In this paper, closed and semi-closed form solutions are presented for the self - and mutual inductance of ordinary and Better disk coils which lie concentrically in a plane. The solutions are given as the combination of the elliptic integral of the first kind and a simple integral or only as the second elliptic integral of the second kind. All formulas or obtained in remarkably simple form and give extremely accurate results with significantly neglectable computational time. All cases either regular or singular (disks in contact or overlap) are covered. The formulas for the mutual inductances can be directly used to calculating the self-inductance of the ordinary disk coil or the Bitter disk coil, respectively. Many presented examples show the excellent numerical agreement with previous publish methods.