Magnetic Force Calculator
Compute the magnetic force on a moving charge, or on a current-carrying wire in a magnetic field. Two 3D diagrams show the right-hand-rule geometry for both cases, with charts showing how force depends on angle and field strength.
Reviewed by the ToolNestr Editorial Team — July 2026
Right-hand-rule geometry
1. Moving charge in a field
Velocity (amber), field lines (slate), and the resulting force (indigo) — all mutually perpendicular, exactly as the right-hand rule predicts.
2. Current-carrying wire in a field
A straight wire (amber) carrying current through a field (slate arrows) feels a force (indigo) perpendicular to both — the working principle of every electric motor.
Magnetic force graphs
How it works
The core idea in one line: a magnetic field only pushes on charges that are actually moving through it, and only on the part of their motion that runs perpendicular to the field — that's why the force always depends on sin(θ), never on the parallel component of motion.
F = qvB sin(θ)
force on a moving charge — q in coulombs, v in m/s, B in tesla
F = BIL sin(θ)
force on a current-carrying wire — I in amps, L in metres
Direction: right-hand rule
point fingers along v (or I), curl toward B — thumb gives the force direction
For a single moving charge, F = qvB sin(θ) gives the magnitude of the force, always directed perpendicular to both v and B via the right-hand rule. A current-carrying wire is just a huge number of moving charges together, so summing their individual forces gives the wire equation F = BIL sin(θ), where the current I and length L replace the single charge's q and v.
Worked example 1 — electron in a magnetic field
Given: An electron moves at v = 2×10⁶ m/s perpendicular (θ = 90°) to a field B = 0.5 T. Charge q = 1.6×10⁻¹⁹ C. Find the force.
This is the same physics used in mass spectrometers and old CRT televisions to steer charged particles along curved paths.
Worked example 2 — current-carrying wire in a motor
Given: A straight wire segment carries I = 5 A over a length L = 0.3 m, perpendicular (θ = 90°) to a field B = 0.8 T.
This is exactly the force that spins the rotor coil in a DC electric motor — many turns of wire multiply this force many times over.
How angle affects magnetic force
Force scales with sin(θ) — holding qvB (or BIL) fixed at 1 (arbitrary units) shows how the force changes with the angle between velocity and field.
| Angle θ | sin(θ) | Relative force |
|---|---|---|
| 0° | 0 | 0 (no force) |
| 30° | 0.500 | 0.500 |
| 60° | 0.866 | 0.866 |
| 90° | 1.000 | 1.000 (maximum) |
Force is maximum when velocity (or current) is perpendicular to the field, and zero when it runs parallel to the field lines.
Where magnetic force actually matters
🧲 Electric motors
The force on current-carrying coils inside a magnetic field (F = BIL sinθ) is exactly what makes electric motors spin, converting electrical energy into rotational mechanical work.
🔬 Mass spectrometers
Charged particles moving through a magnetic field curve along a radius that depends on their mass-to-charge ratio, letting scientists identify unknown compounds by their curved paths.
🏥 MRI machines
Powerful magnetic fields interact with the magnetic moments of hydrogen nuclei in the body — a specialized quantum version of the same underlying magnetic force principles.
⚛️ Particle accelerators
Magnetic fields steer and focus beams of charged particles around circular accelerator rings, using precisely calculated magnetic forces to keep particles on their intended path at near light speed.
Common misconceptions
"Magnetic force does work on a moving charge, speeding it up or slowing it down."
Magnetic force is always perpendicular to velocity, so it can only change the direction of motion, never the speed. It does zero work and never changes the particle's kinetic energy — only electric fields can do that.
"The magnetic force is strongest when a charge moves along the field lines."
It's the opposite — force depends on sin(θ), which is zero when velocity is parallel to the field (θ=0°) and maximum when velocity is perpendicular to the field (θ=90°).
"A stationary charge in a magnetic field feels a force."
F = qvB sinθ requires the charge to be moving (v > 0). A charge at rest in a purely magnetic field feels no magnetic force at all — only electric fields exert force on stationary charges.
"Reversing the current direction has no effect on the force on a wire."
Reversing the current reverses the direction of the force (though not its magnitude) — this is exactly how commutators in DC motors keep the rotor spinning in one consistent direction.
Formula sources & further reading
The formulas here are standard, traceable to:
- • OpenStax, University Physics Volume 2 — Chapter 11, "Magnetic Forces and Fields" (free, peer-reviewed). openstax.org
- • Halliday, Resnick & Walker, Fundamentals of Physics — Chapter 28, Magnetic Fields.
- • Serway & Jewett, Physics for Scientists and Engineers — Chapter 29, Magnetic Fields.
F = qvB sin(θ) for a moving charge; F = BIL sin(θ) for a current-carrying wire. Direction found via the right-hand rule. Results are rounded for display.
How to use this calculator
Pick the mode
"Moving charge" solves F = qvB sinθ; "Current-carrying wire" solves F = BIL sinθ.
Enter the values
Use consistent SI units — charge in coulombs, velocity in m/s, current in amps, length in metres, B in tesla.
Read the result
Force solves live in newtons, shown in scientific notation for very small or large values.
Related tools
Frequently asked questions
What is the formula for magnetic force on a moving charge?
F = qvB sin(θ), where q is the charge (C), v is its speed (m/s), B is the magnetic flux density (T), and θ is the angle between the velocity and field vectors. The force is always perpendicular to both v and B.
What is the formula for the force on a current-carrying wire?
F = BIL sin(θ), where I is the current (A), L is the length of wire in the field (m), B is the field strength (T), and θ is the angle between the wire and the field. This follows directly from summing the force on every moving charge in the wire.
Why is the force zero when velocity is parallel to the field?
Because the formula depends on sin(θ), and sin(0°) = 0. A charge moving exactly along the field lines experiences no magnetic force — sideways deflection only happens when there is a velocity component perpendicular to B.
How do you find the direction of the magnetic force?
Use the right-hand rule: point your fingers in the direction of v (or current I), curl them toward B, and your thumb points along v × B — this is the direction of the force for a positive charge (reverse it for a negative charge).
Does magnetic force do work on a moving charge?
No. Because the magnetic force is always perpendicular to the velocity, it can only change the charge's direction, never its speed — so it does zero work and never changes the particle's kinetic energy.