# What equation should I use to calculate inductance of wire coil?

I've been working on a project recently which requires me to build an inductor, however in my research I found many different equations (with a range of variables used and giving very different results to the same coil specifications) and I was wondering what equation I should use. I have attached some links below to sites with different equations on them.

https://sciencing.com/calculate-inductance-coil-6026538.html

https://en.m.wikipedia.org/wiki/Inductance

• Define L, AMPS AND f first Commented Jan 15, 2021 at 1:27
• Then define how you are going to measure it. E.g slew rate or LC oscillator Commented Jan 15, 2021 at 1:36

The proper formula depends upon a) whether your coil has a core and b) whether your coil is long or short, fat or thin, etc.

The most efficient air-core coil in terms of copper is a Brooks coil. It has a square cross section, and an outside diameter twice its inside diameter. You can see an image of the coil here.

The formula for the inductance of a Brooks coil is:

$$L \approx 0.025491rN^2$$

where N is the number of turns, r is the inside radius in cms, and L is the inductance in uH

There are also formulae for single layer long coils, multi-layer short coils and flat "pancake" coils found at this page

This image from AllAboutCircuits, shows various coil cross sections, and their corresponding (approximate) inductance formulae.