The three-boson low energy effective interaction influences the dynamic and the static properties of many bosons, including the ground state energies of dilute Bose-Einstein condensates. The three-body scattering hypervolume, which is a three-body analogue of the two-body scattering length, characterizes this effective interaction. For bosons with a soft-ball potential -- the Gaussian potential, we determine the scattering hypervolume by solving the three-body Schrödinger equation numerically, and matching the solution with the asymptotic expansions for the wave function at large hyperradii.