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What is the equation to determine a coil's inductance? Answered

I have been looking for the equation to determine a coils inductance in henries, but I can't find it. I want the one that uses core diameter, wire thickness, and wire length to calculate it. (But I'll take any equation that will allow me to calculate it easily without test equipment) Could someone help me out?                                                                                                                                                         Thanks!



Best Answer 9 years ago

If you feed that exact question into Google, it pops up with plenty of answers, one of which is


Answer 9 years ago

That's actually a pretty useful site. I did not find it in my searches. Thanks!

Jack A Lopez

9 years ago

Is this the same toroidal core you were asking about in your previous question?

If so the last equation in the table on this page:
gives the formula for such an inductor.  

For winding a toroid it is convenient to start with a fixed length of wire wound onto a thin shuttle that can pass through the center of the toroid as you wind it.  And I'm guessing that's why you want a formula that includes the total length of the wire.

You might have noticed all the formulas on the page I linked to include a factor of N2.  Find N by dividing the total length of your wire by the length of one turn.   Example: if your turn radius is r=5mm, then the length of one turn is 2*pi*r = 31.4 mm.  Supposing the total length of your wire is 10 m, then N = (10 m)/(31.4e-3m) = 318 turns.  Use that N in your inductance formula.

The only thing left is the relative permittivity of the core, and that varies from one material to another.  If you have data on this from the core's manufacturer, then that's great.  In the more likely event that you salvaged the core out of some piece of discarded electronics, well then, that's sort of going to make you wish you owned some sort of tool for measuring inductance. 

transistorguyJack A Lopez

Answer 9 years ago

No, this is for a tesla coil project, but I have an old engineering book that lists the permeability for different materials- so I'm good in that area. I just needed the equation. Thanks!


9 years ago

The formulae are easy, the data on the core material is a lot harder. Basically, you can't calculate it, you have to measure it, since you don't know Al