Inductor & Coil Calculator

Design and analysis of air-core coils, ferrite cores, and toroids

This calculator covers four coil types — single-layer air-core, multi-layer air-core, ferrite-rod, and toroidal — in two directions: Design mode takes a target inductance and frequency and returns the required winding dimensions and number of turns, while Analysis mode takes coil geometry and turn count and returns inductance, quality factor Q and self-resonant frequency. It is intended for winding RF chokes, oscillator tank coils and filter inductors.

Calculator Modes:
Design: Enter required inductance L and frequency → get dimensions and number of turns
Analysis: Enter coil dimensions and number of turns → get L, Q, self-resonant frequency
Configuration
Design Parameters

Wheeler formula (metric units):
L (μH) = (d² · N²) / (45.72·d + 101.6·l)

where:
  d = coil diameter (cm)
  l = winding length (cm)
  N = number of turns
Wire length:
l_wire = π · d · N
DC resistance:
R_dc = ρ · l_wire / A_wire
ρ (copper) = 1.68×10⁻⁸ Ω·m

Empirical formula:
L (μH) = 0.8 · a² · N² / (6·a + 9·b + 10·c)

where:
  a = mean radius (cm)
  b = winding height (cm)
  c = radial winding thickness (cm)
  N = total number of turns

Inductance:
L = (μ₀ · μᵣ_eff · N² · A) / l_coil

where:
  μ₀ = 4π×10⁻⁷ H/m
  μᵣ_eff = effective permeability (shape-dependent)
  N = number of turns
  A = rod cross-section (m²)
  l_coil = winding length (m)
Using AL factor:
L (nH) = AL · N²
AL is specified in nH/turn²

Using AL factor (simplest):
L (μH) = AL · N² / 1000
where AL is in nH/N²
Precise calculation:
L = (μ₀ · μᵣ · N² · h · ln(OD/ID)) / (2π)

where:
  OD = outer diameter (m)
  ID = inner diameter (m)
  h = toroid height (m)

Quality factor:
Q = ω·L / R = 2π·f·L / R

where:
  f = operating frequency (Hz)
  L = inductance (H)
  R = AC resistance (Ω) - includes skin effect
Self-resonant frequency (SRF):
f_SRF = 1 / (2π · √(L · C_s))

where:
  C_s = self-capacitance of coil (parasitic)
  For simple solenoid: C_s ≈ (ε₀ · π · d · l) / p
  p = turn pitch
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