The gyroradius (also known as radius of gyration, Larmor radius or cyclotron radius) is the radius of the circular motion of a charged particle in the presence of a uniform magnetic field. In SI units, the non-relativistic gyroradius is given by
The angular frequency of this circular motion is known as the gyrofrequency, or cyclotron frequency, and can be expressed as
It is often useful to give the gyrofrequency a sign with the definition
In cgs-units the gyroradius
For relativistic particles the classical equation needs to be interpreted in terms of particle momentum :
For calculations in accelerator and astroparticle physics, the formula for the gyroradius can be rearranged to give
If the charged particle is moving, then it will experience a Lorentz force given by
Notice that the direction of the force is given by the cross product of the velocity and magnetic field. Thus, the Lorentz force will always act perpendicular to the direction of motion, causing the particle to gyrate, or move in a circle. The radius of this circle, , can be determined by equating the magnitude of the Lorentz force to the centripetal force as