# Confusion about calculating inductance of a coil

I'm a little confused about how to calculate the inductance of a wire coil. While I thought this would be really clear, what is confusing me is that there seems to be different ways to calculate it. In this question, the result of the inductance formula is dependent on cross sectional area, number of turns, permeability and the length of the coil. For the calculator on EEWeb, the inputs are the diameter (and hence the cross sectional area), the number of turns, permeability and the wire diameter, and the wire diameter, rather than the length of the coil. I'm unclear how the formulas are related or which one to use. My guess is that the 2nd calculation determines the inductance for a coil one meter long and I have to divide by the length of the coil I'd want to find the inductance of, but I'm not sure.

• I believe the former formula is assuming the wire diameter is negligible. The later probably assumes a particular geometry so the length is dependent on the number of turns and the two diameters. Different assumptions were made is all. – jramsay42 Feb 17 '18 at 0:46
• Wire diameter is the same as wire gauge, which does affect the Q of the inductor, or its efficiency as an inductor. Q = L/R, so fine gauge wire will get you the same inductance as heavy gauge wire, but its DC resistance will affect RF performance. – user105652 Feb 17 '18 at 0:51

My guess is that the 2nd calculation determines the inductance for a coil one meter long and I have to divide by the length of the coil I'd want to find the inductance of, but I'm not sure.

No, it's got nothing to do with a 1 metre length of solenoid.

The EEweb calculator is definitely problematic because it assumes all the "turns" are stacked on top of each other and not laid out like a solenoid. This can be easily proven. For instance if I set up the loop diameter to be 279 mm and the wire diameter 1mm, I get an inductance of 1 uH.

If I double the turns I get 4 uH. If I make the turns 100, I get 10 mH - this is exactly how inductance would change if wound on a core with no leakage flux i.e. inductance is proportional to turns squared. However, 100 turns cannot occupy a close-knit volume of space and at all possibly hope to have 100% coupling from every turn to each other turn.

Basically, it's a pile of doo doo.

Inductance calculations are very sensitive to winding geometry and scholarly correction factors exist. This is because there many more variables from simple designs to complex.

The basic calculation must include wire diameter, length and average winding diameter as fill factor , insulation and overlap have some variations.

The effective diameter Deff obtained from here is used to calculate the inductance of the single-layer helical coil:

where:

μ: permeability of the coil core
N: number of turns
l: length of the coil, measured from the connecting wires centre to centre
kL: field non-uniformity correction factor according to Lundin
ks: round wire self-inductance correction factor according to Rosa
km: round wire mutual-inductance correction factor according to Grover and Knight