Abstract: We study the random variables of radial asymmetry based on copulas. We research on the structure of random variables which radial asymmetry degree is and get the exact best-possible bounds of random variables which radial asymmetry degree is equal to . Then we expand to general case. We propose an essential condition of radial asymmetry degree is and study the structure of copula. We provide a broad bounds of copula that the radial asymmetry degree is .