Lorentz Force Calculator
Find the complete electromagnetic force on a moving charge given its charge, velocity, and the surrounding electric and magnetic fields.
C
Total Lorentz force on the charge
How does this calculator work?
The Lorentz force is F = q(E + v x B). Enter the charge plus the electric field, velocity, and magnetic field as 3D vectors. The calculator computes the cross product v x B, adds E, scales by q, and returns the three force components Fx, Fy, Fz and the total magnitude |F| in newtons.
Formula
How this is calculated
The Lorentz force is the total electromagnetic force on a point charge q moving with velocity v through an electric field E and magnetic field B. Enter the scalar charge in coulombs and each of the three field/velocity quantities as a 3-component vector (x, y, z), separated by commas or spaces. Electric field is in volts per metre (V/m), velocity in metres per second (m/s), and magnetic field in teslas (T).
The magnetic contribution comes from the cross product v x B = (vy*Bz - vz*By, vz*Bx - vx*Bz, vx*By - vy*Bx), which is perpendicular to both v and B. This is added component-wise to the electric field E, and the whole sum is scaled by the charge q to give the force vector F = q(E + v x B). Each component is reported in newtons (N), along with the magnitude |F| = sqrt(Fx^2 + Fy^2 + Fz^2).
A negative charge simply reverses the direction of every force component. The purely magnetic part of the force does no work because it is always perpendicular to the velocity, so it changes direction but not speed; the electric part can do work. If any vector does not contain exactly three finite numbers, the result is withheld.
Frequently asked questions
Because it is built from the cross product v x B, which is by definition perpendicular to both v and B. This means the magnetic force can curve a charge's path but never change its speed or kinetic energy.
Use the signed charge in coulombs (C). A proton is about +1.602e-19 C and an electron is about -1.602e-19 C. A negative charge flips the direction of the resulting force vector.
Set E to "0, 0, 0". The force then reduces to the purely magnetic term F = q (v x B), which is zero whenever v is parallel to B.
Also known as
TG we-Calculate Editorial Team. (2026). Lorentz Force Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/lorentz-force-calculator
TG we-Calculate Editorial Team. "Lorentz Force Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/lorentz-force-calculator.
TG we-Calculate Editorial Team, "Lorentz Force Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/lorentz-force-calculator
@misc{wecalculate_lorentz_force_calculator, title = {Lorentz Force Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/lorentz-force-calculator}}, year = {2026}, note = {TG we-Calculate} }
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