What is the Lorentz force?

The Lorentz force is the force exerted on a charged particle moving through a magnetic field. Its magnitude is F = qvB sin θ, where q is charge, v is speed, B is magnetic field strength, and θ is the angle between the velocity and field vectors. The direction is given by the right-hand rule.

What happens when θ = 0° or 180°?

When the velocity is parallel (0°) or anti-parallel (180°) to the magnetic field, sin θ = 0 so the force is zero. The particle continues in a straight line with no deflection.

What happens when θ = 90°?

At θ = 90° the force is maximum (F = qvB). The particle moves in a circular path perpendicular to the field — the basis of cyclotrons and mass spectrometers.

Why can the force be negative?

The sign reflects the charge sign. An electron (q = −1.6 × 10⁻¹⁹ C) experiences a force in the opposite direction to a proton under the same conditions. The magnitude |F| is what matters for speed; the sign determines direction.

Does this tool include the electric component of the full Lorentz force?

No. The full Lorentz force is F = q(E + v × B). This calculator covers only the magnetic term F = qvB sin θ. If an electric field is also present, calculate the electric force qE separately and add it vectorially.

What units should I use?

SI base units give the force in newtons: charge in coulombs (C), velocity in meters per second (m/s), and magnetic field in tesla (T). The dropdown converters handle microcoulombs, nanocoulombs, millitesla, and km/s automatically.

Lorentz Force Calculator

Name: Lorentz Force Calculator
Availability: InStock
Author: Nham Vu

Enter charge, velocity, magnetic field strength, and angle to compute the magnetic Lorentz force F = qvB sin θ instantly.

Inputs

Charge (q)

Velocity (v)

Magnetic Field (B)

Angle θ between v and B

Result

Fill in the inputs and press Calculate.

Formula Reference

F = q · v · B · sin(θ)

F — magnetic force (newtons, N)
q — particle charge (coulombs, C)
v — particle speed (m/s)
B — magnetic field strength (tesla, T)
θ — angle between v and B vectors (degrees)

sin θ vs Angle

Summary

Enter charge, velocity, magnetic field strength, and angle to compute the magnetic Lorentz force F = qvB sin θ instantly.

How it works

Enter the particle charge (q) in coulombs. Use negative values for electrons.
Enter the particle velocity (v) in meters per second.
Enter the magnetic field strength (B) in tesla.
Enter the angle θ between the velocity vector and the magnetic field in degrees.
The Lorentz force F = qvB sin θ is computed instantly and displayed with the formula breakdown.
Switch units using the dropdowns to work in µC/nC, km/s, mT, or µT.

Use cases

Solve introductory physics problems on charged particles in magnetic fields.
Verify homework or exam calculations for electromagnetism courses.
Explore how varying the angle affects the force magnitude.
Understand cyclotron and mass spectrometer operating principles.
Calculate forces on ions in plasma physics or particle accelerator contexts.
Compare force magnitudes for different charge carriers (proton vs. electron).

Frequently Asked Questions

Last updated: 2026-06-11 · Reviewed by Nham Vu