Magnetic Moment Calculator

Magnetic moment is a compact measure of how strongly a source behaves like a magnetic dipole and which way that dipole points. For one planar loop carrying steady current, the magnitude is μ = IA: current multiplied by enclosed loop area. The SI unit is ampere square metre (A·m²). Direction is perpendicular to the loop. Curl the fingers of your right hand with conventional current and your thumb points along the magnetic moment vector. An external magnetic field can rotate the loop. The torque magnitude is τ = μB sin(θ), where θ is the angle between moment and field. It is greatest when those vectors are perpendicular and zero when they are parallel or antiparallel. This rotational effect is central to moving-coil instruments, direct-current motors, loudspeakers, and demonstrations in introductory electromagnetism. The calculator converts degree input before applying the sine function. The same interaction has potential energy U = -μB cos(θ). Alignment with the field gives negative, minimum energy under this reference convention. Antiparallel orientation gives positive, maximum energy. A perpendicular orientation has zero potential energy but maximum torque, so the loop immediately tends to rotate if unconstrained. Torque and energy therefore describe complementary aspects of the same magnetic interaction. This page models a single ideal loop. For a coil of N closely packed identical turns, multiply IA by N or use a dedicated dipole moment calculation that includes turns. The area must be the area enclosed by the current path, not wire surface area or cross-sectional area. For a circular loop it is πr²; for a rectangle it is width times height. Convert square centimetres to square metres before entry and convert milliteslas to teslas. The uniform-field approximation assumes the same field magnitude and direction over the entire loop. Large loops in varying fields, magnetic cores, irregular geometries, and strongly coupled systems may require vector integration or measured material data. Within those assumptions, this tool provides internally consistent moment, torque, and potential energy values for coursework, experiment planning, engineering estimates, and quick unit checks. Comparing all three outputs also helps catch an incorrect angle definition: the angle is measured from the loop's normal moment vector, not from the plane itself.