Magnetic Force Calculator
Choose a scenario and calculate magnetic force magnitude instantly.
Force is maximum at 90°, zero at 0° or 180°.
What is magnetic force?
Magnetic force is the push or pull experienced by a moving electric charge or a current-carrying wire when it enters a magnetic field. This effect is central to electric motors, particle accelerators, magnetic sensors, loudspeakers, and countless engineering systems.
A key idea is that magnetic force depends not only on magnitudes (charge, current, field strength, speed), but also on the angle between motion/current and the magnetic field lines. If motion is parallel to the field, force is zero. If it is perpendicular, force is maximum.
Core formulas used in this calculator
1) Moving charge in a magnetic field
The magnitude of force on a moving charge is: F = |q|vBsin(θ)
- F: force (newtons, N)
- q: charge (coulombs, C)
- v: velocity (m/s)
- B: magnetic flux density (tesla, T)
- θ: angle between velocity vector and magnetic field
2) Current-carrying wire in a magnetic field
The magnetic force on a straight wire segment is: F = BILsin(θ)
- I: current (A)
- L: length of wire in the field (m)
- θ: angle between current direction and magnetic field
How to use this magnetic force calculator
- Select your scenario from the dropdown.
- Enter known values using SI units.
- Set angle θ in degrees (0 to 180).
- Click Calculate Force.
The result shown is the magnitude of the force. For direction, use the right-hand rule (or left-hand rule for conventional motor analysis contexts).
Units reference (quick table)
| Quantity | Symbol | SI Unit |
|---|---|---|
| Magnetic force | F | newton (N) |
| Charge | q | coulomb (C) |
| Velocity | v | meter per second (m/s) |
| Magnetic field | B | tesla (T) |
| Current | I | ampere (A) |
| Length in field | L | meter (m) |
Common mistakes to avoid
- Using degrees in the formula but treating them as radians.
- Forgetting the sin(θ) term.
- Mixing units (for example, cm instead of m, mT instead of T).
- Expecting nonzero force when θ is 0° or 180°.
Why this matters in real life
Magnetic force calculations are useful in designing electric motors, estimating Lorentz force in charged particle paths, predicting wire forces in power systems, and understanding electromagnetic devices in robotics and automation. Even a quick back-of-the-envelope force estimate can help validate prototypes and avoid design errors.
Final note
This calculator gives a fast and reliable magnitude estimate for standard textbook scenarios. For advanced systems (non-uniform fields, curved conductors, time-varying fields, plasma dynamics), the full vector form and differential methods should be used.