Spiral coil calculator

Spiral coil inductance calculator

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.

Number of turns Turns
Inner diameter mm
Wire diameter mm
Turn spacing mm
Outer diameter mm
Wire length (estimate) m
Inductance uH
Optional extra f.ex. tank capacitance size
Capacitance nF
Resonant frequency kHz

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.

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

27 thoughts on “Spiral coil calculator

  1. 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,

  2. 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

  3. 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.

    wireless energy coil

  4. 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

  5. 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.

  6. 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


  7. 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?

  8. Hello
    Resonance frequency place major role in designing of spiral Transmitter coil.
    How much to be maintain for QI charger?

  9. 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.

  10. 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.

  11. Hi,
    How I can get the Mutual inductance for the same properties of secondary coil?
    I need the equation.

    Thank you.

  12. 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
    Sorry for my possible spelling mistakes because I used a translator

  13. 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?

  14. 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
    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.


  15. 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

  16. 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

  17. Hi folks,

    We used your calculator last month, and thanks for it!

    Have changed dimensions and tried to enter new data – box for lenght
    is in red and won’t accept entry.

    Any thoughts?


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