Circular Loop Inductance
Calculates the self-inductance of a single-turn circular conductor loop using the Rosa/Neumann formula. This is the starting point for MRI surface coil design, tuning capacitor calculation, and any loop antenna.
Equations & Parameters ▸
\(L = \mu_0 r \!\left[\ln\!\left(\tfrac{8r}{a}\right) - 2\right]\)
| D | Loop diameter (mm) — centre-to-centre of wire. |
| d | Wire (or tube) diameter (mm). |
| L | Self-inductance. Increases with loop size; decreases with thicker wire. |
Physical constants used
| c | Speed of light = 2.998×10⁸ m/s |
| µ₀ | Permeability of free space = 4π×10⁻⁷ H/m ≈ 1.2566×10⁻⁶ H/m |
| ε₀ | Permittivity of free space = 8.854×10⁻¹² F/m |
Inputs
mm
Centre-to-centre of conductormm
Conductor diameter (not radius)Results
Inductance
Self-inductance, L—
Diagram