Calculate the axial magnetic field of a circular loop
Estimate the magnetic field strength on the symmetry axis of an idealized circular current loop or flat coil. The calculation uses the loop diameter, number of closely spaced turns, current, and axial distance from the loop center.
This is a magnetostatic or quasi-static model for a thin circular loop in air or vacuum. It does not calculate off-axis fields, frequency-dependent current distribution, resonance, reactive-to-radiating field transitions, or far-field radiation.
Model equations:
H = (N × I × r²) / (2 × (R² + r²)3/2)
B = μ₀ × H
dBµA/m = 20 log₁₀(H / 1 µA/m)
dBpT = 20 log₁₀(B / 1 pT)
R is measured on the symmetry axis from the center of the loop.
Where:
- H = magnetic field strength on the loop axis (A/m)
- B = magnetic flux density in air or vacuum (T)
- N = number of closely spaced turns
- I = current in each turn (A)
- r = loop radius measured to the conductor centerline (m)
- R = axial distance from the loop center (m)
This calculator provides:
Magnetic field strength H in A/m and dBµA/m.
Magnetic flux density B in tesla, picotesla, gauss, and dBpT, using B = μ₀H for air or vacuum.
An idealized axial estimate for comparison and engineering orientation, not a substitute for an antenna simulation, field measurement, EMC assessment, or compliance evaluation.
Author: IBL-Editors Team
Technical Review: Andreas Bender - Deputy Managing Director | IBL-Lab GmbH Give feedback on this article