Radius = number of jumps (or maybe number of jumps + 1 - I forget).
As Erik said, the radius grows more slowly than the level. If forget if level(radius) is roughly quadratic (i.e. L = R^2) or roughly exponential (i.e. L = 2^R), but what I do remember is that neither formula is exact - there's some off-by-one stuff going on.
There's an old thread (a year or two maybe? probably in Academy) somewhere where people went through and found the exact relationship experimentally. So if you want to know the exact relationship (i.e. where the break points are to jump to a new level) you can either search for that thread or temporarily SM new sector commands onto your homeworld one-by-one and see where the radius jumps.
John