What is the formula for Cyclotron Frequency?

The Cyclotron Frequency formula is f = q × B / (2π × m), where f—Cyclotron frequency (Hz); q—Particle charge (C); B—Magnetic flux density (T); m—Particle mass (kg).

Cyclotron Frequency

Q: How do you calculate Cyclotron Frequency?

Use the formula f = q × B / (2π × m). A charged particle moving in a magnetic field circles at the cyclotron frequency, which depends only on the charge-to-mass ratio and the field strength—not on the particle’s speed or orbit radius. Enter the values you know in the calculator above and it solves for the remaining variable.

f = q · B / (2π · m)

Calculator

Frequency

Charge

Flux Density

Particle Mass

Result

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Formula

f = q × B / (2π × m)

Description

A charged particle moving in a magnetic field circles at the cyclotron frequency, which depends only on the charge-to-mass ratio and the field strength—not on the particle’s speed or orbit radius. This frequency-independence of energy is what makes cyclotron particle accelerators and electron-cyclotron-resonance sources work, and it sets the resonance used in mass spectrometry.

Variables

f — Cyclotron frequency (Hz)
q — Particle charge (C)
B — Magnetic flux density (T)
m — Particle mass (kg)

Practical Notes

For an electron (q/m ≈ 1.76×10¹¹ C/kg), the cyclotron frequency is about 28 GHz per tesla. The orbit radius r = m·v/(q·B) grows with speed even though the frequency stays fixed.

Related Concepts

All Fields & Electromagnetism formulas →

Coulomb’s Law Electric Field of a Point Charge Electric Potential of a Point Charge Gauss’s Law (Electric Flux) Lorentz Magnetic Force Force on a Current-Carrying Wire Force Between Parallel Wires Magnetic Field of a Straight Wire

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