Magnetic Force on a Wire Calculator
Enter a magnetic field strength, a current, and a wire length to get the force in newtons — the BIL formula behind every electric motor.
The BIL formula, instantly
Enter the field strength, current, and wire length and this magnetic force calculator returns the force (F = BIL) in newtons.
Use SI units
Field in teslas, current in amperes, and length in metres give the force in newtons — and the current is assumed perpendicular to the field.
What is the magnetic force on a wire?
The push behind every motor
This magnetic force calculator finds the force a magnetic field exerts on a straight current-carrying wire. Whenever charge moves through a magnetic field it feels a sideways push, and a wire is just a stream of moving charge, so the whole conductor is shoved at right angles to both the current and the field. The size of that push depends on three things: how strong the field is (in teslas), how much current flows (in amperes), and how much of the wire sits inside the field (in metres). Multiply them and you get the force in newtons. It is the principle that makes electric motors turn, loudspeakers move air, and rail guns accelerate.
Enter a field strength in teslas, a current in amperes, and a wire length in metres to get the magnetic force in newtons instantly.
The force is the field strength multiplied by the current and by the length of wire in the field, when the current runs perpendicular to the field.
F = B × I × LTake a 0.2 m length of wire carrying 10 A, placed across a 0.5 T magnetic field. The force is 0.5 × 10 × 0.2 = 1 N. Each factor enters in direct proportion: double the current and the force doubles; halve the field and the force halves. Use teslas, amperes, and metres and the force comes back in newtons.
The newton figure is the steady sideways push on the wire while the current flows. In a motor that push acts on every turn of the coil, and the many turns add up to a torque strong enough to spin a shaft under load. Because all three inputs enter linearly, the result tells you exactly which lever to pull: a stronger magnet, a larger current, or a longer wire each scale the force the same way. That is why motor designers stack many windings (more effective length) and feed them as much current as the wire can safely carry inside the strongest field the magnets allow. The direction of the force is given by the right-hand rule and flips if you reverse either the current or the field — the trick that keeps a motor turning the same way each half-cycle.
The formula is exact for the ideal case, but a couple of points are worth keeping in mind.
Perpendicular current and consistent units
This calculator assumes the current runs perpendicular to the magnetic field, which gives the maximum force. In the general case the force is F = B × I × L × sin θ, where θ is the angle between the wire and the field; at θ = 0 (wire parallel to the field) the force is zero. Keep your units consistent — teslas, amperes, and metres — or the newtons will be wrong, and remember a uniform field is assumed along the whole length of wire.