Background: Sequence comparison is a fundamental step in many important tasks in bioinformatics; from phylogenetic reconstruction to the reconstruction of genomes. Traditional algorithms for measuring approximation in sequence comparison are based on the notions of distance or similarity, and are generally computed through sequence alignment techniques. As circular molecular structure is a common phenomenon in nature, a caveat of the adaptation of alignment techniques for circular sequence comparison is that they are computationally expensive, requiring from super-quadratic to cubic time in the length of the sequences. Results: In this paper, we introduce a new distance measure based on q-grams, and show how it can be applied effectively and computed efficiently for circular sequence comparison. Experimental results, using real DNA, RNA, and protein sequences as well as synthetic data, demonstrate orders-of-magnitude superiority of our approach in terms of efficiency, while maintaining an accuracy very competitive to the state of the art.