Cyclotron Frequency Calculator

About this calculator

The cyclotron frequency is the frequency at which a charged particle circles around magnetic field lines, given by f = q·B / (2π·m), where q is the particle's charge, B is the magnetic field strength, and m is its mass. Remarkably, at non-relativistic speeds this frequency depends only on the charge-to-mass ratio and field strength — not on the particle's speed or the radius of its circular path, which is what makes it possible to accelerate particles to ever-higher energies using a fixed driving frequency.

This relationship is the physical basis of the cyclotron particle accelerator, used in nuclear physics research and in medical facilities that produce radioisotopes for PET scans and proton therapy, and it underlies ion cyclotron resonance mass spectrometry (FT-ICR MS), an ultra-high-precision technique used by analytical chemists to identify molecules by mass. Physics students and plasma physicists also use the cyclotron frequency formula when studying charged-particle motion in magnetic fields, including in fusion reactor and space plasma research.