In physics, magnetic pressure is an energy density associated with a magnetic field. In SI units, the energy density ${\displaystyle P_{B}}$ of a magnetic field with strength ${\displaystyle B}$ can be expressed as

where ${\displaystyle \mu _{0}}$ is the vacuum permeability.

Any magnetic field has an associated magnetic pressure contained by the boundary conditions on the field. It is identical to any other physical pressure except that it is carried by the magnetic field rather than (in the case of a gas) by the kinetic energy of gas molecules. A gradient in field strength causes a force due to the magnetic pressure gradient called the magnetic pressure force.

In SI units, the magnetic pressure ${\displaystyle P_{B}}$ in a magnetic field of strength ${\displaystyle B}$ is

where ${\displaystyle \mu _{0}}$ is the vacuum permeability and ${\displaystyle P_{B}}$ has units of energy density.

In ideal magnetohydrodynamics (MHD) the magnetic pressure force in an electrically conducting fluid with a bulk plasma velocity field ${\displaystyle \mathbf {v} }$, current density ${\displaystyle \mathbf {J} }$, mass density ${\displaystyle \rho }$, magnetic field ${\displaystyle \mathbf {B} }$, and plasma pressure ${\displaystyle p}$ can be derived from the Cauchy momentum equation:

where the first term on the right hand side represents the Lorentz force and the second term represents pressure gradient forces. The Lorentz force can be expanded using Ampère's law, ${\displaystyle \mu _{0}\mathbf {J} =\nabla \times \mathbf {B} }$, and the vector identity

to give