  The binding energies of two-dimensional clusters (puddles) of $^4$He are
calculated in the framework of the diffusion Monte Carlo method. The results
are very well fitted by a mass formula in powers of $x=N^{-1/2}$, where $N$ is
the number of particles. The analysis of the mass formula allows for the
extraction of the line tension, which turns out to be 0.121 K/A. Sizes and
density profiles of the puddles are also reported.
