The circular decoding algorithm for tail-biting convolutional codes is executed using a fixed number of computations and is suitable for DSP/ASIC implementations. This letter presents the performance and complexity trade-off in the circular decoding algorithm using an analytic bound on the error probability. An incremental performance improvement is shown as the complexity increases from O(L) to O(L+10K) where L is the length of the decoding trellis and K is the constraint length. The decoding complexity required to produce the maximum-likelihood performance is presented, which is applicable to many codes of practical interest.