Force on Current-Carrying Wire Calculator
When a wire carrying electric current sits in a magnetic field, the moving charges experience a force that pushes the whole wire. This is the principle behind every electric motor, loudspeaker, and electromagnetic actuator. The force depends on the current, the length of wire inside the field, the magnetic flux density, and the angle between the wire and the field. Enter the current in amperes, the wire length in metres, the magnetic flux density in tesla, and the angle in degrees; this calculator returns the magnetic force in newtons, the force per metre, and the maximum possible force at 90 degrees.
Magnetic force formula
Force = B * I * L * sin(theta)
Force per metre = B * I * sin(theta)
Maximum force = B * I * L (at theta = 90 degrees)
Fraction of maximum = sin(theta)
B is magnetic flux density in tesla, I is current in amperes, L is the wire length within the field in metres, and theta is the angle between the current direction and the field. The result is in newtons.
Magnetic force context
- The force is a special case of the Lorentz force acting on the moving charges that make up the current.
- The force is perpendicular to both the current and the field, given by the right-hand rule.
- One tesla equals 10,000 gauss; the Earth's field is roughly 0.00005 tesla while strong lab magnets reach several tesla.
- Force is maximum when the wire is perpendicular to the field and zero when parallel.
- For a coil of N turns, multiply the single-wire force by N to get the total force on the windings.
Force on a wire: frequently asked questions
What is the force on a current-carrying wire?
A straight wire carrying current I in a uniform magnetic field B experiences a force F = B x I x L x sin(theta), where L is the length of wire in the field and theta is the angle between the current direction and the field. The force is greatest when the wire is perpendicular to the field.
What is the unit of magnetic flux density?
Magnetic flux density B is measured in tesla (T) in SI. One tesla equals one weber per square metre. The gauss is a common non-SI unit where 1 tesla equals 10,000 gauss. Enter B in tesla in this calculator.
When is the force zero?
The force is zero when the wire runs parallel to the magnetic field, because sin(0) equals zero. The force is maximum when the wire is perpendicular to the field (90 degrees), where sin(90) equals one.
What direction does the force act?
The force direction is given by the right-hand rule: point the fingers in the direction of the current, curl toward the field, and the thumb points along the force. The force is perpendicular to both the current and the magnetic field.
How does this relate to electric motors?
Electric motors use this force to produce torque. Current flowing through coils sitting in a magnetic field experiences forces that turn the rotor. The same equation governs loudspeaker voice coils, rail guns, and magnetic levitation systems.
Official sources
Reviewed by the CalculatorHub team, edited by James Graham, 17 June 2026. See our methodology.