Using the wall theorem, the osmotic pressure of ring polymers in solution has been determined using an off-lattice topology conserving Monte Carlo algorithm. The ring polymers are modeled as freely-jointed chains with point-like beads, i.e., under conditions corresponding to theta -conditions for the linear chains. The equation of state is determined. It is furthermore demonstrated that a similar equation of state is found for the corresponding linear chains taking beads of size 0.113 in units of bond length.