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Cyclotron Frequency Calculator

Find how fast a charge orbits in a magnetic field.

Result

2.2866e+7 Hz
22.87 MHz

How it is calculated

A charged particle in a uniform magnetic field circles at f = |q| × B / (2π × m). Enter the charge q in coulombs, the field B in tesla and the mass m in kilograms. The tool takes the absolute value of the charge, so the sign does not matter for frequency. The result is shown in hertz in scientific notation and in MHz. Mass must be above zero and the charge cannot be zero. The speed and the radius of the orbit do not appear, as long as the particle is much slower than light.

Worked example

A proton (q = 1.602e-19 C, m = 1.6726e-27 kg) in a 1.5 T field. Numerator: 1.602e-19 × 1.5 = 2.403e-19. Denominator: 2π × 1.6726e-27 ≈ 1.0509e-26. Divide: 2.2866e+7 Hz, which is 22.87 MHz.

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Common mistakes

  • Entering the mass in atomic mass units or the charge in elementary charges. The engine needs kilograms and coulombs.
  • Entering the field in gauss. One tesla is 10,000 gauss, so convert first.
  • Confusing frequency f with angular frequency ω = qB/m. The angular value is 2π times larger.
  • Applying it to particles close to light speed. Relativistic mass increase lowers the real frequency, and this formula does not include it.

About this calculator

The cyclotron frequency is the rate at which a charged particle circles around magnetic field lines, given by f = qB / (2πm), where q is the particle's charge, B is the magnetic field strength, and m is its mass. Remarkably, this frequency doesn't depend on the particle's speed or the radius of its orbit — a faster particle just traces a wider circle in the same amount of time, which is the principle that made the original cyclotron particle accelerator possible.

Physicists and engineers use this formula to design cyclotron accelerators (used in nuclear physics research and medical isotope production), to interpret cyclotron resonance in mass spectrometers and plasma devices, and to understand charged-particle motion in the Van Allen belts and other astrophysical magnetic fields. Enter the charge, magnetic field, and mass to find the orbital frequency.

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