Coil resonant
frequency calculator



This calculates the coil's resonant frequency (f), inductance (L), and self capacitance (C), given the length and width of the coil as input.

Assuming that the coil will be a quarter wave oscillator ( λ = 4 ℓ ),  the full length of the wire can be found by:

  c  =  λ f    

  c  =  ( 4 ) f    

    4 f



    •  c   is the speed of light in air, ( 29,970,254,700 cm/s ) 
    •  λ   is the wavelength,  
    •  f   is the frequency and,
    •  ℓ   is the total length of the wire.

The coil used here for this calculation is solenoid shaped, and it is assumed to be made of copper.

The input for this calculation requires these properties:

    • resonant frequency desired, f,
    • and the wire's gauge.

( units are in:   Hz, and AWG,   respectively )

The output calculated properties of the coil will be:

    • the total length of wire used for the coil, ℓ,
    • diameter of the coil, d,
    • length of the coil, l,
    • inductance. L,
    • approximate self capacitance, C,
    • mass of the coil, M,
    • and the number of turns, N.

( units are in:   cm, cm, cm, Henries, Farads, kg, and turns,  respectively )

  (ℓ), in centimeters,



       M primary   =   M secondary   +   M extra



This tool allows us to try different diameters, lengths, (and gauges) for the primary, and then it solves for a variety of properties of the coil..


     mass of copper coil:      kg


     total wire length, in cm:      cm    

     diameter:       cm


     length:       cm

           wire gauge:  







The total number of turns for the coil:

        N =  0.0000000000  turns




mass   (M primary):  0.00000  kg  
coil diameter  (d) :  0.00  m  
coil length  (ℓ) :  0.000  m  
wire gauge   :    AWG  
wire radius (inches)  :  1.00000  in  
wire radius (meters)  :  1.00000  m  
wire length (inches)  :  0.00000  in  
wire length (meters)  :  0.00000  m  
L   :  0.000000000000   μH

density of copper (ρ)  =  8940 kg / m3

  The number of turns (N) is computed from:  
    M primary
N   =  
     π 2  ρ  d  r 2


    •  N   = the number of turns of the coil 
    •  M primary   = the mass of the coil (kilograms)
    •  ρ   = the density of copper (kg / m3)
    •  d   = diameter of the coil (meters)
    •  r   = radius of the wire (meters)

  The above is derived from:  

      total length of the wire for the coil :    ℓ = N C    

       ( length of the wire = turns, times, circumference of the coil )


      total length of the wire for the coil :   ℓ = M / ( ρ A )

       ( length of the wire = mass of the wire, divided by:
                               density of copper times
                                       the cross-sectional area of the wire )


  The inductance, in μH,  is estimated by the following, with the length and diameter measured in inches. **  
                  Inductance ( μH )      
    d 2  N 2
L    =  
    18 d  +  40 ℓ

** The ARRL Handbook for Radio Communications 2011
section 2.8 Inductance and Inductors

radiant arcs
tesla coils
self-oscillating voltage demo
audio tests
techstars application
violet ray documents
coil frequency calculator
coil dimensions calculator
wire length spool calculator
capacitance calculator
primary coil turns calculator