The cytokinetic ring generates tensile force that drives cell division, but how tension emerges from the relatively disordered ring organization remains unclear. Long ago, a musclelike sliding filament mechanism was proposed, but evidence for sarcomeric order is lacking. Here we present quantitative evidence that in fission yeast, ring tension originates from barbed-end anchoring of actin filaments to the plasma membrane, providing resistance to myosin forces that enables filaments to develop tension. The role of anchoring was highlighted by experiments on isolated fission yeast rings, where sections of ring became unanchored from the membrane and shortened ∼30-fold faster than normal. The dramatically elevated constriction rates are unexplained. Here we present a molecularly explicit simulation of constricting partially anchored rings as studied in these experiments. Simulations accurately reproduced the experimental constriction rates and showed that following anchor release, a segment becomes tensionless and shortens via a novel noncontractile reeling-in mechanism at about the velocity of load-free myosin II. The ends are reeled in by barbed end-anchored actin filaments in adjacent segments. Other actin anchoring schemes failed to constrict rings. Our results quantitatively support a specific organization and anchoring scheme that generate tension in the cytokinetic ring.