Inductance of Conductors

Geometry-based inductance calculator for non-magnetic conductors (µ_r ≈ 1)

Calculation Mode

Single Straight Wire

Valid for long, thin wires in air; accuracy best when l ≫ r

Two Parallel Wires

Loop inductance of a go/return pair; spacing D is center-to-center

Coaxial Cylinders

Ideal coaxial geometry; result depends on ln(b/a)

ℹ️ Note: For non-magnetic conductors (Cu, Al, brass) µ_r ≈ 1 → geometry defines L. Frequency increases AC losses but does not change L.

Geometry Parameters

Wire Length [mm]

Wire Diameter [mm]

Geometry Visualization

Enter geometry parameters and click Calculate to see results

Calculation Formulas

Single Straight Wire - Exact Formula

This exact formula is valid for all aspect ratios (l/D). No approximations required - works for thin wires (l/D > 100) and thick wires (l/D < 10) equally well.

L = \mu_0 \cdot l \cdot \left[\ln\left(\frac{2l}{D} \cdot \left(1 + \sqrt{1 + \left(\frac{D}{2l}\right)^2}\right)\right) - \sqrt{1 + \left(\frac{D}{2l}\right)^2} + \frac{D}{2l}\right]

Where:

L = Inductance [H]
μ₀ = 4π × 10⁻⁷ H/m (permeability of free space)
l = Wire length [m]
D = Wire diameter [m] (not radius!)

This exact formula replaces older approximations like L ≈ 2×10⁻⁷·l·(ln(2l/r) - 0.75) which require l ≫ r.

Physical Background

Magnetic Permeability: For non-magnetic conductors (copper, aluminum, brass) and air, the relative permeability µ_r ≈ 1, so µ = µ₀ (vacuum permeability).

Frequency Independence: These formulas give the DC/low-frequency inductance. Frequency affects AC losses (skin effect, proximity effect) but does not change the inductance value for µ_r ≈ 1.

Assumptions: All formulas assume conductors in free space (air) with uniform geometry. Nearby magnetic materials or ground planes will alter the inductance.