Inductance Calculator — Solenoid and Toroid
Calculate inductance for solenoid and toroid coils from core permeability, turns, and geometry.
Includes inductive reactance at frequency and stored energy.
Inductance L measures how strongly a coil opposes changes in current. A higher inductance means the coil stores more magnetic energy per amp of current and resists faster.
For a solenoid (a straight coil of N turns, length l, cross-section area A):
L = mu0 * mu_r * N^2 * A / l
mu0 = 4pi x 10^-7 H/m (permeability of free space). mu_r is the relative permeability of the core – 1 for air, around 200-10,000 for silicon steel or ferrite cores. The N^2 dependence is why doubling the number of turns quadruples the inductance.
For a toroid (a donut-shaped coil, mean radius R, cross-section area A):
L = mu0 * mu_r * N^2 * A / (2pi * R)
Toroids are preferred in power electronics because the closed magnetic path contains the flux, reducing EMI. Air-core toroids (mu_r = 1) are used in RF applications where a predictable, stable inductance matters more than high inductance per turn.
Inductive reactance at frequency f is XL = 2pi * f * L (in ohms). This is what makes inductors block high-frequency signals while passing DC – the foundation of low-pass filters and power supply chokes.
Energy stored in the magnetic field when carrying current I: U = 0.5 * L * I^2 (in joules). The chart shows inductive reactance vs frequency, showing how an inductor becomes increasingly resistive to higher frequencies.
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