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Lorentz Force Calculator

Enter charge, fields, velocity and angle to find the Lorentz force.

How it is calculated

Inputs are in SI units: charge q in coulombs, electric field E in V/m, speed v in m/s, magnetic field B in tesla, and the angle θ between v and B in degrees (90 if left blank). The tool computes Felectric = q·E and Fmagnetic = q·v·B·sin θ, then adds them: F = qE + qvB·sin θ, in newtons. It treats both forces as acting along one line, so the total is a plain signed sum and not a full vector sum. Negative values give negative forces. Very small forces, such as on single electrons, are printed in scientific notation, for example 8.026 × 10−14 N.

Worked example

A charge of 0.002 C moves at 20 m/s through a field with E = 500 V/m and B = 0.3 T, at θ = 30° to B. The electric force is 0.002 × 500 = 1.000000 N. The magnetic force is 0.002 × 20 × 0.3 × sin 30° = 0.012 × 0.5 = 0.006000 N. Adding the two gives a total Lorentz force of 1.006000 N. The electric part dominates here, because at 20 m/s the magnetic term is small.

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Common mistakes

  • Entering the charge in microcoulombs or elementary charges without converting. The field expects coulombs, so one electron is 1.602e-19 and 2 mC is 0.002.
  • Typing the angle between velocity and the magnetic field in radians. It is read in degrees, and sin 30° is 0.5 while sin of 30 radians is not.
  • Using the angle to the electric field. θ is only the angle between v and B; the electric term does not depend on it.
  • Forgetting the sign of the charge. A negative charge flips both terms, so −0.002 C gives −1.006000 N for the example.
  • Expecting a full 3D vector sum. The tool adds the two magnitudes as if the electric and magnetic forces point along the same line, so for crossed fields work out the directions yourself.

About this calculator

The Lorentz force law describes the total electromagnetic force on a charged particle: F = qE + qv×B, which for a velocity at angle θ to the magnetic field reduces to a magnitude of F = qE + qvB·sin(θ). The electric-field term always acts along the field direction, while the magnetic-field term acts perpendicular to both the particle's velocity and the field — which is why it curves a moving charge's path instead of speeding it up or down.

This single equation underlies how charged particles behave in everything from a CRT electron beam to a mass spectrometer to the magnetic confinement in a tokamak. Physics students, electrical engineers, and plasma and accelerator physicists use it to size deflection fields, predict particle trajectories, and design components like velocity selectors and magnetic lenses.

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