Explore spiral motion in uniform magnetic fields. Switch between particle presets or enter custom properties. Download results as CSV or PDF for reports fast.
For a charged particle moving in a uniform magnetic field, the perpendicular motion forms a circle. The Larmor radius (also called gyroradius) is:
rL = \( \dfrac{m\,v_\perp}{|q|\,B} \) and \( \omega_c = \dfrac{|q|B}{m} \)
| Particle | B (T) | Input | Pitch (deg) | Approx. Larmor radius (m) |
|---|---|---|---|---|
| Proton | 1.0 | v = 1.0×105 m/s | 90 | ~1.04×10-3 |
| Electron | 0.10 | E = 100 eV | 90 | ~3.4×10-4 |
| Alpha (He²⁺) | 2.0 | E = 10 keV | 45 | ~2.3×10-3 |
These examples assume simple uniform fields and idealized inputs.
The Larmor radius is the circular radius traced by the perpendicular component of a charged particle’s motion in a uniform magnetic field. A smaller radius indicates tighter gyromotion and stronger magnetic confinement. In this calculator, the radius is computed from mass, charge magnitude, magnetic field strength, and the perpendicular speed.
Because the radius is inversely proportional to the field, doubling B halves rL when all other inputs remain unchanged. This sensitivity is important in laboratory magnets, fusion devices, and space plasmas where field magnitude varies with position. The unit selector helps compare millimeter-scale radii to kilometer-scale drift orbits.
Only the perpendicular component v⊥ contributes to circular motion. The pitch angle θ sets v⊥ = v·sin(θ), so the radius approaches zero as θ → 0° and reaches its maximum at 90°. This is why the calculator restricts θ to 0–90 degrees for clarity.
The same parameters that set the radius also set the cyclotron angular frequency ωc = |q|B/m. For a given particle, higher B produces faster rotation and a smaller orbit. The output includes ωc, frequency f, and period T so you can connect spatial scales to time scales in diagnostics and simulations.
In velocity mode, you provide v directly and the calculator derives kinetic energy from E = ½mv². In energy mode, you provide kinetic energy in eV, keV, MeV, GeV, or joules, and the calculator converts energy to speed before applying the same Larmor-radius equation. Both routes should agree when the non‑relativistic assumption is valid.
At high energies, speed approaches the speed of light and the non‑relativistic energy–speed relation becomes inaccurate. Enabling relativistic correction in energy mode uses γ = 1 + E/(mc²) and v = c·√(1 − 1/γ²) to estimate speed. This improves consistency for fast electrons and high‑energy beams.
In plasmas, the Larmor radius helps judge whether particles are “magnetized” relative to gradients, turbulence, or device size. When rL is much smaller than characteristic length scales, guiding‑center approaches are often reasonable. In accelerators, the radius is linked to beam rigidity and how strongly magnets bend particle trajectories.
Use realistic signs and magnitudes: the radius uses |q|, so reversing charge changes rotation direction but not orbit size. Verify units—Tesla for B, kilograms for mass, coulombs for charge—and keep θ within the allowed range. Export CSV for spreadsheets and PDF for lab notes or quick sharing.
No. The radius depends on |q|. The sign only reverses the rotation direction around the magnetic field line, not the orbit size for the same speed and field.
It means the velocity is parallel to the magnetic field, so v⊥ is zero. The circular gyromotion vanishes and the computed Larmor radius tends toward zero.
The formula uses the magnitude of the field. A negative sign only indicates direction. The calculator treats B as a magnitude to avoid confusion and keep validation simple.
Enable it when the entered energy is high enough that the implied non‑relativistic speed approaches c, or when you see the warning suggesting relativistic effects. This is common for electrons above keV–MeV scales.
Yes. Select the J option in energy mode. The calculator then uses joules directly rather than converting from electron‑volt based units.
Large radii usually come from weak fields, heavy particles, or large perpendicular speeds. Check that B is in Tesla (not Gauss) and confirm your speed or energy is physically reasonable.
No. They are approximate, rounded values intended to demonstrate typical scales. Your computed result may differ slightly due to pitch angle, unit choices, and whether relativistic correction is enabled.
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.