Coil inductance is the ability of a conductor wound into a coil to store energy in a magnetic field and oppose rapid changes in current. Measured in henries (H), it forms the cornerstone of inductive reactance, transformers, RF filters, switching power supplies, and LC resonant circuits. Every time current flows through a coil, a proportional magnetic flux is generated — and when that current changes, a back-EMF is induced that resists the change.

Key Inductance Formulas

For a single-layer air-core solenoid, the classic Wheeler formula gives: L = (µ₀ × N² × A) / l, where µ₀ = 4π × 10⁻⁷ H/m, N is the number of turns, A is the cross-sectional area (m²), and l is the coil length (m). For a toroid, inductance is: L = (µ₀ × µᵣ × N² × A) / (2π × r), where µᵣ is the relative core permeability and r is the mean radius. The multilayer (Nagaoka) formula accounts for winding build depth: L (µH) = (0.8 × r² × N²) / (6r + 9l + 10b), with all dimensions in inches.

Practical Examples

  • RF inductor: 50 turns, 10 mm diameter, 20 mm long air-core coil → approximately 2.5 µH, suitable for AM/FM filter networks.
  • Power toroid: 30 turns on a T50-2 core (µᵣ ≈ 10), OD 12.7 mm, ID 7.7 mm, H 4.4 mm → approximately 2.7 µH at 1 MHz.
  • Choke coil: Multilayer 200 turns, 15 mm radius, 20 mm length → several mH, useful in low-frequency EMI suppression.

Air Core vs Toroid Inductors

Air-core inductors are completely linear, produce no core saturation, and are the preferred choice for RF circuits above 1 MHz. However, they require more turns for equivalent inductance compared to cored inductors. Toroid inductors use a donut-shaped ferrite or iron-powder core to greatly multiply inductance per turn through high relative permeability (µᵣ from 10 to over 10,000). Their closed magnetic path also minimises stray radiation, making them ideal for noise-sensitive power electronics and audio applications.

Inductive Reactance (XL)

Inductive reactance is the AC resistance of an inductor: XL = 2π × f × L. At 100 kHz, a 10 µH inductor presents XL = 6.28 Ω. Knowing XL helps engineers size inductors correctly in LC filters, impedance matching networks, and switching converters.