Cyclotron Frequency Calculator
Frequency, period and gyroradius of a charged particle circling in a magnetic field — electrons, protons, alpha particles or a custom ion — with the relativistic correction.
How it works
f = qB ÷ (2πm); r = p ÷ (qB) = γmv ÷ (qB); relativistic f = qB ÷ (2πγm)
A charge in a uniform magnetic field moves in a circle whose frequency depends only on q/m and B — not on speed — which is what lets a cyclotron accelerate particles with a fixed-frequency voltage: faster particles simply trace bigger circles in the same time. That holds until relativity increases the effective mass, which is why cyclotrons top out around tens of MeV for protons and synchrocyclotrons or synchrotrons take over. The same physics sets electron gyration in plasmas, magnetrons, and ion cyclotron resonance mass spectrometers.
Worked example
A proton in 1.5 T: f = 22.9 MHz. At 10 MeV it moves at 14.5% of c with a 30.6 cm orbit; γ = 1.011 lowers the frequency about 1%.
Frequently asked questions
Why does the frequency not depend on speed?
Faster particles feel a larger force and follow a larger circle; the two effects cancel exactly in the non-relativistic limit.
What is the electron cyclotron frequency in Earth’s field?
About 1.4 MHz in 50 µT — the ordinary-mode cutoff radio scientists see in the ionosphere.
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This calculator is for educational purposes. Double-check important results before acting on them.