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Formula Collection 
FORMULA NAME: Single Layer Coil Formula  
FORMULA USAGE: To calculate inductance in single layer coils.  
APPLICATION: Use to ballpark Tesla coil secondary inductance.  
FORMULA DEFINTIONS 
L is the inductance in microhenrys.  N is the number of turns. 
A is the mean radius in inches.  B is the length of the coil in inches. 
(N * A)^2 L =  (9 * A) + (10 * B) 
SQR(L * ((9 * A) + (10 * B))) N =  A 
9L + SQR(81 * L^2 + 40 * B * N^2* L) A =  2 * (N^2) 
(((N * A)^2) / L)  (9 * A) B =  10 
EXAMPLE APPLICATION  
Secondary diameter is 4 inches. (Let's call this SD) Length of coil windings is 15 inches. Wire diameter is .03 inches.(Let's call this WD) Turns per inch = 1 / wd = 33.3333 (Let's call this TPI) With this prior information we can now determine N, A, and B. B = 15 N = B * TPI = 15 * 33.33333 = 500 A = (SD + WD) / 2 = (4 + .03) / 2 = 2.015 Now plugging into to the above formula to solve for L (500 * 2.015)^2 L =  (9 * 2.015) + (10 * 15) 1015056.25 L =  168.135 L = 6037.150207 microhenrys (Multiply by 10^6 for henrys) L = .0063715 henrys 
FORMULA NAME: Resonance Formula  
FORMULA USAGE: To find resonant frequency  
APPLICATION: Guess!  
FORMULA DEFINITIONS  
RF is the resonant frequency in hertz.  L is the inductance in henrys. 
C is the capacitance in farads.  pi = 3.141592654 
1 RF =  2 * pi * SQR(L * C) 

L = (1 / (2 * pi * RF * SQR(C)) ^ 2)  C = (1 / (2 * pi * RF * SQR(L)) ^ 2) 
EXAMPLE APPLICATION  
Let's use the inductance calculated from single layer example. L = .0063715 henrys Lets say that the seondary and torroid capacitance = 10pf C = .00000000001 Now plugging into to the above formula to solve for RF 1 RF =  2 * 3.141592654 * SQR(.0063715 * .00000000001) RF = 630520.6113 hertz 