Density is a physical quantity describing how much mass is contained in a given volume. It is defined as density equals mass divided by volume, written rho = m divided by V. The SI unit is kilograms per cubic metre, kg per m3, although grams per cubic centimetre, grams per millilitre, and other units are common in particular contexts.
Density is an intensive property, meaning that for a homogeneous material under specified conditions it does not depend on the total amount of material present. A sample containing twice as much of the same homogeneous substance has twice the mass and approximately twice the volume, so its density remains the same. Density provides a way to distinguish materials because substances often have characteristic density ranges, although density can change with temperature, pressure, composition, phase, and structure. It is therefore not simply an intrinsic constant in every circumstance.
The microscopic origin of density is connected to how much matter is packed into a given region of space. In a solid, atoms or molecules are constrained into a relatively stable structure, while in liquids they remain closely packed but can move relative to one another. Gases generally have much lower densities because their particles are widely separated compared with their dimensions.
The density of a gas can change dramatically with pressure and temperature, whereas liquids and solids are often much less compressible under ordinary conditions. At the atomic level, density depends on both the masses of constituent particles and the spacing and arrangement of those particles. Crystal structure can therefore affect the density of a solid even when its chemical composition is the same. Different allotropes or polymorphs of a substance can have different densities because their atoms are arranged differently.
Density varies with temperature because thermal expansion or contraction changes volume. For many materials, heating causes expansion and therefore reduces density if mass remains constant. Water exhibits an important exception to simple thermal expansion behaviour over a limited temperature range. Liquid water reaches maximum density near 4 degrees Celsius at atmospheric pressure, and its density decreases as it approaches freezing. Ice is less dense than liquid water because its crystalline structure contains a relatively open arrangement of water molecules.
This is why ice floats on liquid water and why lakes in cold climates can freeze from the surface downward rather than freezing uniformly from the bottom upward. Pressure can also influence density, particularly for gases and under extreme conditions for liquids and solids. Consequently, scientific density values should be associated with relevant temperature, pressure, composition, and phase conditions.
Density is central to fluid mechanics because it influences buoyancy, pressure variation, inertia, momentum transport, and flow behaviour. Hydrostatic pressure in a fluid increases with depth according to the density dependent relation Delta p = rho gh under appropriate assumptions. Two fluids of different densities therefore develop different pressure differences over the same vertical distance.
Density also affects whether an object tends to float or sink when compared with the surrounding fluid, although the full condition depends on the object's average density and how it displaces fluid. In a mixture, density may vary spatially if composition is nonuniform. Density stratification can occur in oceans, lakes, and atmospheres and can influence convection and mixing. Temperature and salinity differences in seawater, for example, produce density differences that contribute to large scale ocean circulation.
Density should be distinguished from closely related quantities such as specific volume, specific gravity, mass concentration, and weight density. Specific volume is the volume per unit mass and is the reciprocal of density for a homogeneous material. Specific gravity is the ratio of a substance's density to the density of a chosen reference substance, often water for liquids and solids, and is dimensionless.
Weight density, sometimes called specific weight, is weight per unit volume and equals rho g near a location where gravitational acceleration is g. Mass concentration describes the amount of a particular component per volume of a mixture and is not necessarily the same as the total density. These distinctions matter because using the wrong quantity can produce incorrect calculations or misleading comparisons.
Density is measured using different techniques depending on the material and required precision. A simple method is to measure mass with a balance and volume geometrically, but irregular objects may require displacement methods. A pycnometer can determine density of liquids or finely divided solids with high precision, while hydrometers estimate liquid density through buoyancy. Modern instruments can determine density using oscillating tubes, X ray methods, helium pycnometry, or other specialised techniques.
For gases, pressure and temperature measurements can be combined with an equation of state to estimate density. Measurement uncertainty can arise from errors in mass, volume, temperature, pressure, calibration, trapped air, surface tension, evaporation, or sample composition. Reporting density without specifying measurement conditions can therefore be insufficient for technical work.
Density has many applications outside basic mechanics. Geologists use density to characterise rocks and minerals and to interpret subsurface structures. Oceanographers use temperature and salinity dependent density to study water masses and circulation. Atmospheric scientists use density in fluid dynamics and weather models. Engineers use density when calculating loads, buoyancy, flow rates, fuel requirements, material selection, and structural properties. In chemistry and manufacturing, density can indicate composition, concentration, purity, or process changes. In medicine, imaging methods can exploit differences in tissue density or related physical properties. Density can also be estimated statistically from a distribution of data points, but statistical density is a different mathematical concept from physical mass density despite the shared terminology.
Density is not the same thing as heaviness. An object can have a large mass because it is large while having a relatively low density, whereas a small object can have a much greater density. Similarly, an object's average density can differ from the density of the material from which its walls are constructed if the object contains cavities or lower density material. This distinction is crucial for understanding floating objects such as ships.
A steel block has a density much greater than water and tends to sink, while a hollow steel ship can have an average density lower than water because its total mass is distributed over a large enclosed volume. Density is therefore a property that must be considered together with geometry, composition, phase, and environmental conditions when predicting physical behaviour.
