Inductor Calculator

A solenoid is a cylindrical coil where wire is wound around a tube or bobbin in a helical pattern. A flat spiral coil (also called a pancake coil) is wound in a single plane, like a spiral on a printed circuit board. Solenoids are better for high inductance values, while flat spirals are ideal for planar PCB designs and RFID antennas.

Each turn of wire both creates magnetic flux and links with the flux created by every other turn. Doubling the number of turns doubles the flux created and also doubles the flux linked, giving a quadratic (N²) relationship. This means that adding more turns increases inductance much faster than linearly.

Core materials with high relative permeability (μr) dramatically increase inductance. Air has μr = 1, while ferrite cores can have μr from 10 to 10,000. An iron core can increase inductance by thousands of times compared to an air core. However, ferromagnetic cores saturate at high magnetic fields, which causes the inductance to drop sharply.

The permeability of free space is μ₀ = 4π × 10&supmin;&sup7; H/m ≈ 1.2566 × 10&supmin;&sup6; H/m. This constant relates the magnetic field to the current producing it in a vacuum. For air-core inductors, this is the effective permeability. When using magnetic cores, the effective permeability is μ = μr × μ₀.

Wheeler's approximation is used for flat spiral (pancake) coils where the solenoid formula is inaccurate. It is widely used for PCB trace inductors, RFID antenna coils, and wireless charging coils. The formula is accurate to within about 5% when the coil radius is much larger than the winding width.

Inductors are used in power supply filters to smooth output current, in RF circuits for tuning and impedance matching, in transformers for voltage conversion, in switching regulators for energy storage, and in EMI filters to suppress electromagnetic interference. Every modern electronic device contains multiple inductors.