth Memorizing

Why Ice Floats and Lead Sinks

Anything less dense than water (below 1.00 g/cm3) floats in it, and anything denser sinks. Ice is a rare case of a solid being less dense than its own liquid form, at 0.92 g/cm3 versus water's 1.00 g/cm3, which is why ice cubes float instead of settling at the bottom of a glass. This is also why icebergs show only about 8-10% of their volume above the waterline: the ratio of ice density to seawater density (roughly 1.025 g/cm3 for seawater) determines exactly how much stays submerged, following Archimedes' principle of buoyancy.

Unit Conversions You Will Actually Need

Density is commonly expressed in g/cm3, kg/m3, or g/mL (g/cm3 and g/mL are numerically identical since 1 cm3 equals 1 mL). To convert g/cm3 to kg/m3, multiply by 1,000, since there are 1,000,000 cm3 in a cubic meter but only 1,000 grams in a kilogram. So water's density of 1 g/cm3 becomes 1,000 kg/m3, and gold's 19.3 g/cm3 becomes 19,300 kg/m3. Mixing up these unit systems is a common source of errors that are off by a factor of 1,000, so always double check which unit a density value was reported in before plugging it into a formula.

Using Density to Detect a Fake

The classic gold test: a genuine 1 oz (31.1 gram) gold coin has a volume of 31.1 / 19.3 = 1.61 cm3. If you submerge that coin in water and it displaces only 1.4 cm3, something is wrong, since a real gold coin of that mass should displace 1.61 cm3. A lower displacement than expected for the stated mass means the coin is denser than gold's known value would allow for that mass, or more likely, the coin is not solid gold and contains a lighter alloy core, since counterfeiters often use tungsten (19.25 g/cm3, remarkably close to gold) specifically to defeat this exact test.

Density in Everyday Engineering Decisions

• Shipping companies calculate dimensional weight using volume and a standard density factor to decide whether to bill by actual weight or box size.
• Concrete mix design targets a specific density (around 2,400 kg/m3 for standard concrete) to ensure structural strength calculations hold up.
• Fuel is often sold by volume but taxed or measured by mass in aviation, where jet fuel density (around 0.8 kg/L) shifts with temperature and must be recalculated before every flight for accurate fuel-load planning.

Calculate Density in Seconds

Our free density calculator solves for mass, volume, or density whenever you know the other two values, with unit conversion built in so you never have to worry about g/cm3 versus kg/m3 mismatches.