Magnetic Force Calculator
Find the magnetic force on a moving charge or a current-carrying wire in a magnetic field. Switch modes below for either situation.
Calculator verified • Last updated: August 2026
Not sure which mode? Click here.
- Moving Charge — you have a single charged particle (like an electron or ion) traveling through a magnetic field, and want the force on it.
- Current-Carrying Wire — you have a wire carrying current through a magnetic field, and want the total force on the length of wire inside the field.
Moving Charge
Current-Carrying Wire
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Vector Diagram (3D)
The green arrow (velocity or current) and purple arrow (magnetic field) both lie flat in the shaded ground plane, θ apart. The orange force arrow always stands perpendicular to that plane — this is exactly why the real force is perpendicular to both v and B, not just a diagram convention. As θ grows toward 90°, the purple arrow swings further from the green one and the orange arrow grows tallest; at 0° or 180°, purple lines up with (or against) green and the orange arrow disappears.
Every value here is a vector, and a negative sign flips its arrow to the opposite side of the same axis rather than changing how long it is: a negative velocity or current sends the green arrow backward instead of forward, and a negative field sends the purple arrow backward along its θ line instead of forward. The θ arc always tracks between wherever the two arrows actually point, not a fixed position.
The reported force is always a magnitude (never negative) — but the orange arrow still shows its direction, standing up when the combined sign of charge, velocity, and field is positive, and flipping to point down through the plane when it's negative, matching the right-hand rule applied to whichever way v and B actually point.
Magnetic Force Explained
A magnetic field exerts a force on any moving charge — and since an electric current is just charges in motion, it exerts a force on current-carrying wires too. Both situations follow the same underlying relationship, just written in terms of different quantities.
For a single moving charge:
F: magnetic force on the charge, in newtons (N).
q: the moving charge, in coulombs (C).
v: the charge's speed, in meters per second (m/s).
B: magnetic flux density (field strength), in tesla (T).
θ: the angle between the velocity and the magnetic field.
For a current-carrying wire:
F: magnetic force on the wire, in newtons (N).
B: magnetic flux density, in tesla (T).
I: current through the wire, in amperes (A).
L: length of wire within the field, in meters (m).
θ: the angle between the current direction and the magnetic field.
In both cases, is the angle between the direction of motion (or current) and the magnetic field . The term means the force is strongest when the motion is perpendicular to the field () and disappears entirely when the motion is parallel to the field ( or ).
Worked Example: Electron in a Magnetic Field
Using the calculator's own defaults for the moving-charge mode — an electron's charge (1.602 × 10⁻¹⁹ C) moving at 2 × 10⁶ m/s perpendicular to a 0.5 T field — the force works out to N. That may sound tiny, but acting on a particle as light as an electron, it's enough to bend its path into a tight circular arc, the same principle used to steer particle beams in old CRT televisions and modern particle accelerators.
Magnetic Force vs. Electric Force
Coulomb's Law describes an electric force that acts on any charge, moving or not, and always points along the line between the charges. Magnetic force is different in a fundamental way — it only acts on moving charges, and it always points perpendicular to the direction of motion, so it can never speed up or slow down a charge, only change its direction. That's why a charged particle moving through a uniform magnetic field traces a circle rather than a straight line.
A Brief History of Magnetic Force
Hans Christian Ørsted's 1820 discovery that an electric current deflects a nearby compass needle first revealed the deep connection between electricity and magnetism, kicking off a wave of experiments by André-Marie Ampère and others. Hendrik Lorentz later formalized the full force law bearing his name (of which both formulas here are special cases) in the 1890s, tying together electric and magnetic forces into the single unified expression still used today.
Common Magnetic Force Mistakes
Forgetting the term — and simply multiplying or without it — is the most common error, and it only happens to give the right answer when the motion is exactly perpendicular to the field. Mixing up the direction rule (using a left-hand instead of right-hand convention, or forgetting to flip the direction for a negative charge) is another frequent slip. Confusing magnetic flux density (measured in tesla) with the related but distinct magnetic flux (measured in weber) is a third common mix-up.
Magnetism Terms You Should Know
Tesla (T) — the SI unit of magnetic flux density; Earth's own magnetic field is only about 0.00005 T at the surface.
Right-Hand Rule — a hand mnemonic for finding the direction of the magnetic force from the directions of motion and field.
Lorentz Force — the combined electric-plus-magnetic force on a moving charge, of which both formulas here are the magnetic component.
Magnetic Flux Density — the technical name for what's commonly just called "magnetic field strength," symbol .
This calculator gives the magnitude of the force only. The direction follows the right-hand rule (see the FAQ below) and isn't computed automatically.
Frequently Asked Questions
Why is the magnetic force zero when the charge moves parallel to the field?
Because the magnetic force depends on sin(θ), the angle between the velocity (or current) and the magnetic field — when the charge moves exactly parallel to the field, θ is 0° and sin(0°) = 0, so there is no force at all. The force is strongest when the motion is perpendicular to the field, at θ = 90°, where sin(θ) = 1.
How do I find the direction of the magnetic force?
This calculator gives you the magnitude of the force; the direction follows the right-hand rule. For a positive charge, point your fingers in the direction of velocity, curl them toward the direction of the magnetic field, and your thumb points in the direction of the force (reverse it for a negative charge). For a current-carrying wire, point your fingers along the current direction instead of velocity.
What's the difference between the two modes on this calculator?
Both modes use the same underlying physics, just applied to different situations. "Moving Charge" finds the force on a single charged particle (like an electron) traveling through a magnetic field. "Current-Carrying Wire" finds the total force on a wire, which is really the combined force on all the moving charges inside it — that's why the formula swaps qv for IL, current times length, instead of charge times velocity.