  The finite-size scaling function of the magnetization of the ferromagnetic
Heisenberg chain is argued to be universal with respect to the magnitude of the
spin. The finite-size scaling function is given explicitly by an analytical
calculation in the classical limit $S=\infty.$ The universality is checked for
$S=1/2$ and $1$ by means of numerical calculations. Critical exponents are
obtained as well. It is concluded that this universal scaling function
originates in the universal behavior of the correlation function.
