Coil Inductance Formulas
Inductance is defined as the property of a conductor by which it opposes the flow of current.
Inductance formulas  

To directly calculate inductance of any coil  L =
µN^{2}A
/
l

To determine the stored energy in inductor/inductance  L =
2 W
/
I^{2}

In terms of EMF  EMF = 
L ΔI
/
Δt^{2}

where
L = Inductance of inductor (coil)
µ = Absolute permeability of core material
N = Number of turns in coil
A = Area of coil
W = Energy
l = average length
How to calculate the inductance of coil
The inductance of any coil depends on four factors. It is directly related to magnetic permeability, the number of coil turns and area of the coil. However, it is inversely related to the length of the coil.
L = µN^{2}A/I
Example # 1: An iron core inductor has 7 number of turns. The radius of the core is 0.1 cm^{2}. The length of coil is 0.1 cm. Find the inductance of coil created by 2 A current.
Solution: Area = πr^{2 }= 3.14 * 10^{6}
The magnetic permeability of iron is 6.3×10^{−3}. So µ = 6.3×10^{−3}
L = [ 6.3×10^{−3 }* 49 * 3.14 * 10^{6}] / 2 A = 461 nF
Energy stored in coil
The energy stored in an inductor (coil) is half the inductance times square of the current. Mathematically
W = [L * I^{2}] /2
From above equation, the inductance can be defined as twice the energy to current.
L = 2 W/I^{2}
Example 2: The inductor coil stores 20 J energy when a steady current of 2 amps current flows through it. Find the inductance of the coil.
Solution: L = 2 W/I^{2} = {2 * 20 J} / 4 amps = 10
In terms of EMF
We can also define inductance as the change which is generated to oppose the current flow. In that case, we can mathematically write. EMF = LΔI/Δt^{2}