# Cyclotron Frequency Calculator

URL: https://speedycalculator.com/calculators/physics/cyclotron-frequency/
Last updated: 2026-10-30

> The cyclotron frequency calculator finds how fast a charged particle circles in a magnetic field, and the radius of its orbit for a given speed.

## Inputs

- Particle
- Mass m (kg, u (Da))
- Charge q (e, C)
- Magnetic field B (T, mT, µT, G, nT)
- Speed v (m/s, km/h, mph, ft/s, knots, km/s)

## Results

- Cyclotron frequency f
- Angular frequency ω
- Orbit radius
- Period

## Formula

```
f = |q|·B / (2π·m),  ω = |q|·B/m,  r = m·v / (|q|·B)
```

## Explanation

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

FieldWhat to enterParticleChoose one: Electron, Proton, Alpha particle, Deuteron …Mass mUnits: kg, u (Da)Charge qUnits: e, CMagnetic field BUnits: T, mT, µT, G, nTSpeed vUnits: 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-2815,245,186.45821.2545e-2715,245,186.45821.6726e-2715,245,186.45822.0908e-2715,245,186.45822.5089e-2715,245,186.45823.3452e-2715,245,186.4582

## 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.

## FAQ

**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.


## Sources

- [OpenStax – University Physics Volume 2](https://openstax.org/details/books/university-physics-volume-2)
- [HyperPhysics (Georgia State University)](http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html)