Spiral Coil Calculator

Spiral coil inductance calculator

Here you can calculate the inductance for a given size of a spiral coil wound in one layer. Secondly you can to add the capacitance for f.ex. a primary tank capacitor or topload capacitance to find the resonant frequency of the resulting LC circuit. If you want to calculate the inductance of a helical air core coil, like a Tesla Coil secondary, use the Helical Coil Calculator.

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

This calculator does not take other factors in, that could affect the calculated resonant frequency. A secondary coil in a Tesla Coil would affect the resonant frequency due to the magnetic coupling factor k and proximity effect.

Formulas and math used in the spiral coil calculator

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

Published July 10, 2014. Updated November 1, 2021.

34 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,
    David

  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
    Mads

  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
    Mads

  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

    Regards
    David

  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
    Henri
    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?
    -Sid

  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
    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

  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
    Regards,
    Farshad

  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
    Mads

  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?

    Gerry

  18. Hi Mads, I want to make a wireless charge receiver coil

    If the resonant frequency of the receiver coil is 50khz then is it OK if the oscillation frequency of the transmitter is a multiple of this (ie 150khz, 200khz, 250khz?)

  19. Hi Jason

    For each order you move away from the fundamental frequency, the amplitude of the signal is reduced. It will lower the efficiency significantly if you do not match the transmitter and receiver coil.

    Kind regards
    Mads

  20. I’ve just noticed that the calculator also allows me to enter the coupling capacitance. Thank you for making such a fantastic website!

    I’m making this on FPC (flex pcb), 2 layers. So being able to try out parameters before ordering the boards is incredibly useful. I’m also using this excellent Kicad footprint wizard (https://gitlab.com/-/snippets/1916811#)

    My copper is only 35um per side (2oz/CuFt) which means the resistance is substantially higher than the wire diameter suggests.

    Is there any way to estimate the Q@frequency given the expected resistance?

    I found this trace calculator which lets me estimate the resistance.
    https://www.allaboutcircuits.com/tools/trace-resistance-calculator/

    My maximum diameter is 30mm so by varying the trace width I can choose from the following options

    0.1mm trace width, 70 turns, inductance = 47uH and 1.55ohms resistance.
    0.2mm trace width, 45 turns, inductance= 20uH and 0.48ohms resistance.
    0.3mm trace width, 35 turns, inductance= 12uH and 0.25ohms resistance.
    0.4mm trace width, 28 turns, inductance = 7.6uH and 0.15 ohms resistance.

    I appears that the inductance / resistance ratio is
    47uH / 1.55 = 30
    20uH / 0.48ohm = 41,
    12uH / 0.25ohm = 48,
    7.6uH / 0.15 ohm = 50

    So it appears the thinnest traces (0.1mm) with 70 turns is actually preferable.

    Is there a way to estimate the Q for each inductance, resistance pair?

  21. The resonant frequency formula is off by one decimal place.
    Example: 16.95 should read as 1.695 kHz.

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