Magnetic Force on a Moving Charge Calculator
Find the magnetic (Lorentz) force on a charged particle moving through a uniform magnetic field.
C
m/s
T
°
Force perpendicular to both velocity and field
- 1
Angle in radians
90° × π ÷ 180 = 1.570796 - 2
sin θ
sin(90°) = 1 - 3
|q| × v
0 × 2,500,000 = 0 - 4
|q| × v × B
0 × 0.5 = 0 - 5
Magnetic force F
|q|·v·B × sin θ = 0 × 1 = 0Force is perpendicular to both velocity and field — it changes direction only, never speed.
How does this calculator work?
The magnetic force on a moving charge is F = |q| v B sin(θ), where q is the charge, v its speed, B the field strength, and θ the angle between velocity and field. The force peaks when motion is perpendicular to the field and is zero when parallel. Enter q, v, B, and θ to get the force in newtons.
Formula
How this is calculated
A charge q moving with speed v through a magnetic field B experiences a force given by the magnetic part of the Lorentz force law, F = |q| v B sin(θ), where θ is the angle between the velocity vector and the field vector. Enter the charge in coulombs (C), the speed in metres per second (m/s), the field strength in tesla (T), and the angle in degrees; the angle is converted to radians internally before taking the sine.
The force is largest when the velocity is perpendicular to the field (θ = 90°, sin θ = 1) and is zero when the particle moves parallel or anti-parallel to the field (θ = 0° or 180°, sin θ = 0), since the cross product v × B vanishes. The calculator uses the absolute value of the charge, so the result is the force magnitude in newtons (N); the actual direction is perpendicular to both v and B as given by the right-hand rule.
This assumes a uniform static magnetic field and ignores any electric-field contribution and relativistic mass effects. Because the magnetic force is always perpendicular to the velocity it does no work on the particle and changes only its direction, which is why charges follow circular or helical paths in magnetic fields.
Frequently asked questions
When the velocity is parallel (θ = 0°) or anti-parallel (θ = 180°) to the field, sin(θ) = 0, so F = qvB sin(θ) = 0. The magnetic force depends on the component of velocity perpendicular to the field.
No. The magnetic force is always perpendicular to the velocity, so it does no work and cannot change the speed or kinetic energy — it only changes the direction of motion, producing circular or helical paths.
Use coulombs for charge, metres per second for speed, tesla for field, and degrees for the angle. The resulting force is in newtons.
Also known as
TG we-Calculate Editorial Team. (2026). Magnetic Force on a Moving Charge Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/magnetic-force-charge-calculator
TG we-Calculate Editorial Team. "Magnetic Force on a Moving Charge Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/magnetic-force-charge-calculator.
TG we-Calculate Editorial Team, "Magnetic Force on a Moving Charge Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/magnetic-force-charge-calculator
@misc{wecalculate_magnetic_force_charge_calculator, title = {Magnetic Force on a Moving Charge Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/magnetic-force-charge-calculator}}, year = {2026}, note = {TG we-Calculate} }
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