A charged particle in a magnetic field moves in a circle at a frequency that doesn’t depend on its speed. Cyclotrons use this to accelerate particles; mass spectrometers and plasma physics rely on it too.
How to use the Cyclotron Frequency Calculator
- Particle
- Mass m
- Charge q
- Magnetic field B
- Speed v
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Choose the particle (or enter its mass and charge), the magnetic field and the speed.
Inputs explained
| Field | What to enter |
|---|---|
| Particle | Choose one: Electron, Proton, Alpha particle, Deuteron … |
| Mass m | Units: kg, u (Da) |
| Charge q | Units: e, C |
| Magnetic field B | Units: T, mT, µT, G, nT |
| Speed v | Units: m/s, km/h, mph, ft/s, knots, km/s |
What each result means
- Cyclotron frequency f = [q]×[Magnetic field B]÷(2×pi×[m])
- Angular frequency ω = [q]×[Magnetic field B]÷[m]
- Orbit radius = [m]×[Speed v]÷([q]×[Magnetic field B])
- Period = 2×pi×[m]÷([q]×[Magnetic field B])
Example values
How the main result changes when Mass m changes and everything else stays at the example values above:
| Mass m (kg) | Cyclotron frequency f (Hz) |
|---|---|
| 8.3631e-28 | 15,245,186.4582 |
| 1.2545e-27 | 15,245,186.4582 |
| 1.6726e-27 | 15,245,186.4582 |
| 2.0908e-27 | 15,245,186.4582 |
| 2.5089e-27 | 15,245,186.4582 |
| 3.3452e-27 | 15,245,186.4582 |
Formula
f = |q|·B / (2π·m), ω = |q|·B/m, r = m·v / (|q|·B)
Worked example
Inputs — Particle: Proton; Magnetic field B: 1 T; Speed v: 1,000,000 m/s.
Results — Cyclotron frequency f = 15,245,186.45821 Hz; Angular frequency ω = 95,788,331.559436 rad/s; Orbit radius = 0.01044 m; Period = 65.59447 ns.
Key terms
- Larmor radius
- Radius of a charged particle's circular orbit.
Frequently asked questions
Why doesn't the frequency depend on speed?
Faster particles move in bigger circles, taking the same time.
What is the electron cyclotron frequency at 1 T?
About 28 GHz.
How do cyclotrons accelerate particles?
An alternating voltage at the cyclotron frequency kicks them each half-turn.
What limits cyclotrons?
Relativistic mass increase at high speeds.