What this calculator does
A loop of current behaves like a small magnet, and its strength is described by the magnetic dipole moment. It depends on three things multiplied together: the number of turns, the current and the area enclosed.
Notice that the shape of the loop does not matter, only the area it encloses. A circular loop and a square one of the same area and current have identical dipole moments.
The formula
Multiply the number of turns by the current and by the loop area. The result is in ampere square metres, and dividing by the turn count gives the contribution of a single turn.
| Term | Meaning |
|---|---|
| Magnetic dipole moment (μ) | A measure of a current loop's magnetic strength and orientation, in A·m². |
| Current loop | Any closed circuit carrying current, which produces a field resembling a bar magnet's. |
| Torque on a dipole | A dipole in an external field experiences a torque trying to align it with that field, which is how motors and galvanometers work. |
The inputs explained
| Field | What to enter |
|---|---|
| Number of turns (N) | The number of turns in the coil. |
| Current (I) (A) | The current in amps. |
| Loop area (A) (m²) | The area enclosed by one turn, in square metres. |
When to use it
Designing a moving-coil meter
The deflection depends on the torque on the coil, which is proportional to its dipole moment.
Understanding motor torque
A motor coil in a magnetic field experiences a torque proportional to its dipole moment, which is the basis of how it turns.
Modelling a coil as a magnet
At a distance the field of a current loop is indistinguishable from that of a bar magnet with the same moment.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How does the coil design change the magnetic moment?
The same current and area with different turn counts.
| Number of turns | Magnetic dipole moment (μ) | Per-turn moment |
|---|---|---|
| 10 turns | 0.160000 A·m² | 0.016000 A·m² |
| 50 turns | 0.800000 A·m² | 0.016000 A·m² |
| 100 turns | 1.6000 A·m² | 0.016000 A·m² |
| 200 turns | 3.2000 A·m² | 0.016000 A·m² |
Questions
Does the loop shape matter?
No, only the enclosed area. A circle, a square and an irregular loop of identical area carrying the same current all have the same dipole moment, which is a genuinely useful simplification.
How does this relate to a bar magnet?
A bar magnet's field comes from the aligned magnetic moments of its atoms. At a distance a current loop with the same total moment produces an indistinguishable field, which is why the two are described by the same quantity.
What happens to a dipole in an external field?
It experiences a torque that tries to align it with the field. That is exactly what turns a compass needle and what drives an electric motor.
Why is it a vector?
Because orientation matters as much as magnitude. The direction is perpendicular to the loop, given by the right-hand rule, and that direction determines which way the torque acts.
For the field a coil produces along its axis, see the solenoid magnetic field calculator. For the force between current-carrying conductors, see the magnetic force between wires calculator.