What Is Density in Physics? Mass, Volume, and the Density Formula

The density formula is density equals mass divided by volume. In SI units, mass is measured in kilograms, volume in cubic metres, and density in kilograms per cubic metre. In school problems, you may also see grams per cubic centimetre, especially for smaller objects and materials.

Suppose a block has a mass of 600 grams and a volume of 200 cubic centimetres. Divide 600 by 200 and you get a density of 3 grams per cubic centimetre. If another block has the same volume but a mass of only 200 grams, its density is 1 gram per cubic centimetre. The first block contains more mass in the same amount of space.

This calculation is the central answer to what density in physics is. Density is not the same as mass, and it is not the same as weight. A large object made from a low-density material can have more total mass than a tiny object made from a dense material. Density compares mass with volume.

Under the same conditions, a pure substance often has a characteristic density. That makes density useful for identifying or comparing materials. Aluminium is less dense than iron, for example, so two equal-sized solid pieces would not have the same mass. The iron piece would contain more mass in the same volume.

Temperature can affect density because substances expand or contract. Most materials become slightly less dense when heated because their particles spread farther apart while the amount of matter stays the same. Gases show especially large density changes when temperature or pressure changes.

When learning about density in physics, it helps to imagine a fixed box. Ask how much mass would fit into that same box for each material. A denser substance would place more mass inside the fixed volume.

For a regular solid, measure its dimensions and calculate its volume using the correct geometric formula. Then measure its mass with a balance and divide. For an irregular object, you can often find volume by water displacement. Submerge the object in a measuring cylinder and record how much the water level rises, as long as the object does not dissolve or react with the water.

Liquids can be measured by finding the mass of a known volume. First measure the empty container, then the container with the liquid, and subtract to get the liquid's mass. Divide that mass by the measured volume.

Units deserve care. One cubic centimetre is not the same as one cubic metre, and volume conversions involve powers of three. If a question gives mass in grams and volume in cubic centimetres, you can often keep those units together and report grams per cubic centimetre unless SI units are required. Density also connects to floating, but density alone is not the whole story for every shaped object. Comparing average density with the surrounding fluid gives a useful clue. Revising density in physics first makes buoyancy easier to understand later.

Most liquids become denser as they cool and denser still when they freeze, so their solid form sinks. Water behaves differently. As it cools it does get denser, but only down to about 4 degrees Celsius, where it reaches its maximum density. Below that it expands slightly, and when it freezes the molecules lock into an open, hexagonal arrangement held together by hydrogen bonds. Ice is therefore about nine percent less dense than liquid water, which is why ice cubes float and icebergs show only a small part of their bulk above the surface.

This small oddity has large consequences. In winter, a lake cools from the surface downwards until the deeper water sits at about 4 degrees. Colder water then stays on top, and ice forms as a floating lid that insulates the water beneath it, so fish and other organisms survive in the liquid layer below. The same expansion is less welcome elsewhere: water that freezes in cracks can split rock apart, and frozen pipes burst because the ice needs more room than the water it came from.

According to a story told by the Roman writer Vitruvius, King Hiero of Syracuse suspected that a goldsmith had mixed silver into a gold crown, and asked Archimedes to find out without damaging it. Density gives the answer. Gold has a density of about 19.3 grams per cubic centimetre and silver about 10.5. A pure gold crown of 1,000 grams would have a volume of about 52 cubic centimetres. If 300 grams of that were silver, the volume would rise to about 65 cubic centimetres, so the crown would displace roughly 13 cubic centimetres more water than an equal mass of gold.

Historians doubt the famous bathtub detail, and Galileo pointed out in 1586 that measuring such a small rise in water level would have been very hard. He suggested a cleverer method Archimedes could have used. Hang the crown and an equal mass of pure gold from opposite ends of a balance, so they balance in air, then lower both into water. The less dense crown has more volume, so it receives a larger upward push from the water and rises, tipping the balance. This turns a tiny volume difference into an obvious movement, and it relies on buoyancy rather than precise measuring.

Density can reveal what lies inside objects you cannot open. In 1798 Henry Cavendish used a delicate torsion balance to measure the tiny gravitational pull between lead spheres, and from it worked out the average density of the whole Earth, about 5.5 grams per cubic centimetre. That was a puzzle, because the rocks of the crust that you can pick up and test are only around 2.7 to 3 grams per cubic centimetre. If the surface is light but the planet as a whole is dense, something far denser must lie deeper down, and the iron-rich core is now known to fill that role.

The same reasoning works across the solar system. Divide a planet's mass, found from the orbits of its moons or passing spacecraft, by its volume, found from its measured size, and you get its average density. Saturn comes out at roughly 0.7 grams per cubic centimetre, less than water, because it is made mostly of hydrogen and helium. That does not mean Saturn would float in some giant bathtub in any real sense, but it tells astronomers it is a gas giant rather than a rocky world. Average density, not the material at the surface, is what such calculations measure.

Density is mass per unit volume, found by dividing mass by volume. Density lets you compare how tightly mass is packed in different materials. Measure mass and volume carefully, keep units consistent, and remember that density is a material comparison rather than simply another word for heaviness.