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.

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.

MiguelThank you thank you

rubashkahello

i have a inductor how can i mak it?

L: 1.5 / 3mm 0.5CU 2.5 mm

Mads BarnkobHi rubashka

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

Kind regards

Mads

DavidHello, 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

Mads BarnkobHi 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

IyadHi 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.

Mads BarnkobHi 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

Wayne TomHi,

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.

David WhitworthHi,

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

Mads BarnkobHi 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

DHANUSHHow to find circumferential area

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

KrishnaHello

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?

Mads BarnkobHey 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

krishnaHello

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

How much to be maintain for QI charger?

Mads BarnkobHi krishna

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

Kind regards

Mads

HariharanVery 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.

Raagavi BHi 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.

Rakib RaihanHi,

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

I need the equation.

Thank you.

Mads BarnkobHi Rakib Raihan

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

Kind regards

Mads

warie henriHello 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

SiddharthHello,

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

A.K.M.Morshed AlamHi 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

FarshadHi 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

Mads BarnkobHi 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

Gerry JonssonHi 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

Mads BarnkobHi Gerry

Its only the green text fields that are meant for entry. The red ones are results.

Kind regards

Mads

Jason RennieHi 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?)

Mads BarnkobHi 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

Jason RennieI’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?

Jason RennieHi Mads, I found this which explains the complexities of estimating the Q factor (https://www.apogeeweb.net/electron/what-is-the-Q-factor-of-an-inductor-in-circuits.)

I’ve realised there’s no way to really accurately estimate this on paper so I need to order some test boards with various coil parameters to test with.

Thanks again for the excellent webpage!

Mads BarnkobHi Jason

You could calculate Q from the load resistance divided by the primary reactance, as shown here: https://kaizerpowerelectronics.dk/tesla-coils/kaizer-vttc-i/

Kind regards

Mads

DanielThe resonant frequency formula is off by one decimal place.

Example: 16.95 should read as 1.695 kHz.

Mads BarnkobHi Daniel

Are you sure? I just double checked to another calculator, to be sure: https://goodcalculators.com/resonant-frequency-calculator/ and I get the same results there as here.

What are your input values for which you think the result should be different?

Kind regards

Mads

EricMads,

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?

Mads BarnkobHi Eric

For impedance matching, check out this thread: https://highvoltageforum.net/index.php?topic=113.0

As the high frequency current runs on the outside of the conductor of a tube, you just enter it as its outer diameter. If it was a wire, the current would still only run in the same material as in a tube, due to the skin effect.

Kind regards

Mads

EricThanks Mads,

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!

Mads BarnkobHi 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

Mads

EricMads,

Any chance we could converse via email? I’d like to talk with you in greater detail about this and a project I am working on.