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A tiny steel pebble drops straight to the bottom of an ocean, but a massive steel cruise ship weighing 100,000 tons floats effortlessly on top of the waves.
The secret to whether something floats or sinks isn't total massβ€”it is all about how tightly that mass is packed into its volume.

What Is Density?

Density is defined as the mass of a substance contained within a unit volume, represented by the Greek letter ρ\rho (rho).
Because it measures mass divided by space occupied, the mathematical formula is:
ρ=mV\rho = \frac{m}{V}
In the standard International System of Units (SI), mass mm is measured in kilograms (kg\text{kg}) and volume VV in cubic meters (m3\text{m}^3), making the standard unit of density kg/m3\text{kg/m}^3.
In laboratory chemistry, density is often expressed in g/cm3\text{g/cm}^3, where pure liquid water at 4∘C4^\circ\text{C} has a density of exactly 1.0 g/cm31.0\,\text{g/cm}^3 (or 1,000 kg/m31{,}000\,\text{kg/m}^3).
Around 250 BCE, the Greek polymath Archimedes realized he could test if King Hiero's crown was pure gold by submerging it in water to measure its exact volume and compare its density against known gold.
How do we convert between these common units when solving physics problems? Let's walk through the math.

Converting Density Units

Since 1 kg=1,000 g1\,\text{kg} = 1{,}000\,\text{g} and 1 m3=(100 cm)3=1,000,000 cm31\,\text{m}^3 = (100\,\text{cm})^3 = 1{,}000{,}000\,\text{cm}^3, converting from g/cm3\text{g/cm}^3 to kg/m3\text{kg/m}^3 requires multiplying by 1,0001{,}000.