The magnetic force on a wire calculator above evaluates F = BIL sin θ, the force an external magnetic field exerts on a straight current-carrying conductor. It reports the total force, the force per metre of conductor, the maximum force available at perpendicular orientation, and a comparison against the conductor's own weight.
Arb Digital publishes free physics calculators, and the boundary between this page and its neighbours is worth stating clearly before anything else. The live Lorentz force calculator computes the force on a single moving charge — qvB with an angle, plus the cyclotron radius and period of the resulting circular path. This page computes the force on a current-carrying conductor: different inputs, different outputs, different audience. And the live magnetic field of a wire calculator answers the opposite question again — the field a wire produces, rather than the force it feels.
What This Magnetic Force on a Wire Calculator Does
A conductor carrying current in an external magnetic field experiences a sideways push. This is the effect that makes every electric motor, loudspeaker and moving-coil instrument work, and it is the mechanism behind the electromagnetic forces that a short circuit imposes on busbars and windings.
The tool takes the flux density in tesla, millitesla, microtesla or gauss, the current in amperes, the length of conductor actually inside the field, and the angle between the current direction and the field. It returns the force in newtons, scaled automatically to millinewtons or kilonewtons where that reads better, along with the force per metre so you can apply it to a different length without re-entering everything.
It treats the field as uniform over that length and the conductor as straight. Real geometries with curved conductors or strongly varying fields need the force integrated along the path, which is a different calculation.
How to Use It
- Enter the external flux density and pick its unit. Tesla and gauss are both common; one tesla is ten thousand gauss.
- Enter the current in amperes flowing through the conductor.
- Enter the angle between the direction of current flow and the field vector. Ninety degrees gives the maximum force.
- Enter the length of conductor inside the field, not the total wire length, and pick its unit.
- Optionally enter the conductor mass to see the force expressed as a multiple of its own weight.
The Formula: How the Force on a Conductor Is Calculated
For a straight conductor of length L carrying current I in a uniform field of flux density B, with θ the angle between the current direction and the field,
F = B I L sin θ
with F in newtons when B is in tesla, I in amperes and L in metres. Written properly it is a vector cross product, F = I L × B, which carries the direction as well as the magnitude: the force is perpendicular to both the current and the field, so it points out of the plane the two of them define.
The relation follows directly from the force on the individual charge carriers. Each carrier of charge q moving at drift velocity v feels qv × B, and summing over all the carriers in a length L of conductor gives IL × B, because current is charge per unit time. HyperPhysics at Georgia State University gives the same relation, noting that when the current is perpendicular to the field the force is simply the product of current, length and field. The carriers transfer that force to the lattice of the metal through collisions, which is why the wire as a whole moves rather than just the electrons within it.
The sine term is what makes the orientation matter so much. A conductor lying along the field lines feels no force whatever, however large the current. Rotate it to 30 degrees and it feels half the maximum; at 90 degrees it feels all of it.
Work the defaults through by hand. A field of 0.8 T, a current of 5 A, 25 cm of conductor in the field, at 60 degrees. The force is 0.8 × 5 × 0.25 × sin 60° = 1 × 0.8660 = 0.8660 N. The force per metre is 0.8 × 5 × sin 60° = 3.464 N/m. At 90 degrees the same arrangement would give a full 1.000 N. Expressed as a weight, 0.8660 N is 0.8660 / 9.80665 = 0.08831 kg-force, or 88.31 grams-force — nearly nine times the weight of a 10 g conductor.
The Boundary Between This Page and Its Neighbours
Four closely related tools are easy to confuse, so here is what each one actually answers.
This page gives the force on a current-carrying conductor placed in a field that something else produces. Inputs: flux density, current, length, angle. That is the motor problem.
The Lorentz force calculator gives the force on a single moving charge, from its charge, its speed, the field and the angle, together with the radius and period of the circular path it follows. That is the particle-physics and mass-spectrometry problem, and its inputs are velocity and charge rather than current and length.
The magnetic field of a wire calculator gives the field a long straight current produces at a distance, from the Biot–Savart result. It is the source side rather than the receiving side: the field a wire makes, not the force it feels.
The force between wires calculator combines the two. One wire produces a field, the second wire sits in that field and feels a force, and the result is the mutual force per unit length between two parallel conductors — the arrangement that used to define the ampere. That definition was retired in the 2019 redefinition of the SI base units, and the vacuum magnetic permeability it fixed exactly is now a measured constant with a published uncertainty — see the NIST CODATA value for the vacuum magnetic permeability. If both wires are yours, that is the page you want; if the field comes from a magnet, this one is.
Why Short-Circuit Forces on Busbars Are Not a Footnote
The force scales with the product of field and current, and in a fault the field is itself produced by that same current. That makes the force scale with the square of the current, which is why short-circuit forces are so much larger than intuition suggests.
A busbar system carrying a few hundred amperes normally feels forces measured in a fraction of a newton per metre. During a fault carrying tens of thousands of amperes, the same geometry can see forces of several kilonewtons per metre, applied as a mechanical shock in the first few milliseconds. Supports, insulators and spacing are dimensioned for that peak rather than for normal running, and the same effect explains why a transformer winding needs radial and axial bracing designed for a through-fault it may never experience.
