  Saturn's rings consist of a huge number of water ice particles, with a tiny
addition of rocky material. They form a flat disk, as the result of an
interplay of angular momentum conservation and the steady loss of energy in
dissipative inter-particle collisions. For particles in the size range from a
few centimeters to a few meters, a power-law distribution of radii, $\sim
r^{-q}$ with $q \approx 3$, has been inferred; for larger sizes, the
distribution has a steep cutoff. It has been suggested that this size
distribution may arise from a balance between aggregation and fragmentation of
ring particles, yet neither the power-law dependence nor the upper size cutoff
have been established on theoretical grounds. Here we propose a model for the
particle size distribution that quantitatively explains the observations. In
accordance with data, our model predicts the exponent $q$ to be constrained to
the interval $2.75 \le q \le 3.5$. Also an exponential cutoff for larger
particle sizes establishes naturally with the cutoff-radius being set by the
relative frequency of aggregating and disruptive collisions. This cutoff is
much smaller than the typical scale of micro-structures seen in Saturn's rings.
