The circular flow number of a signed graph is the minimum r for which an orientation of admits a circular r-flow. We prove that the circular flow number of a signed graph is equal to the minimum imbalance ratio of an orientation of . We then use this result to prove that if G is 4-edge-connected and has a nowhere zero flow, then (as well as ) is at most 4. If G is 6-edge-connected and has a nowhere zero flow, then is strictly less than 4.