# Coil Inductance Calculator

## This calculator helps you compute the inductance of a coil.

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### 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. • SLK001 April 08, 2016

Can you make the output to display in engineering notation (e+3, e-3, e-6, e-9, etc)?

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• Antonio Braz Eufrazio October 23, 2016
• Khalid AlHashemi October 17, 2017

dear sir ... what is the value of relative permeability please

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• RK37 October 17, 2017
Relative permeability is the ratio of the permeability of the inductor's core to the permeability of free space. So it depends on the core material. If there is no core material, the relative permeability is 1. With a ferrite core, the relative permeability might be 600. You can find more values here: https://en.wikipedia.org/wiki/Permeability_(electromagnetism)#Values_for_some_common_materials
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• Henry Zhang 1 March 14, 2018

Hello sir, do you think a 100 Henries inductor coil normal?
The inductor is a common school use transformer 5000 turn coil, with wire diameter about 0.15mm, the official air-core value is 0.6H, however when I calculate the iron core got a result of 105H. Could this be possible? So it suggests the permeability of the iron core is about 175

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• RK37 March 15, 2018
Please take a look at this table: https://en.wikipedia.org/wiki/Permeability_(electromagnetism)#Values_for_some_common_materials You will see that 175 is not an unreasonable number for the relative permeability of an inductor core. The table indicates that ferrite can have a relative permeability greater than 600.
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• Rookietron March 29, 2018

The calculator is very good.  But it can be improved by providing drop-down menus for (a) relative permeability for common materials including air(which is ~1.0), and for (b) the result in H, mH, and microH.

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• C
cubetron May 16, 2019

I am not sure about the results of this coil inductance calculator,  by using the following parameters:
N=110 turns
D=35 mm coil diameter
d=0.5 mm wire diameter
relative permeability=1 (air core)

the calculator provides 1150 uH (microH). This is in agreement with your formula but it does not apper to be correct. By using equations from electronics texts or manuals (like Bleaney, 1989, Electricity and Magnetism) I obtain a value around 270 uH. I have actually built such a coil, and measured a value around 300 uH. Am I using your calculator in the wrong way? Or is there some error in it?
Thanks

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• W
Waveform May 16, 2019

This is way out, to the point of not even being useful.  It is actually worse than when I used to calculate turns using area and AL values back in about 1983.  That got you within a few turns but this is out by a factor of at least 3.  I have in front of me an air core coil of 0.47mH with 160 turns of 1.25mm and an inner dia. of 25mm and an od. of 41mm.  It has 6 and a bit layers.  You say that it should be 1.71mH for a mean value of 32mm for the diameter!  If only life were so cheap.

I measured to approximately layer 3.5, but we are still miles out if I do it by average area cut per turn (it goes up) and, even at the minimum diameter of 25mm, which cannot be the average area per turn,  it is still 1.24mH - out by a factor of 2.66.  You might be helpful to the people selling copper wire, but how does it help me trying to make a 0.56mH inductor.  It doesn’t - and that surely is the role of a tool on the internet?

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