Magnetic Dipole Moment Calculator — Far-Field B from a Current Loop
Find the magnetic dipole moment of a current loop and the far-field magnetic flux density it produces on its axis and perpendicular equatorial plane.
A
m²
m
m = I × A
- 1
Dipole moment m
I × A = 2 × 0.01 = 0.020000 - 2
Distance cubed r³
0.5³ = 0.125 - 3
B on axis
(μ₀/4π) × 2m ÷ r³ = 0.0000001 × 2 × 0.02 ÷ 0.125 = 0.00000003Field on the symmetry axis — twice the equatorial value at the same distance.
How does this calculator work?
A current loop of I amperes enclosing area A m² has magnetic dipole moment m = I·A (A·m²). At a far distance r, the field on axis is B = (μ₀/4π)·2m/r³ and at the equator B = (μ₀/4π)·m/r³, both falling as 1/r³ — doubling the distance cuts the field by a factor of 8.
Formula
How this is calculated
A flat loop carrying current I and enclosing area A behaves, at distances much greater than the loop radius, like a magnetic dipole with moment m = I × A (in A·m²). The quantity m is a vector pointing perpendicular to the loop plane by the right-hand rule; this calculator returns its magnitude. For a multi-turn coil the total moment is N × I × A.
In the far field (r >> loop dimensions), the field simplifies to the dipole approximation. On the symmetry axis the field is B_axis = (μ₀/4π) × 2m/r³, pointing parallel to m. At the equatorial plane (perpendicular bisector of the axis) it is B_eq = (μ₀/4π) × m/r³, pointing antiparallel to m — exactly half the on-axis strength. Both components fall off as 1/r³, so the field drops rapidly with distance; doubling the distance cuts the field to one-eighth. The plot shows both curves versus r to illustrate this steep fall.
This model is valid only in the far field where r is much larger than the loop radius. Close to the loop the exact Biot-Savart integral must be used. Earth's magnetic field is itself well modelled as a magnetic dipole at distances beyond a few Earth radii, with a moment of about 8×10²² A·m².
Frequently asked questions
It is the fundamental quantity describing how strongly a current loop (or any equivalent magnetic source) responds to an external field and how strong a field it produces. Numerically, m = I × A for a flat loop, with units of A·m². It is analogous to the electric dipole moment p = q·d for charge pairs.
For a pure dipole, B_axis = 2(μ₀/4π)m/r³ and B_eq = (μ₀/4π)m/r³ — the factor of 2 difference arises from the geometry of how the field lines spread along the axis (they are closer together) versus at the equator (they spread outward). Both fall off as 1/r³.
When the observation distance r is comparable to or smaller than the loop radius. In that near-field regime the exact Biot-Savart integral is needed. As a practical rule, use the dipole formula only when r is at least five times the loop radius; the error is then less than a few percent.
TG we-Calculate Editorial Team. (2026). Magnetic Dipole Moment Calculator — Far-Field B from a Current Loop [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/magnetic-dipole-moment-calculator
TG we-Calculate Editorial Team. "Magnetic Dipole Moment Calculator — Far-Field B from a Current Loop." TG we-Calculate. 2026. https://we-calculate.com/calculator/magnetic-dipole-moment-calculator.
TG we-Calculate Editorial Team, "Magnetic Dipole Moment Calculator — Far-Field B from a Current Loop," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/magnetic-dipole-moment-calculator
@misc{wecalculate_magnetic_dipole_moment_calculator, title = {Magnetic Dipole Moment Calculator — Far-Field B from a Current Loop}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/magnetic-dipole-moment-calculator}}, year = {2026}, note = {TG we-Calculate} }
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