The consequence for using this page: entering a fault current with a normal-operation field will understate the force badly, because in a fault both terms rise together. Fault-force calculations follow published methods in the applicable installation standards and belong to a qualified electrical engineer.
Where the Relation Shows Up in Working Equipment
A loudspeaker is the cleanest example. A voice coil sits in the radial gap of a permanent magnet, so the current is always perpendicular to the field. Force is therefore proportional to current alone, the cone follows the waveform, and the product BL — flux density times conductor length in the gap — is quoted on datasheets as the force factor, in newtons per ampere. It is exactly the BIL relation with the current divided out.
A motor is the same idea arranged to rotate. Conductors on the rotor carry current across a radial field, each feels a tangential force, and the sum of those forces around the radius is the torque. Motor designers keep the geometry perpendicular for the same reason speaker designers do: the sine term is a pure loss if it is anything less than one.
A railgun and an electromagnetic pump work on the same relation with no moving winding at all — in the pump's case, the conductor is a liquid metal, and the force is applied to the fluid itself.
Where This Sits Next to the Other Magnetism Tools
Beyond the four tools compared above, the magnetic dipole moment calculator handles a closed loop rather than a straight segment, which gives a torque instead of a net force. The solenoid magnetic field calculator gives the field inside a coil, which is often the field you would enter here.
For units and material response, the magnetic field converter moves between tesla, gauss and oersted, and the magnetic permeability calculator derives permeability from B and H. The Faraday's law calculator covers the reverse effect, where moving a conductor through a field generates a voltage instead of consuming one.
Arb Digital builds free tools like this one because useful pages earn attention. If you want tools, calculators or content built for your own audience, we can help.
Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Using the total wire length instead of the length inside the field — only the part actually in the field produces force, and that is often a few centimetres of a much longer run.
- Entering the field the wire itself produces — a conductor exerts no net force on itself. The B in this relation is the external field from a magnet, a pole piece or another conductor.
- Measuring the angle from the wrong reference — it is between the current direction and the field, not between the field and the plane of a coil.
- Expecting the force along the current or the field — it is perpendicular to both, which is what makes rotation possible at all.
- Applying a normal-operation field to a fault current — in a short circuit both the field and the current rise together, so the force scales with the square of the current.
Related Free Tools From Arb Digital
Pair this with the live Lorentz force calculator for a moving charge, the live magnetic field of a wire calculator for the field a conductor produces, and the force between wires calculator for two parallel conductors acting on each other. The magnetic dipole moment calculator covers closed loops, the solenoid magnetic field calculator gives the field inside a coil, and the magnetic field converter and magnetic permeability calculator handle units and material response. The Faraday's law calculator covers the induced-voltage side. Everything Arb Digital publishes sits on the free online tools hub.
Frequently Asked Questions
The force equals the flux density multiplied by the current, the length of conductor inside the field, and the sine of the angle between the current direction and the field. In vector form it is the current times the length vector crossed with the field, which also gives the direction: perpendicular to both.
They are the same physics with different inputs. The Lorentz force is on a single charge and depends on its charge and velocity, producing a circular path with a cyclotron radius and period. This page sums that effect over all the charge carriers in a conductor, so the inputs are current and length instead of charge and speed, and the output is a force on a solid object.
Because the force is a cross product, and it depends on the sine of the angle between the current and the field. At zero or 180 degrees that sine is zero. Physically, the charge carriers are moving along the field lines rather than across them, and a charge moving parallel to a magnetic field experiences no magnetic force at all.
Perpendicular to both the current and the field, in the direction given by the right-hand rule: point the fingers along the current, curl them towards the field, and the thumb gives the force. Reversing either the current or the field reverses the force; reversing both leaves it unchanged, which is why alternating current in an alternating field still gives steady thrust.
Not to the force on itself. A conductor exerts no net force on its own straight length, so the B in this relation is always an external field from a magnet, a pole piece or a separate conductor. Two separate conductors do act on each other, which is a different calculation and the reason parallel busbars need mechanical restraint.
Because in a fault the field is produced by the same current that is being acted on, so the force rises with the square of the current rather than in proportion to it. A busbar arrangement that feels a fraction of a newton per metre in normal service can see several kilonewtons per metre during a fault, applied as a mechanical shock within the first few milliseconds.
It is the force factor, in newtons per ampere: the flux density in the magnet gap multiplied by the length of voice-coil conductor sitting in that gap. It is this same relation with the current divided out, and because the gap field is radial the current is always perpendicular to it, so the sine term stays at one and force is proportional to current alone.
Not directly. The relation assumes a straight segment in a uniform field. A curved conductor has to be divided into short straight elements, each with its own angle to the field, and the vector forces summed. For a closed loop in a uniform field the net force comes out zero and you get a pure torque instead, which is the dipole moment calculation.
This tool is provided for educational and preliminary engineering use only. It evaluates a published relation for a straight conductor in a uniform external field and does not perform electromagnetic force calculations for fault conditions, busbar systems, transformer windings or any installation subject to an electrical code. Short-circuit forces scale with the square of the current and are governed by the applicable installation standards. Any work on electrical equipment, and any mechanical design intended to withstand fault forces, belongs to a qualified electrical engineer.
