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 ℓ ) f    

where,

    •  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..

density of copper (ρ)  =  8940 kg / m³

where,

    •  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)

      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 ARRL Handbook for Radio Communications 2011
section 2.8 Inductance and Inductors