quantity

volume

The amount of three-dimensional space occupied by a substance.
10 related articles · 3 formulas

Description

Volume is the measure of the three-dimensional space that a substance or object occupies. It is a fundamental physical quantity, typically measured in cubic meters in the SI system, and is distinct from mass, which measures the amount of matter. Volume is an extensive property, meaning it scales with the size of the system, and it plays a crucial role in determining density, pressure, and other thermodynamic properties.

History

The concept of volume has been understood since antiquity, with early methods for measuring volumes of irregular objects attributed to Archimedes in the 3rd century BCE. The modern mathematical formalization came with the development of calculus by Newton and Leibniz in the 17th century.

How it works

For a regular solid, volume can be calculated from its geometric dimensions. For liquids and gases, it is often measured directly using graduated containers or by displacement. In physics, volume is a state variable in equations of state, such as the ideal gas law, where it relates to pressure and temperature. In more advanced contexts, volume can be defined in curved spacetime or in higher-dimensional spaces, where it may not behave intuitively.

In practice

Volume measurements are essential in fields ranging from medicine (dosage calculations) to engineering (fuel tank design) and physics (determining the density of celestial bodies).

Fun fact

In the context of the universe, the total volume of the observable universe is estimated to be about 4 × 10^80 cubic meters, yet it may be only a tiny fraction of the entire universe's volume.

Concept graph →

Formulas

$$\rho = \frac{m}{V}$$
Density is mass divided by volume.
What is in the formula
ρvariabledensity — density kilogram per cubic metre
mvariablemass — mass kilogram
Vvariablevolume — volume cubic metre
$$K = -V rac{dP}{dV}$$
Bulk modulus measures resistance to uniform compression.
What is in the formula
Kvariablebulk modulus of the material — bulk modulus pascal
Vvariablevolume of the material — volume cubic metre
Pvariablepressure applied to the material — pressure pascal
dP/dVoperatorinstantaneous rate of change of pressure as volume changes — derivative
$$\frac{dP}{dT} = \frac{\Delta S}{\Delta V}$$
Relates pressure and temperature changes along a phase boundary.
What is in the formula
Pvariablepressure — pressure pascal
Tvariabletemperature — temperature kelvin
ΔSvariableentropy change during phase transition — entropy joule per kelvin
ΔVvariablevolume change during phase transition — volume cubic metre
d/dToperatorderivative with respect to temperature — derivative

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