Magnetic Force on Wire Calculator
When a current flows through a wire that sits in a magnetic field, the field pushes on the wire. That push is the magnetic force on a current-carrying conductor, and it is the principle behind electric motors and loudspeakers. The force depends on four quantities: the magnetic flux density, the current, the length of wire inside the field, and the angle between the wire and the field lines. The angle matters because only the part of the wire that runs across the field feels the push, which the sine of the angle captures exactly. Line the wire up with the field and the force vanishes; hold it square and the force is at its strongest. This calculator takes the magnetic flux density in tesla, the current in amperes, the wire length in meters and the angle in degrees, converts the angle to radians, and returns the force in newtons. The defaults describe two meters of wire carrying ten amperes through a half-tesla field at a right angle. The result is the force magnitude; its direction follows the right-hand rule. Every figure here is computed deterministically from the standard physics formula shown below, with a worked example that reconciles exactly to the calculator so you can follow each step.
The magnetic force on a wire is flux density times current times length times the sine of the angle: F = B I L sin(theta). With B = 0.5 T, a current of 10 A, a length of 2 m and an angle of 90 degrees, the force is 10.00 N.
Magnetic force formula
F = B I L sin(theta)
F = magnetic force in newtons
B = magnetic flux density in tesla
I = current in amperes
L = wire length in meters
theta = angle between wire and field in degrees
The angle is entered in degrees and converted to radians before the sine is taken. Multiply the flux density by the current, by the wire length, and by the sine of the angle. The force is greatest at 90 degrees and zero at 0 degrees.
Worked example
A wire carries 10 amperes through a magnetic flux density of 0.5 tesla. The length inside the field is 2 meters, and the wire sits at 90 degrees to the field.
- sin(90 degrees) = 1
- B x I = 0.5 x 10 = 5
- B x I x L = 5 x 2 = 10
- F = 10 x 1 = 10.00 N
The magnetic force is 10.00 newtons. These are the calculator's default inputs, so the result above matches the widget exactly.
Force at different angles
| Angle (degrees) | sin(theta) | Force (N) |
|---|---|---|
| 0 | 0.00 | 0.00 |
| 30 | 0.50 | 5.00 |
| 90 | 1.00 | 10.00 |
Each row holds B at 0.5 tesla, current at 10 amperes and length at 2 meters, varying only the angle. The force tracks the sine of the angle.
Magnetic force on wire calculator: frequently asked questions
What is the magnetic force on a current-carrying wire?
A straight wire carrying a current in a magnetic field feels a force equal to the magnetic flux density times the current times the wire length times the sine of the angle between the wire and the field. The force is maximum when the wire is perpendicular to the field and zero when it lies along the field. This is the principle behind electric motors and loudspeakers.
What units does this calculator expect?
Magnetic flux density B is in tesla. Current I is in amperes. Wire length L is in meters. The angle theta is entered in degrees and converted to radians internally before taking the sine. The output, the force F, is in newtons. Keeping every input in these SI units gives a force directly in newtons with no extra conversion.
Why does the angle matter?
Only the component of the wire that is perpendicular to the field contributes to the force, and the sine function captures that. At 90 degrees the sine is one and the force is at its maximum. At 0 degrees the wire runs parallel to the field, the sine is zero, and there is no force. Intermediate angles scale smoothly between those extremes.
What do the default inputs give?
The defaults are a magnetic flux density of 0.5 tesla, a current of 10 amperes, a wire length of 2 meters and an angle of 90 degrees. Since the sine of 90 degrees is one, the force is 0.5 times 10 times 2 times 1, which equals 10.00 newtons. That is the force on the wire under those conditions.
Which way does the force point?
The direction is given by the right-hand rule and is perpendicular to both the current and the magnetic field. This calculator returns the magnitude of the force in newtons, not its direction. To find the direction, point your fingers along the current, curl them toward the field, and your thumb points along the force.
Official sources
- Electromagnetism references and SI units: US National Institute of Standards and Technology (NIST). As at 25 June 2026.
Reviewed by the CalculatorHub team, edited by James Graham, 25 June 2026. See our methodology. This is general information, not financial, tax, legal or investment advice.