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Calculations of inductance for helical toroidal coils are of great interest to researchers since they are the basis of optimal design with target functions such as the maximization of the ratio of the stored magnetic energy with respect to the volume of the toroid or the used conductor, the elimination or the balance of stress in certain coordinate directions, and the attenuation of leakage flux. In this paper, using Neumann's equation, formulas are presented to calculate the self-inductance and mutual inductance of the helical toroidal coil in superconductivity conditions. It is shown that calculation of self-inductance is similar to that of mutual inductance if the diameter of the conductor's cross section is smaller than 0.4 of the minor radius. Comparison between experimental and empirical results with numerical results indicates that the presented formulas are highly reliable. Plotting contours for the magnetic flux density shows that a special design approach must be taken so that the coil eliminates the leakage flux. It is also shown that the optimal design of the coil to eliminate or balance the stress in certain coordinate directions requires selection of geometrical parameters from accurate inductance equations, and therefore, the use of approximate equations for this purpose is not recommended.