Magnetic Dipole Moment Calculator

Background.

A loop of wire carrying a current behaves, seen from a distance, just like a small bar magnet. It has a north face and a south face, it twists to line up with an outside magnetic field, and its own field fades with the cube of distance in the same pattern a magnet's does. The magnetic dipole moment is the one number that says how strong that magnet is. For a flat loop it is the current multiplied by the area the loop encloses; wind N identical turns and the moment is N times larger, m = N I A, measured in ampere-square metres.

The moment decides how a coil and a field act on each other. In a uniform field B the coil feels a torque of m B sin θ, which is what swings the needle of a moving-coil meter and what lets the magnetorquer coils on small satellites turn the spacecraft against the Earth's field without burning propellant. The coil's own field, well away from it, scales directly with m: on the axis it is μ₀m ÷ (2πz³), so doubling the distance cuts the field to an eighth.

The same quantity spans an enormous range. An electron carries about one Bohr magneton, 9.274 × 10⁻²⁴ A·m²; a bench coil of a few hundred turns manages a fraction of an A·m²; the Earth's own dipole is about 8 × 10²² A·m².

The relationship is exact for flat, identical loops carrying a steady current, and a tightly wound coil comes very close. What you get here is the magnitude only. The direction, perpendicular to the loop, follows the right-hand rule, and the calculation ignores any iron core, which can multiply a coil's effective moment many times over.

What is magnetic dipole moment calculator?

The magnetic dipole moment of a current loop is a vector whose size equals the current times the area the loop encloses and whose direction is perpendicular to the loop, set by the right-hand rule: curl the fingers of your right hand along the current and the thumb points along the moment. For a coil of N identical turns the moments of the individual turns add, giving m = N I A. The SI unit is the ampere-square metre, A·m², which is the same thing as a joule per tesla.

How to use this calculator.

1. 01Enter the Turn count, the number of complete turns in the winding. For a coil wound in several layers, count every turn in every layer.
2. 02Enter the Current in amperes, the steady current through the winding. With alternating current the moment follows the instantaneous current, so a peak current gives the peak moment.
3. 03Enter the Area per turn in square metres. For a circular turn of radius r it is πr², so a 5 cm radius gives about 0.007854 m²; divide an area in cm² by 10,000 to get m².
4. 04If the layers of a thick coil enclose noticeably different areas, enter the average area per turn. Because the moments of individual turns add, the average gives the exact total.

The formula.

m = N × I × A. Each turn contributes a moment equal to the current it carries times the area it encloses, and because all N turns carry the same current in the same direction, their contributions simply add. The result is linear in every input, so doubling the turns, the current or the area doubles the moment. Area is where mistakes creep in. A coil's radius enters squared, so a winding 10% larger in radius has 21% more moment, and an area typed in cm² instead of m² is out by a factor of 10,000. The units multiply directly, amperes times square metres, with the turn count a pure number. Only the magnitude is returned, to 12 significant digits; direction, orientation in an outside field and the response of nearby magnetic materials are not part of the calculation.

A worked example.

Frequently asked questions.

References& sources.

1. [1]OpenStax, University Physics Volume 2, section 12.5, Magnetic Field of a Current Loop.
2. [2]Griffiths, Introduction to Electrodynamics, 4th ed. (PRINT), magnetic dipoles.
3. [3]BIPM, The International System of Units (SI Brochure), 9th ed., version 3.01, coherent derived units and quantity equations.