# Inductance and designing a coil

by Hussman
Tags: coil, design, inductance
 P: 39 There is a simple equation that describes the inductance of a solenoid - basically any coil with many turns of wire on it. This is it: $$L = \frac{\mu_0 n^2 A}{l}$$ where $$\mu_0$$ is the magnetic permeability of free space, n is the number of turns of the wire, A is the area of one of the wire loops, and l is the length of the coil, measured from the first turn to the last. Just make sure everything is entered in SI units (meters, amps, etc.) and you should be fine. Take note that the wire diameter is not part of this equation. The only reason it will matter for you is you know that given the inner and maximum outer dimensions of the coil, the wire will need to be a certain thickness to get the needed number of turns to fit into the space you have.