Density

A block of wood and a rock of roughly the same size feel very different when you lift them. Both are "one big lump", so why the gap? Because they pack different amounts of mass into each cubic centimetre. That crowdedness is called density.

Density = mass ÷ volume

Density answers the question: how much mass sits in each unit of volume.

$\rho = \dfrac{m}{V}$

Here m is the mass, V the volume, and ρ (the Greek letter rho) the density. The common unit is grams per cubic centimetre (g/cm³): grams packed into each 1 cm³.

Try it: the density of a rock

A rock has a mass of 500 g; dipping it in a measuring cylinder displaces 250 cm³ of water. Density = $500 \div 250 = 2$ g/cm³. Every cubic centimetre of this rock weighs 2 grams — twice as heavy as the same volume of water.

Equal volume, fair comparison

"Rock is heavier than wood" is loose talk: a pebble weighs less than a wooden beam. Density restates the question fairly — which weighs more in the same volume. 1 cm³ of water weighs 1 g, 1 cm³ of rock about 2 g, 1 cm³ of wood only about 0.5 g. With volume locked, density does the deciding. A balloon drifts skyward while an iron nail drops — same story, equal volumes.

Water is a built-in ruler

Pure water at 4 °C has a density of exactly 1 g/cm³, which makes it a perfect yardstick:

Materials denser than 1 sink in water: rocks, iron, most metals;
Materials less dense than 1 float: wood, ice (about 0.9), cooking oil (about 0.9).

Honey runs about 1.4 — thicker and heavier than water; petrol about 0.7 — lighter than water, which is why an oil slick always rides on top.

Try it: does the block float?

A wooden block has a mass of 60 g and a volume of 100 cm³. Density = $60 \div 100 = 0.6$ g/cm³ — less than water's 1, so it floats. Steel ships stay afloat by the same trick: their hulls are mostly air, so the ship's average density is smaller than water's.

Converting units without panic

Density comes in two unit systems, g/cm³ and kg/m³, joined by 1 g/cm³ = 1000 kg/m³. Nothing mysterious: 1 m³ = 100 × 100 × 100 = 1000000 cm³, and if each cubic centimetre holds 1 g, one cubic metre holds 1000000 g — exactly 1000 kg.

Water's density is therefore 1000 kg/m³ — one tonne per cubic metre. Memorise once, use in both systems. Try another: iron is about 7.9 g/cm³, which reads 7900 kg/m³ — the shortcut is sliding the decimal point three places right.

Density is a material's fingerprint

Density depends on the material, hardly on the size: a tiny gold nugget and a gold bar share the same density (about 19.3 g/cm³). Measure the density and you can often identify the substance — the classic way to tell solid gold from gold-plated.

Density is the ID card of the material world. It is a close cousin of Pressure — liquid pressure is computed from depth and density. For a refresher on mass and volume units, revisit Metric Units & Conversion; for how to measure volume, see Volume.

Check yourself

Quick quiz

1. An object has a mass of 500 g and a volume of 250 cm³. What is its density?
2. A wooden block of density 0.6 g/cm³ is placed in water. It will…
3. 1 g/cm³ equals how many kg/m³?