The Magnetic Prandtl number (Pr_m) is a dimensionless quantity occurring in magnetohydrodynamics which approximates the ratio of momentum diffusivity (viscosity) and magnetic diffusivity.^[1] It is defined as:

${\displaystyle \mathrm {Pr} _{\mathrm {m} }={\frac {\mathrm {Re_{m)) }{\mathrm {Re} ))={\frac {\nu }{\eta ))={\frac {\mbox{viscous diffusion rate)){\mbox{magnetic diffusion rate))))$

where:

• Re_m is the magnetic Reynolds number
• Re is the Reynolds number
• ν is the momentum diffusivity (kinematic viscosity)
• η is the magnetic diffusivity

At the base of the Sun's convection zone the Magnetic Prandtl number is approximately 10⁻²,^[2] and in the interiors of planets and in liquid-metal laboratory dynamos is approximately 10⁻⁵.