Coil Inductance Calculator

This calculator helps you compute the inductance of a coil.

Output

Overview

The coil is the most recognizable form of an inductor. This tool is designed to calculate the inductance of a coil of wire given the number of turns, the loop diameter, wire diameter, and the permeability of the medium. Note that you can choose the unit of measurements for the loop diameter and wire diameter. The number of turns is always assumed as a whole number (it's hard to do a 3.4 turn, for example), but you can still input fractional turns. 

Equation

$$L_{coil} \approx N^{2} \mu_{0} \mu_{r} \left(\frac{D}{2}\right) \left[ln\left(\frac{8D}{d}\right) - 2\right]$$

Where:

$$L_{coil}$$ = inductance of the coil in henries (H)

$$N^{2}$$ = number of turns

$$\mu_{0}$$ = permeability of free space = 4π×10⁻⁷

$$\mu_{r}$$ = relative permeability

$$D$$  = loop diameter

$$d$$ = wire diameter

Applications

Camera Flash Lamp

The inductor (or coil) plays an important role in the camera flash lamp circuitry. For the camera, it is the important component that resulted in the high spike voltage across the trigger coil which was then magnified by the autotransformer action of the secondary to generate the 4000 V necessary to ignite the flash lamp. The capacitor in parallel with the trigger coil charged up to 300 V using the low-resistance path provided by the SCR. However, once the capacitor was fully charged, the short-circuit path to ground provided by the SCR was removed, and the capacitor immediately started to discharge through the trigger coil. Since the only resistance in the time constant for the inductive network is the relatively low resistance of the coil itself, the current through the coil grew at a very rapid rate. A significant voltage was then developed across the coil. This voltage was in turn increased by transformer action to the secondary coil of the autotransformer, and the flash lamp was ignited. That high voltage generated across the trigger coil will also appear directly across the capacitor of the trigger network. The result is that it will begin to charge up again until the generated voltage across the coil drops to zero volts. However, when it does drop, the capacitor will again discharge through the coil, establish another charging current through the coil, and again develop a voltage across the coil. The high-frequency exchange of energy between the coil and capacitor is called flyback because of the “flying back” of energy from one storage element to the other. 

Household Dimmer Switch

Inductors can be found in a wide variety of common electronic circuits in the home. The typical household dimmer uses an inductor to protect the other components and the applied load from “rush” currents—currents that increase at very high rates and often to excessively high levels. This feature is particularly important for dimmers, since they are most commonly used to control the light intensity of an incandescent lamp. At “turn on,” the resistance of incandescent lamps is typically very low, and relatively high currents may flow for short periods of time until the filament of the bulb heats up. The inductor is also effective in blocking high-frequency noise (RFI) generated by the switching action of the triac in the dimmer. A capacitor is also normally included from line to neutral to prevent any voltage spikes from affecting the operation of the dimmer and the applied load (lamp, etc.) and to assist with the suppression of RFI disturbances.

Further Reading

• Textbook - Magnetic Fields and Inductance
• Textbook - Inductor Sizing Equation
• Worksheet - Inductance