Compute cyclotron frequency for charged particles in fields. Switch units, include relativistic effects, export results. Get clean outputs for labs, design, and study today.
The cyclotron (angular) frequency for a charged particle in a uniform magnetic field is:
If speed is known, the orbit radius follows: r = γmv / (|q|B).
Constants used: c = 299,792,458 m/s, e = 1.602176634×10⁻¹⁹ C.
| Case | Particle | B (T) | z | Motion input | f (Hz) | Notes |
|---|---|---|---|---|---|---|
| 1 | Proton | 1.50 | +1 | None | ≈ 2.29×107 | Classic frequency in a strong field. |
| 2 | Electron | 0.10 | -1 | β = 0.20 | ≈ 2.80×109 | Relativistic option slightly lowers f. |
| 3 | Alpha (He²⁺) | 2.00 | +2 | KE = 5 MeV | ≈ 1.53×107 | Energy defines γ and radius estimate. |
These values are illustrative and depend on the selected settings.
Article: Practical notes and reference values for interpreting cyclotron frequency results.
A charged particle in a uniform magnetic field feels the Lorentz force, bends into circular motion, and repeats the orbit at a steady rate. That rotation rate is the cyclotron frequency. This calculator reports angular frequency ω (rad/s), ordinary frequency f (Hz), and period T (s).
In the nonrelativistic limit, frequency is independent of speed and orbit size: f = |q|B/(2πm). For an electron, f ≈ 28.0 GHz per tesla. For a proton, f ≈ 15.2 MHz per tesla. These reference values help sanity‑check outputs for quick comparison across common units.
At high speeds, inertia increases and the rotation rate drops. The corrected form is f = |q|B/(2πγm), where γ = 1/√(1−β²). For β = 0.60, γ ≈ 1.25, so frequency falls about 20% versus the classic value.
Field strength sets the scale. Earth’s field is roughly 25–65 µT, so a proton cycles at about 380–990 Hz, while an electron cycles near 0.7–1.8 MHz. Typical lab magnets reach 0.1–2 T, giving proton frequencies from ~1.5 to ~30 MHz and electron frequencies from ~2.8 to ~56 GHz.
Changing particle type changes m and q. An alpha particle has charge +2e and mass about 4 proton masses, so its frequency is roughly half the proton frequency at the same B (≈7.6 MHz/T). Increasing charge state z scales frequency linearly when mass stays constant.
If you supply velocity, β, or kinetic energy, the calculator estimates orbit radius using r = γmv/(|q|B) and reports momentum p = γmv. For a proton at B = 1.5 T and v = 2×10⁷ m/s, the radius is on the order of centimeters, depending on γ.
Use Tesla, millitesla, microtesla, or gauss and keep units consistent. For mass, kilograms are direct, while atomic mass units (u) are convenient for ions. If you enter energy, MeV is common in accelerator work. The form flags non‑physical entries like β ≥ 1.
Cyclotron frequency supports magnet design, beam diagnostics, plasma physics, and resonance measurements. It is central to ion cyclotron resonance and helps interpret charged‑particle motion in space and laboratory plasmas. Exported CSV/PDF files make lab notebooks and reports easier to document.
No. The direction of rotation reverses with sign, but the magnitude of cyclotron frequency uses |q|. This calculator shows frequency based on absolute charge.
Use it when β is significant or when kinetic energy is high enough that γ differs from 1. As a rule, above β≈0.1 the shift can be noticeable for light particles.
Radius needs speed information. Provide velocity, β, or kinetic energy so the calculator can estimate γ and compute r = γmv/(|q|B).
Yes. Choose u for ions and MeV/c² for particle‑physics style masses. The tool converts inputs to kilograms internally before calculating ω, f, and T.
Select G for gauss. The calculator converts 1 G to 1×10⁻⁴ T automatically, so your results remain consistent across units.
For nonrelativistic motion of a free charged particle in a uniform magnetic field, they coincide in magnitude. In other contexts, Larmor can also refer to spin precession.
Use known benchmarks: electrons are about 28.0 GHz/T and protons about 15.2 MHz/T. Multiply by B in tesla and compare with your computed frequency.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.