In classical electromagnetism, polarization density (or electric polarization, or simply polarization) is the vector field that expresses the volumetric density of permanent or induced electric dipole moments in a dielectric material. When a dielectric is placed in an external electric field, its molecules gain electric dipole moment and the dielectric is said to be polarized.

Electric polarization of a given dielectric material sample is defined as the quotient of electric dipole moment (a vector quantity, expressed as coulombs*meters (C*m) in SI units) to volume (meters cubed). Polarization density is denoted mathematically by P; in SI units, it is expressed in coulombs per square meter (C/m²).

Polarization density also describes how a material responds to an applied electric field as well as the way the material changes the electric field, and can be used to calculate the forces that result from those interactions. It can be compared to magnetization, which is the measure of the corresponding response of a material to a magnetic field in magnetism.

Similar to ferromagnets, which have a non-zero permanent magnetization even if no external magnetic field is applied, ferroelectric materials have a non-zero polarization in the absence of external electric field.

An external electric field that is applied to a dielectric material, causes a displacement of bound charged elements.

A bound charge is a charge that is associated with an atom or molecule within a material. It is called "bound" because it is not free to move within the material like free charges. Positive charged elements are displaced in the direction of the field, and negative charged elements are displaced opposite to the direction of the field. The molecules may remain neutral in charge, yet an electric dipole moment forms.

For a certain volume element ${\displaystyle \Delta V}$ in the material, which carries a dipole moment ${\displaystyle \Delta \mathbf {p} }$, we define the polarization density P: $${\displaystyle \mathbf {P} ={\frac {\Delta \mathbf {p} }{\Delta V}}}$$

In general, the dipole moment ${\displaystyle \Delta \mathbf {p} }$ changes from point to point within the dielectric. Hence, the polarization density P of a dielectric inside an infinitesimal volume dV with an infinitesimal dipole moment dp is: