- A precise formulation of the hoop conjecture for four-dimensional spacetimes proposes that the Birkhoff invariant for an apparent horizon in a spacetime with mass M should satisfy 4M. The invariant is the least maximal length of any sweepout of the 2-sphere apparent horizon by circles. An analogous conjecture in five spacetime dimensions was recently formulated, asserting that the Birkhoff invariant for S1S1 sweepouts of the apparent horizon should satisfy 163M. Although this hoop inequality was formulated for conventional five-dimensional black holes with 3-sphere horizons, we show here that it is also obeyed by a wide variety of black rings, where the horizon instead has S2S1 topology. 2013 Elsevier B.V.