Electronics

Coil Inductance Formulas

Formulas for calculating inductance of air-core solenoids, multilayer coils, and toroids.

Air-core solenoid (Wheeler)

L (µH)= (r²·N²) / (9r + 10ℓ) — all in inches
SI formL = μ₀ · N² · A / ℓ (for long solenoid)
rCoil radius
Coil length
NNumber of turns

Multilayer (Wheeler)

L (µH)= (0.8·a²·N²) / (6a + 9ℓ + 10c)
aMean radius (in)
Winding length (in)
cWinding depth (in)

Toroid

L (H)= μ₀ μ_r · N² · A_e / ℓ_e
A_eEffective cross-section area
ℓ_eMean magnetic path length
A_LCore-specific factor: L (nH) = A_L · N²

Design notes

  • Adding ferromagnetic core increases L by μ_r (hundreds to thousands for ferrite).
  • Saturation current I_sat: above it, the core loses permeability and L drops sharply.
  • For RF, air-core is preferred for highest Q and zero saturation.
  • Self-resonant frequency (SRF) is where parasitic capacitance makes the coil look like a capacitor.
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