Air core inductor equations

Here are some air core inductor equations,because sometimes in electronic projects it's needed to design air core inductor, specially in radio frequency circuits.
These air core inductor equations can be used for design most used air core inductors used in electronic circuits.

Classified by the numbers of layers, coils can be: single layer inductor , multilayer inductor .

To calculate Single layer coil you can use the these formula :

,where : d is the diameter of the coil, in mm;
l - coil length in mm
n - number of turns

Or you can use the Wheeler formula :

, where : L = inductance (in microhenries)
r = radius of coil (in inches)
N = number of turns
l = length of winding (in inches )

For Multilayer coil you can use Wheeler formula :

, where : d is the diameter of the coil, in mm;
l - coil length in mm
h - height coil, in mm

Also the air-core planar spiral inductor can be calculated with the Wheeler formula :

, where L = inductance in microhenries

r = radius to center of windings in inches

w = width of the conductor in inches

n = # of turns

If you want to calculate Spiral Wound Coils inductance , you can calculate the inductance with this Wheeler formula :

, where : L = self inductance in microhenrys

N = total number of turns

r = mean radius in inches

b = depth of coil in inches.