Need help with resonance algebra

[cyb0rg777]

I was figuring up some resonant circuits.
I haven't had time to learn latex very well so I'll try to do the best I can.
So I started with this resonant formula.

[latex]F=\frac{1}{2\pi sqrt {LC}}[/latex]

I found the value for L with a 20pf capacitor at 440mhz by changing it to this formula.

[latex]L=\frac{\frac{\frac{1}{F}}{2\pi}^2}{C}[/latex]

Now I'm looking for how many turns of an air core inductor I need to make a 6.5419nH coil with a diameter of 3.175mm(.125") and 12.7mm(.5") length.

I'm starting with this formula.

[latex]L=\frac{.001 N^2 r^2}{228r+254l}[/latex]

L= inductance in henries
r=radius in meters
l=length in meters
N= number of turns

So I rearranged it to this to get the number of turns.

[latex]N=sqrt(\frac{L(228r+254l)}{.001r^2})[/latex]

But when I check my answer it comes out wrong.
Could you help me out ?
My math is not very good.

 

[cyb0rg777]

I think I got it .
I might have been forgetting to take the square root on the last formula.
It comes up to 1.6 turns .I think I'll try it with a smaller capacitor to get more turns.

 

[Nigel Goodwin]

Assuming you're hoping to construct such a coil?, you need to be aware that stray capacitance and inductance will completely change your calculations!.

 

[cyb0rg777]

I was hoping to adjust the coils by spreading them apart and squeezing them together but I've never built anything like that from scratch.From following a set of instructions yes but not from my own design.

 

[Hero999]

Spread apart is often best because it will keep the parasitic capacitance as low a as possible and a long and thin coil is supposed to be better than a long a short and fat coil.