I am having a massive senior moment, all day long. I want to roll an inductor 1.27uH. I have chosen a drill bit 0.228" in diameter, and I will use 24 Ga enamelled wire. According to this page, the wire is 0.0201" in diameter. I am using the formula from this page, L=(N^2 * r^2) / (9 r + 10 l) where L = micro Henrys N = Number of turns in the inductor r = mean radius of inductor l = Length of inductor I have empirically solved this to be 21 turns. However I have a hard head, and would like to do this with math. So I redefine some of the variables to make tracking easier. Redefine: x = N g = 24Ga = 0.02010 i = l, which also = g x So, the formula becomes L = (x^2 * r^2) / (9 r + 10 i) here is where it gets interesting 9 r + 10 i = (x^2 * r^2) / L 9 r + (10 g x) = (r^2 / L) x^2 0 = (r^2 / L) x^2 - (10 g) x - 9 r This is the weakest step for me, where I feel I have most likely made the error. I have translated this into a quadratic equation. OK, the variable numbers are: x = Number of turns r = Mean radius = (dia of core * dia of wire) / 2 = 0.124 g = .0201 L = 1.27 Using the quadratic equation x = ( -b +/- sqr( b^2 - (4 a c)) / (2 a) where 0 = a x^2 + b x + c I get x = 2.5, which is a non-starter. I know I'm messing up somewhere. Help?