Noob question, sorry but there's no clear answer that I could find. 
I'm seeking a rod that is flexible enough to be wound up but which would prefer to be a straight line.
Imagine one of those auto-erecting tents that fold up into a round bag, but in this case would fold up to around 15cm diameter. Something like that would serve that purpose when piped into the outline of fabric.

I think 1, 2, or 3mm carbon rod may do for what I need but I'm not sure.

Thanks.

At the bottom end of the scale, the 1mm rods will coil easily enough, we have had to do that to send one by post where the cheapest possible shipping was requested by the customer.

The bigger diameter rods can be coiled up to around 4mm but the diameter is much bigger and you would probably need to experiment to find the right kind of curvature without it breaking.

Warren Penalver
Easy Composites / Carbon Mods - Technical Support Assistant