Convexity represents a fundamental descriptor of object shape. This paper presents a new convexity measure for both open and closed simple contours. Given such a contour this measure extracts two corresponding open convex hulls. The shape similarity between these two hulls and the original contour is then computed and normalized to give a measure of convexity. The time complexity of the proposed technique is O(n). The authors believe this technique represents the first measure of convexity which uses shape similarity and which can be applied to both open and closed contours. The proposed technique is shown to provide similar or greater performance relative to two other state of the art techniques.