Long polymer chains in concentrated solutions or dense melts interpenetrate extensively. This results in molecular entanglement and topological constraints that severely restrict the motion of polymers and dominate their flow properties. The effect of entanglements on chain motion has long been understood in terms of a confining tube. The tube is characterized by its diameter, which measures the strength of confinement. We show that a purely topological approach can be used to compute the tube diameter by establishing a direct link to the statistics of topological states in simulations of topologically equilibrated ring polymers. We determine how the tube diameter varies with solvent dilution and chain stiffness. We use these results to choose among several phenomenological proposals that relate the tube diameter to the packing length, which sets the scale for close encounters between nearby chain segments.