# Finding a Unknown Inductor Equation

#### trav

Joined Dec 8, 2011
7
Does anybody know the formula to calculate for a unknown inductor?

#### t06afre

Joined May 11, 2009
5,934
Can you elaborate on the problem

#### trav

Joined Dec 8, 2011
7
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.

#### trav

Joined Dec 8, 2011
7
I got the formula of L = 1 / 4(pi^2)(f^2)xC anyone can clarify this?

#### thatoneguy

Joined Feb 19, 2009
6,359
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:

$$\omega=sqrt{\frac{1}{LC}$$

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

$$\omega^2=\frac{1}{LC}$$

now we can "swap" the left with the denominator

$$LC=\frac{1}{\omega^2}$$

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:

#### debjit625

Joined Apr 17, 2010
790
@trav
I also didn't understood your question...
Anyway to find out inductance for a coil you can use Wheeler's Formula

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

where
N = number of turns
B = coil length
C = coil thickness

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

Good Luck