Published July 10, 2014. Updated February 13, 2021.

Here you can calculate the inductance for a given size of a spiral coil wound in one layer. It is optional to add the capacitance for f.ex. a primary tank capacitor or topload capacitance to find the resonant frequency of the LC circuit.

The formulas used to derive the inductance is simplified and correct to within 1%. Source “Harold A. Wheeler, “Simple Inductance Formulas for Radio Coils,” Proceedings of the I.R.E., October 1928, pp. 1398-1400.”

Switch between the input fields to automatically calculate the values.

Formulas used**Outer diameter** = inner diameter + ( 2 * number of turns * ( wire diameter + wire spacing))**Wire length** = ((Pi * number of turns * (outer diameter + inner diameter)) / 2) / 1000

The wire length is calculated as an average of the evenly spaced turns, this results in a estimated spiral length from being calculated as single circles.

Inductance

Width w = ((wire diameter / 25.4) + (wire spacing / 25.4)) * number of turns

Radius r = ((inner diameter / 25.4) + w) / 2**Inductance** = (radius^2 * number of turns^2) / (8 * radius + 11 * width)**Resonant frequency** = (1 / (2 * pi * sqrt((inductance / 1000000) * (capacitance / 1000000000)))) / 1000

Thank you thank you

hello

i have a inductor how can i mak it?

L: 1.5 / 3mm 0.5CU 2.5 mm

Hi rubashka

Could you please describe in more details what it is you need.

Kind regards

Mads

Hello, I found this page through a Google search. Very informative. I do have one question, how do you arrive at inductance from the equation: (radius^2 * number of turns^2) / (8 * radius + 11 * width) when there is no permeability units in the formula? I get the same answer you do, but the units are in meters, not henries.

Thank you for your time,

David

Hi David

The formula is a simple approximation as described first in the article.

Permeability is in it, but only for air cored copper coils, this is all a part of Harolds work, he made it simple so you only have to put in some physical dimensions to get a estimated inductance.

Kind regards

Mads

Hi there,

I have 5 turns

inner diameter is : 18 mm

wire diameter is :0.2 mm

turn spacing is : 10 mm

outer diameter is : 52 mm

wire length : 0.5 meters

The capacitance I use is : 1.36 micro farad .

I could not change the value of outer dimater here so please tell me what is the inductance value.

Thanks in advance.

Hi Iyad

The outer diamter is calculated from inner diameter + number of turns (distance), so you should not put that value in, it is calculated.

Judging from your numbers and the picture, something is not right.

Kind regards

Mads

Hi,

I would have thought that since the inductance goes up as the square of the turns, where as the resistance is linear that I could get a higher Q with copper thin strips, and decreasing the turn spacing, but I don’t get the high Q I’m looking for (not more than 40-50 @ 100khz). Do you have any insight into this problem.

Hi,

What formula should I use to calculate the capacitance?

The formula I am using C=0.29l+0.41r+1.94*(r³/l)^0.5

I am using magnet wire 0.4mm², with ID of coil 1″ and 44 turns. I get a calculated capacitance of 71pF

Regards

David

Hi David

I would use the results from JAVATC as I consider this the best and most though-rough calculator available. My own calculator here is only meant for quick estimates where you can get a result from as few factors as possible. Consider it a ideal world with no losses example 🙂

http://www.classictesla.com/java/javatc3d/javatc3d.html

Kind regards

Mads

How to find circumferential area

In geometry, the area enclosed by a circle of radius r is = π * r * r

Hello

Can this formula will be applicable for what type of materials,

we are planning to customize the wireless transmitter coil using printed silver conductive ink.

Same formula can able to applicable?

Hey Krishna

Read on page 30 of this research paper, there is not large difference between coils of different material that has the same physical dimensions: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.597.8728&rep=rep1&type=pdf

Kind regards

Mads

Hello

Resonance frequency place major role in designing of spiral Transmitter coil.

How much to be maintain for QI charger?

Hi krishna

I am not sure what you are asking me about, you need to add more details.

Kind regards

Mads

Very informative article for coil design.

We are trying to build a wireless charger transmitter module. Transmitter coil using printed silver conductive ink. Reference https://www.nature.com/articles/srep15959

The coil designed is based on the Harold A. Wheeler formula. (Inductance 6.5 uH) Wurth Elektronik “760308101103” 6.5uH (https://katalog.we-online.de/pbs/datasheet/760308101103.pdf)

Can we use the same Wheeler’s formula for design a coil printed in silver conductive ink ? I don’t find ready made (COTS) printed coils in the market. Whether there are any changes to be made to achieve the inductance and resonant frequency ?

Please advise.

Hi Sir,

I’m designing a Planar square coil resonator for metamaterial design.

Can I get the formulae for dimensions to design the metamaterial at 10MHz.

Anticipating a positive reply !!

Thanks in advance Sir.

Hi,

How I can get the Mutual inductance for the same properties of secondary coil?

I need the equation.

Thank you.

Hi Rakib Raihan

Its called a helical coil: http://kaizerpowerelectronics.dk/calculators/helical-coil-calculator/

Kind regards

Mads

Hello Mads,

Can you inform me please on the following subject: how can determine at the ends a voltage (V), an intensity (Amp) or a power (Watt) from the information stipulated in the input fields on the calculator spirals.

Is it possible to have a simple and detailed explanation please

Thanks for your help

Best regards

Henri

Sorry for my possible spelling mistakes because I used a translator

Hello,

I want to print it on a PCB. Can you tell me how to draw this spiral coil of my desired dimensions? Any software?

-Sid

Hi David,

For capacitance calculation you mentioned that you have used magnet wire 0.4mm², with ID of coil 1″ and 44 turns.

Please provide the turn spacing so I can get the outer diameter of the coil. My understanding is that the diameter is the average of inner and outer diameter. If I am wrong please mention.

You have used the the following formula for capacitance calculation

C=0.29l+0.41r+1.94*(r³/l)^0.5

I think that the denomination and unit will be as follows

C =Capacitance is in pF

r=radius of coil in inches

l =length of coil in inches

If I am wrong please mention.

Regards,

Morshed

Hi there,

could you please explain how the formula for wire length has been extracted?

Wire length = ((Pi * number of turns * (outer diameter + inner diameter)) / 2) / 1000

Regards,

Farshad

Hi Farshad

Circle circumference is 2 * pi * r.

Here I add the two diameters and divide by 2 to get the radius of the middle turn, an average, by this the 2 in the above equation is even out.

Kind regards

Mads