Tesla Coil
formule that I have found useful  

V = I * Z

P = I * V

V = volts
I = current in amps
Z = impedance or resistance in ohms
P = power in watts

Non Resonant Transformer Input and Output

E_P*I_P = E_S*I_S

E_P = primary voltage
I_P = primary current in amps
E_S = secondary voltage
I_S = secondary current in amps

Capacitive Reactance

X_C  =  1 / ( 2 *  * F * C )

X_C = capacitive reactance in ohms
F = frequency in hertz
C = capacitance in farads

Inductive Reactance

X_L  =  2 *  * F * L

X_L = inductive reactance in ohms
F = frequency in hertz
L = inductance in henrys

Resonant Circuit Formula

F = 1/( 2 *  * ((L * C))

F = frequency in hertz
L = inductance in henrys
C = capacitance in farads

Spiral Coil Inductance

L = ( N*R )2 / ( 8*R + 11*W ) L = inductance of coil in microhenrys (�H) R = average radius of the coil in inches N = number of turns W = width of the coil in inches

Helical Coil Inductance

L = ( N*R )2 / ( 9*R + 10*H ) L = inductance of coil in microhenrys (�H) N = number of turns R = radius of coil in inches H = height of coil in inches

Inverse Conical Coil Inductance

L1 = ( N*R )2 / ( 9*R + 10*H ) L2 = ( N*R )2 / ( 8*R + 11*W ) L = ( (L1* sin(x))2 + (L2* cos(x)) 2 ) L = inductance of coil in microhenrys (�H) L1 = helix factor L2 = spiral factor N = number of turns R = average radius of coil in inches H = effective height of the coil in inches W = effective width of the coil in inches X = rise angle of the coil in degrees

Medhurst

C = 0.29 * L + 0.41 * R + 1.94 *  (R³ / L )

C = self capacitance in picofarads
R = radius of secondary coil in inches
L = length of secondary coil in inches

Toroid Capacitance

C = 1.4 * ( 1.2781 – (D₂ / D₁) )  ( * D₂ * (D₁ – D₂) )

C = capacitance in picofarads
D₁ = outside diameter of toroid in inches
D₂ = diameter of cross section of toroid in inches

Sphere Capacitance

C = (25.4*R) / 9

C = capacitance in picofarads
R = radius in inches

Plate Capacitors

C =( .224 * K * A ( N -1) ) / (1000000 * D )

C = capacitance in microfarads
K = dielectric constant
A = area of each plate in square inches
N = number of plates
D = distance between plates in inches (thickness of dielectric)

Energy Stored in a Capacitor

J = 0.5 * V² * C

J = joules of energy stored
V = peak charge voltage
I = peak current
C = capacitance in farads

 

Energy for and Inductor

J = 0.5 * I² * L

J = joules of energy stored
V = peak charge voltage
I = peak current
C = capacitance in farads
L = inductance in henries
Inductance of a circular loop of wire (Wheeler)

R = Wire Radius
a = Loop Radius
Lo = Inductance of  loop

 

Lo = m₀* a * (ln((8 * a) /R) -2)
Inductance of two parallel wires (Wheeler)

R = Wire Radius
l = Length of wires
d= spacing of wires
Lo = Inductance of  wires.

 

Lo = (m₀* l / d) * (ln(d / R) -1)
Inductance of two parallel inductors

Lt = Total Inductance
L_x = Inductance
M = mutual inductance between inductors

 

1/L_t = (1 / (L₁* [+/-]M)) + (1 / (L₂* [+/-]M))
Inductance of two series inductors

Lt = Total Inductance
L_x = Inductance
M = mutual inductance between inductors

 

L_t = (L₁ + L₂) + [⁺/-]2M)
Magnetic field around a single conductor

R=radius from wire
I=Current in wire
B=Magnetic Field Strength

B=(m₀* I) / (2 * * R)

Resonant Transformer Voltage Multiplication from Inductance

V_s= Voltage on Secondary
V_p= Voltage on Primary
L_s= Inductance of Secondary
L_p= Inductance of Primary

V_s= V_p (L_s / L_p)

 

Resonant Transformer Voltage Multiplication from Capacitance

V_s= Voltage on Secondary
V_p= Voltage on Primary
C_s= Inductance of Secondary
C_p= Inductance of Primary

V_s= V_p(C_p / C_s)

Current Transformer Turns to Current ratio.

I_p= Primary Current
I_s= Secondary Current
N_p= Turns on Primary
N_s= Turns on Secondary

I_p/ I_s= N_s/ N_p