What is the side-cut? Is the curve on the sides of a snowboard. If extended, that curve on the sides of snowboards will end up forming a circle. That circle's radius is the side-cut radius, since the side-cut is just a part or the circle, the side-cut radious is the same as the circle radious. Most snowboards side-cuts usually range between 7 to 9 meters, but you can find some production snowboards with a side-cut as low as about 6 meters or as high as about 10 meters. By itself, the side-cut limits the maximum turn size for carved turns, a snowboard with a side-cut of 8 meters can not do turns larger than 8 meters. The amount of pressure you apply to the board while turning bends the snowboard (the flex comes into play here) and makes the side-cut smaller, so a snowboard with a 8 meter side-cut can make turns shorter that 8 meters. Straighter, larger side-cuts (bigger radius, until about 9 or 10 meters) will make the turns larger and give you more control and feel less nervous at speed, and deeper side-cuts (smaller radius, from about 6 or 7 meters) will make the turns shorter and feel more snappy.
Various kinds of side-cuts:
Lifted Edges (convex base / base with various flat areas)