Length of wire required for a coil length of $x$

Question

I was doing a recent project and was making a coil around a pipe and I was trying to find the length of wire required to make a coil of length $x$ cm. The wire has a thickness of 1cm and the pipe has an outer diametre of 3cm. I wanted to coil the wire around the pipe with no gaps between the coils so that they are all touching. This was my calculation, $$\pi\cdot\left(3+1\right)\cdot\left(\frac{x}{1}\right)=\operatorname{Length of wire}.$$ I believe this is flawed but can't figure out a better method.