A number of papers had been published upon the subject of the formulas for calculation of the self-inductance of a circular coil of rectangular cross-section around the beginning of the 20th century. At that time, it was quite difficult to calculate those complicated formulas because the modern computer did not yet exist. Therefore, suitable tables or graphs had to be prepared for simplifying the numerical jobs. However, it must be much better to use the computer to calculate them today. In this paper, a numerical method to calculate the mutual-inductance between two coaxial circular coils of rectangular cross-section is presented. In this method, however, it takes a relatively long time because of calculating the total magnetic flux crossing the other coil. By this method, the self-inductance can also be obtained. Next, the more usable ranges of some expressions arranged by Hak for calculation of the self-inductance of a circular coil of rectangular cross-section are presented, and it is concluded that its maximum error is 0.23%.