# Spiral Coil 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.

### 39 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

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.

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. David Whitworth

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 ?

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.

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. A.K.M.Morshed Alam

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,

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. Gerry Jonsson

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

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.

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.

Do you have any resource for determining the voltage and current required to drive the coil using the inductance and resonant frequency?

Also, what if the conductor is not a wire, but a tube? IE a 6mm OD x 0.5mm wall copper tube?

This brings me to a follow up question. In the subsequent equation, the variable k is defined as “coupling” or as above, “magnetic coupling factor”. I browsed some on the forum. But couldn’t find the relative formula. A few references. But nothing specific. Any resources for that?

Good thinking about the skin effect for the tubing. I didn’t think about that.

Thanks!

24. Hi Eric

I guess coupling factor is not discussed, because its a general transformer design factor and quite simple.

If primary and secondary coil was to take up the same physical space (impossible), then the k factor would be 1. So the further away they are from each other, the lower is k.

Kind regards