The Bhattacharyya coefficient is a widely used statistical measure in various application areas of mathematics, such as computer science, which measures the similarity of two normalized distributions. In this report, we extend the measure by defining an n-distribution Bhattacharyya coefficient, which measures the overlap of n normalized distributions instead of just two. To affirm appropriateness of the measure, we provide useful properties, such as boundedness and properties along its boundaries with proofs, and supply illustrative examples in 1-dimension to demonstrate clearly the effect of the measure in various instances.

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