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.
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.