mass density — from formula anatomyMass density (often simply 'density') is a physical property defined as mass per unit volume, typically expressed in kilograms per cubic meter (kg/m³) in SI units. It describes how tightly matter is packed in a substance. Density is a fundamental parameter in physics because it appears in equations for fluid dynamics, buoyancy, wave propagation, and gravitational interactions. It varies with temperature and pressure for most materials, and is crucial for identifying substances and predicting their behavior.
The concept of density dates to antiquity — Archimedes' principle (3rd century BCE) used density to determine whether a crown was pure gold. The modern quantitative definition emerged with the development of precise measurement and the metric system in the 18th century.
Density is calculated by dividing an object's mass by its volume. For a homogeneous material, it is a single value; for composites or mixtures, an average density can be defined. In fluids, density differences drive convection and stratification; in solids, density relates to atomic packing and bond strength. The concept extends to 'mass density' in contrast to 'number density' (particles per volume) or 'charge density' (charge per volume), each serving distinct analytical roles.
Essential in engineering for material selection, in geology for identifying minerals, in meteorology for air density affecting weather, and in medicine for bone density scans.
The density of water at 4°C is exactly 1000 kg/m³, which historically defined the kilogram — a liter of water was its mass standard.
| t_ff | variable | free-fall time — time second |
| G | variable | gravitational constant — gravitational constant cubic metre per kilogram per second squared |
| ρ | variable | mass density — mass density kilogram per cubic metre |
| r_H | variable | Accretion horizon radius — radius metre |
| \dot{M} | variable | Mass accretion rate — mass flow rate kilogram per second |
| \rho | variable | Mass density of accreting material — mass density kilogram per cubic metre |
| c_s | variable | Sound speed in accreting material — speed metre per second |
| \mathcal{R} | variable | Ricci scalar — ricci scalar per metre squared |
| \Lambda | variable | Cosmological constant — cosmological constant per metre squared |
| \rho | variable | Mass density — mass density kilogram per cubic metre |
| \Theta^i_j | variable | Expansion tensor — expansion tensor per second |
| \Theta | variable | Expansion scalar — expansion scalar per second |
| G | constant | Newton's constant of gravitation — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared |
| Ṁ_out | variable | Mass outflow rate — mass flow rate kilogram per second |
| ρ | variable | Mass density of the outflowing material — mass density kilogram per cubic metre |
| v | variable | Flow velocity perpendicular to the area — velocity metre per second |
| A | variable | Cross-sectional area through which material flows — area square metre |
| v_A | variable | Alfvén wave speed — velocity metre per second |
| B | variable | magnetic field strength — magnetic field strength tesla |
| ρ | variable | mass density — mass density kilogram per cubic metre |
| B | variable | Magnetic field strength — magnetic field strength tesla |
| v | variable | Characteristic velocity of plasma flow — velocity metre per second |
| ρ | variable | Mass density of the plasma — mass density kilogram per cubic metre |
| √ | operator | Takes the square root of the argument — square root |
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