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Density and Floating

How to calculate density and use Archimedes' principle to determine if objects float or sink.

Last updated: 21 January 2026

★★☆☆☆ Level 2DensityBuoyancyArchimedesFloatingsinking3 min read

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Density

Density measures how much mass is packed into a given volume.

Density

ρ=mV\rho = \dfrac{m}{V}

ρ = density (kg/m³ or g/cm³), m = mass (kg or g), V = volume (m³ or cm³)

Mass

m=ρ⋅Vm = \rho \cdot V

Volume

V=mρV = \dfrac{m}{\rho}

Density of water = 1 g/cm³ = 1000 kg/m³

Floating and Sinking

  • Object floats if its density < fluid density
  • Object sinks if its density > fluid density

Does a wooden block (density 0.7 g/cm³) float in water?

Wood density (0.7) < Water density (1.0) → floats.

Does a steel bolt (density 7.8 g/cm³) sink in water?

Steel density (7.8) > Water density (1.0) → sinks.

Buoyancy Force (Archimedes)

An object in a fluid experiences an upward buoyancy force equal to the weight of fluid displaced.

Fb=ρfluid⋅Vdisplaced⋅gF_b = \rho_{\text{fluid}} \cdot V_{\text{displaced}} \cdot g
Note

A ship floats because its average density (hull + hollow interior + air) is less than water, even though steel alone would sink.

Real world: The Dead Sea — floating without effort

The Dead Sea in the Middle East has a salt concentration of about 34% — nearly ten times saltier than normal seawater. This gives it a density of roughly 1.24 g/cm³, significantly higher than the human body's average density (~1.0 g/cm³). Visitors famously float on the surface with no effort and can even read a newspaper while lying back — the high-density water provides more than enough buoyant force to support them.

Real world: Hydrometer — testing battery acid and alcohol

A hydrometer is a floating glass tube with a weighted bulb at the bottom and a scale inside. It floats at different depths depending on the density of the liquid it is placed in. Car mechanics use hydrometers to check the density of battery acid (which falls as the battery discharges) and brewers use them to measure the density of fermenting beer to calculate alcohol content.

Real world: Helium balloon rising in air

A helium balloon rises because helium (density ≈ 0.16 kg/m³) is much less dense than air (density ≈ 1.2 kg/m³). The buoyant force from the displaced air exceeds the combined weight of the helium, the balloon skin, and the string — so the balloon floats upward. The same principle explains why hot-air balloons rise: heating air inside the envelope reduces its density below that of the cooler air outside.

Tip Where do you see density and floating in real life? The Dead Sea, hydrometers in garages, helium balloons at parties, icebergs in the ocean, and oil floating on water in your salad dressing — density differences are everywhere!

Practice Problems

A rock has mass 300 g and volume 120 cm³. Calculate its density.

Show answer
ρ = 300 ÷ 120 = 2.5 g/cm³. It is denser than water so it sinks.

A block of wax (density 0.9 g/cm³) is placed in water. Does it float or sink? Explain.

Show answer
0.9 < 1.0 (water) → it floats, with 90% submerged.