Volume in physics is the amount of three-dimensional space an object occupies. Whether you’re measuring a marble, a swimming pool, or a cloud of gas, volume tells you how much space that thing takes up. The standard SI unit is the cubic meter (m³), though liters and cubic centimeters are far more common in everyday life and lab work.
How Volume Is Measured
Because volume describes three-dimensional space, its units are always a length unit cubed: cubic meters, cubic centimeters, cubic inches, and so on. The metric system makes conversions straightforward. One cubic centimeter equals one milliliter. One thousand milliliters equals one liter. And one thousand liters equals one cubic meter. In the U.S. customary system, one gallon is defined as exactly 231 cubic inches.
The liter is technically just a special name for the cubic decimeter, a cube that’s 10 cm on each side. This was officially established by the 12th General Conference on Weights and Measures in 1964. For most practical purposes, you’ll see milliliters on medicine cups and beverage labels, liters for larger liquids, and cubic meters in construction or engineering.
Volume Formulas for Common Shapes
For regular geometric shapes, you can calculate volume directly from measurements. The simplest case is a rectangular box (or rectangular prism): multiply length × width × height. A cylinder uses the same idea but with a circular base: π × radius² × height. Here are the most useful formulas:
- Rectangular box: length × width × height
- Cylinder: π × radius² × height
- Sphere: (4/3) × π × radius³
- Cone: (1/3) × π × radius² × height
- Pyramid: (1/3) × base area × height
- Triangular prism: (1/2) × base × triangle height × prism length
Notice the pattern: prisms and cylinders use base area × height, while pyramids and cones are exactly one-third of that. A sphere is unique because it depends only on the radius, raised to the third power, which makes sense given that volume is inherently a “cubed” measurement.
Measuring Irregular Objects
A rock or a piece of jewelry doesn’t have neat geometric dimensions you can plug into a formula. The classic solution is water displacement, a technique rooted in Archimedes’ principle. You partially fill a graduated cylinder or overflow container with water, note the water level, then submerge the object completely. The rise in water level equals the object’s volume.
This works because Archimedes’ principle tells us that a completely submerged object displaces a volume of fluid exactly equal to its own volume. The shape doesn’t matter at all, only the total space the object takes up. It’s the same reason a crumpled ball of aluminum foil and a flat sheet made from the same foil would displace identical amounts of water: same material volume, different shape.
When reading liquid levels in a graduated cylinder, accuracy depends on reading the meniscus correctly. Most liquids form a slight curve where they meet the glass wall. You read the volume at the bottom of that curve, with your eyes level with the liquid surface. Looking from above or below introduces parallax error and can throw off your measurement.
How Volume Behaves Differently Across States of Matter
Solids and liquids have relatively fixed volumes. You can pour water from a tall glass into a wide bowl and its shape changes, but the volume stays the same. Solids are even more rigid. Gases, however, are a completely different story.
A gas has no fixed volume. It expands to fill whatever container you put it in, and its volume changes dramatically with pressure and temperature. Boyle’s law describes the inverse relationship between pressure and volume at constant temperature: squeeze a gas into half the space and its pressure doubles. Charles’s law captures the other side, showing that volume increases in direct proportion to temperature when pressure stays constant. Heat a balloon and it expands; cool it and it shrinks.
These behaviors are described by the ideal gas law, which treats gas particles as having negligible volume compared to the space they move through. In reality, every gas particle does occupy a tiny amount of space, which is why real gases deviate slightly from ideal behavior, especially at high pressures or low temperatures where particles are forced close together.
Volume, Mass, and Density
Volume is one-third of the most important triangle in introductory physics: density equals mass divided by volume. If you know any two of these quantities, you can find the third. A block of lead and a block of wood can have the same volume but wildly different masses because lead is far denser.
Rearranging the formula, mass equals density times volume. This is useful when you can’t easily weigh something but you can measure or calculate its volume and you know what material it’s made of. Astronomers use this approach to estimate the mass of planets and stars from their size and estimated composition.
In thermodynamics and engineering, you’ll sometimes encounter specific volume, which flips the density relationship. Specific volume is the volume per unit mass (1 divided by density). Instead of asking “how much mass fits in this space,” it asks “how much space does one unit of mass take up?” Steam tables, for instance, list specific volume because it’s more practical for calculating how gases behave in engines and turbines.
Temperature Changes Volume
Almost all materials expand when heated and contract when cooled. This is thermal expansion, and it applies to solids, liquids, and gases alike, though the effect is most dramatic in gases (as Charles’s law describes). For solids and liquids, the change is much smaller but still matters in engineering. Bridges have expansion joints specifically because the steel and concrete grow slightly in summer heat. Railroad tracks can buckle if they don’t have room to expand.
Over small temperature ranges, the volume change is proportional to both the temperature change and the object’s original volume. Different materials expand at different rates, which is why a glass jar can crack when you pour boiling water into it: the inside surface expands faster than the outside, creating stress. Pyrex and similar borosilicate glasses were designed with a very low expansion rate to resist exactly this kind of thermal shock.