Actually, I led you astray. I didn't do the math correctly as I read through your post too quickly and was wrong with my reply. The rigidity is determined by the difference in diameter, not the area of a cross section. This makes an 8mm 1.5872 times stiffer. (8mm / .25 inch) squared, or .315/.25 squared, or 1.2598 squared) In the case of .5 versus .25 it's: .5/.25, or 2 squared, or 4 times stiffer. This is the Easy one. Twice as big equals 4 times as stiff. Either way, these are important differences when it comes to routing. There is a huge difference in actual use between 1/4 inch bits and 8mm bits. Remember, all this talk about stiffness has been about the shank size, but the reality is that bits almost never break through the shank. They break somewhere across the flutes because the cross section of the bit is always smaller than the shank to allow for chip clearance. In a 1/4 bit a very high proportion of material need to be removed compared to its bigger counterparts. The ratio between a 1/4 inch bit to an 8mm bit, through the cross section, could easily be 2 to 1 or more. this is even more true in the case of a brazed carbide bit because the underlying steel needs to be cut away even more to leave room for the carbide. This is also one of the unmentioned benefits to solid carbide. Beside it being inherently more wear resistant, it is also stiffer and the entire tool is amorphous, or monolithic, so all material contributes to stiffness.