^ Yes, that's right. For each doubling of the pipe diameter, the cross sectional area of the pipe quadruples, hence why you can often get much more flow for just a small increase in diameter.
The other thing that works in your favour is that for example, 32mm pipe only costs about 50% more than 25mm pipe, even though as per Oor Wullie's calculations, it will give you nearly twice the flow.