Finding a Unknown Inductor Equation

Thread Starter


Joined Dec 8, 2011
Well I've got the formula F = 1 / 2pi sqrt L x C
and need rearrange to find L but dont really know if my answer is correct.


Joined Feb 19, 2009
Is this for a simple, air core inductor with a single winding?

Or to determine the Fo of an LC circuit?

I see both your formulas have f and C in your equations. I must admit I do not understand the question you are asking.

There is a formula for a wound air coil of Length L and diameter d with a winding density factor.

There is a formula for an inductor wound on a ferrite core, but the permiability of the core would be needed.

The resonant frequency, \(F_o=\frac{1}{2 \pi sqrt{L C}}\)

Please be more verbose with your question, explaining what you do know, and what you'd like to figure out.

First, keep in mind: \(\omega=2\pi F\) and \(F=\frac{\omega}{2\pi}\)

--ETA: Your Post #3 states you want to solve \(F_o=\frac{1}{2 \pi sqrt{L C}\)

The equation is derived from:


to get L out, we need to square both sides:


now we can "swap" the left with the denominator


woops, moved one too many:

\(L=\frac{1}{\omega^2 C}\)

Obviously, the formula is the same to find C if you know f and L

\(C=\frac{1}{\omega^2 L}\)
Last edited:


Joined Apr 17, 2010
I also didn't understood your question...
Anyway to find out inductance for a coil you can use Wheeler's Formula

Inductance (\mu H) = {{0.8(NA)^2} \over {6A + 9B + 10C}}

N = number of turns
A = average coil radius
B = coil length
C = coil thickness

All quantities are in inches and the result is in microhenries \((\mu H)\).

Good Luck


Joined Dec 26, 2010
The OP's problem appears to be stated in terms of the resonant frequency in a tuned circuit, not the coil's construction.