Disk shape frequently appears as a reference in shape characterization applications. We propose a local measure of deviation from a disk as the local difference between numerical solution of a PDE on the shape and an analytical expression in the form of modified Bessel function. The deviation defined at each shape point defines a field over the shape. This field has useful properties, which we demonstrate via illustrative applications ranging from shape decomposition to shape characterization. Furthermore, we show that a global measure extracted from the field is capable of characterizing the body roundness and periphery thickness uniformity.