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We present a detailed study of rotational asymmetry in galaxies for both morphological and physical diagnostic purposes. An unambiguous method for computing asymmetry is developed, which is robust for both distant and nearby galaxies. By degrading real galaxy images, we test the reliability of this asymmetry measure over a range of observational conditions, e.g., spatial resolution and signal-to-noise ratio (S/N). Compared to previous methods, this new algorithm avoids the ambiguity associated with choosing a center by using a minimization method and successfully corrects for variations in S/N. There is, however, a strong relationship between the rotational asymmetry and physical resolution (distance at Ðxed spatial resolution) : objects become more symmetric when less well-resolved. We further investigate asymmetry as a function of galactic radius and rotation. We Ðnd the asymmetry index has a strong radial dependence that diers vastly between Hubble types. As a result, a meaningful asymmetry index must be speciÐed within a well-deÐned radius representative of the physical galaxy scale. We enumerate several viable alternatives, which exclude the use of isophotes. Asymmetry as a function of angle is(AÕ)also a useful indicator of ellipticity and higher order azimuthal structure. In general, we show that the power of asymmetry as a morphological parameter lies in the strong correlation with B[V color for galaxies undergoing normal star formation spanning all Hubble types from ellipticals to irregular gal