Lorentz Force Calculator (F = qvB & F = BIL)
By Santaji GadepatilinUpdated November 2, 2026
A charged particle moving through a magnetic field feels a force at right angles to both its velocity and the field, and a current-carrying wire feels the same force — the principle behind electric motors, loudspeakers and mass spectrometers. This Lorentz force calculator gives the force on a moving charge, the radius of its circular path and its cyclotron frequency, plus the force on a conductor.
How to use the Lorentz force calculator
For a moving charge, enter its charge number, speed, mass in atomic mass units, the magnetic flux density and the angle between velocity and field. You get the force, the radius of the circular (or helical) path and the cyclotron frequency. For a wire, enter the current and the length inside the field; the same B and angle are used.
Lorentz force formulas
F = |q| v B sin θ · r = m v sin θ ÷ (|q| B) · fc = |q| B ÷ (2π m)
Conductor: F = B I L sin θ
Example
A proton (1.007276 u, charge +e) moving at 2 × 10⁶ m/s at right angles to a 0.5 T field:
- F = 1.602 × 10⁻¹⁹ × 2 × 10⁶ × 0.5 = 1.6022 × 10⁻¹³ N
- r = 1.6726 × 10⁻²⁷ × 2 × 10⁶ ÷ (1.602 × 10⁻¹⁹ × 0.5) = 41.76 mm
- fc = 7.623 MHz
A 0.2 m wire carrying 5 A across the same field: F = 0.5 × 5 × 0.2 = 0.50 N.
Cyclotron frequency and radius in a 1 T field
The radius column is for a speed of 10⁶ m/s perpendicular to the field.
| Particle | Charge | Cyclotron frequency | Radius at 10⁶ m/s |
|---|---|---|---|
| Electron | -1 | 2.799e+04 MHz | 0.005686 mm |
| Proton | +1 | 15.25 MHz | 10.44 mm |
| Alpha particle | +2 | 7.675 MHz | 20.74 mm |
| Deuteron | +1 | 7.626 MHz | 20.87 mm |
Notes
- The formulas are non-relativistic; above about 10% of the speed of light use the relativistic momentum γmv.
- A velocity component parallel to B is unaffected, so the particle spirals along the field lines.
- Find the field of a coil or wire first with the magnetic field calculator.
Frequently asked questions
What is the Lorentz force formula?
F = q(E + v × B). With no electric field the magnitude is F = |q| v B sin θ, where θ is the angle between the velocity and the magnetic field.
What is the force on a current-carrying wire?
F = B I L sin θ. A 0.2 m conductor carrying 5 A at right angles to a 0.5 T field feels 0.5 N — the basic force in every electric motor.
Why do charged particles move in circles in a magnetic field?
The magnetic force is always perpendicular to the velocity, so it changes the direction but not the speed. The radius is r = m v⊥ ÷ (|q| B).
Which way does the force act?
Use the right-hand rule for positive charges (or conventional current) — fingers along v, curl towards B, thumb gives F. The force on an electron is in the opposite direction.